L& H23I 
 
 A STUDY OF THE RELATION OF SOME 
 PHYSIGAL DEFEGTS TO ACHIEVE- 
 MENT IN THE ELEMENTARY 
 SGHOOL 
 
 BY 
 
 JASPER N. MALLORY, PH. D. 
 
 GEORGE PEABODY GOLLEGE FOR TEACHERS 
 
 CONTRIBUTION TO EDUCATION 
 
 NUMBER NINE 
 
 PUBLISHED UNDER THE DIRECTION OF 
 
 GEORGE PEABODY COLLEGE FOR TEACHERS 
 
 NASHVILLE, TENN. 
 1922 
 
 MOTlOTT&Pb 
 
A STUDY OF THE RELATION OF SOME 
 PHYSICAL DEFECTS TO ACHIEVE- 
 MENT IN THE ELEMENTARY 
 SCHOOL 
 
 BY 
 
 JASPER NiMALLORY, PH. D. 
 
 GEORGE PEABODY GOLLEGE FOR TEACHERS 
 
 CONTRIBUTION TO EDUCATION 
 
 NUMBER NINE 
 
 PUBLISHED UNDER THE DIRECTION OF 
 
 GEORGE PEABODY COLLEGE FOR TEACHERS 
 
 NASHVILLE, TENN. 
 
 1922 
 

 *w 
 
ACKNOWLEDGMENTS 
 
 Grateful acknowledgment is here made to Dr. Shelton 
 Phelps, under whose direction this study has been made ; to 
 Dr. W. P. Ott, Professor of Mathematics, Vanderbilt Uni- 
 versity, for instruction in the Theory of Probabilities ; and 
 to Dr. Norman Frost, Dr. Joseph Peterson, and other pro- 
 fessors of George Peabody College, from whom many val- 
 uable suggestions were received. Thanks are. also extended 
 to Superintendent H. H. Ellis, of Humboldt, for permitting 
 the data to be collected in his school. Acknowledgment is 
 also made to Prof. L. D. Rutledge, of Union University, who 
 collaborated with the writer in the collection of the data, 
 and to Miss E. N. Sanborn, R. P. H. N., who administered 
 the physical examinations. J. N. M. 
 
CONTENTS 
 
 Introduction 
 
 Historical Background for Present Movements in Health Super- 
 vision 
 
 7 
 
 Chapter I 
 Previous Objective Studies of Related Subjects 11 
 
 Chapter II 
 The Purpose and Scope of the Present Study 19 
 
 Chapter III 
 Material and Methods Used in This Study 22 
 
 Chapter IV 
 
 Preliminary Analysis, Using Percentages and Association Coeffi- 
 cients : 40 
 
 Chapter V 
 Final Analysis, Using Partial Correlations 68 
 
 Chapter VI 
 Summary and Conclusions 74 
 
PREFACE 
 
 The most powerful tendency in education during the past 
 two and one-half decades has been the development of a 
 "body of quantitative technique which make constant use 
 of statistical method" of study. The subjective is fast giv- 
 ing way to the objective. Research in almost every line is 
 being made to conform to the scientific method. There is 
 still one phase of the work, however, in which some writers 
 are seemingly content to make broad generalizing state- 
 ments, often unsupported by scientific facts. 1 The prob- 
 lem referred to is that of the relation of physical defects to 
 progress in school. Who can explain why this, one of the 
 most vital of all school problems, should be among the last 
 to yield itself to modern methods of scientific study — one 
 of the last to be subjected to the searchlight of scientific 
 truth? All kinds of notions still prevail. 2 Who has not 
 heard the "untutored" would-be sage proclaim that "suc- 
 ceeding generations grow weaker as they grow wiser?" 
 How does he know? Does nature compensate for physical 
 incapacity with mental alertness? The truth of the mat- 
 ter is that some relation between these attributes has been 
 suspected, and, in the absence of supporting facts, these 
 broad generalizations have been indulged in. 
 
 Such differences of opinion as that referred to above is 
 not uncommon. Diametrically opposite views are some- 
 times held by prominent writers.-' How can agreement be 
 brought about? It can be done only when facts are made 
 to speak louder than theory. Ayres, together with a few 
 others, a few years ago took the lead in a movement to put 
 the whole discussion on an objective basis, with the effect 
 that at present quite a bit of the literature on the subject 
 shows signs of a change toward a scientific attitude. This 
 is the more important when the fact is faced that medical 
 and physical examinations are becoming the rule rather 
 
 Reference is made here to such statements as that of Frank Allpors, M.D., Chair- 
 man of Committee on Conservation of Vision, Chicago, in his pamphlet entitled 
 '■School Children's Eyes," in which he says: "At least 5,000,000 of these children suf- 
 fer from eye diseases or defects which seriously impair their school progress." Nei- 
 ther Ayres nor Cornell found this statement concerning eyes supported by their data 
 on promotion. Medical Inspection of Schools, page 202, Gulick and Ayres. 
 
 -Cornell, W. S., Psychological Clinic, November 15, 1909. 
 
 :, Albert E. Taussig. M.D., Clinic for St. Louis County, Mo., in Psychological Clinic, 
 November 15, 1909, makes the following statement : "In the first place, there is no 
 agreement as to what constitutes defective vision. In some cities everything less than 
 perfect is reported. Elsewhere vision by both eyes must be less than perfect or must 
 even be less than 20/30. 
 
 Gulick and Ayres make the following statement in Medical inspection of Schools, 
 page 82 : "Bayonne reports 7.7 r '< defective vision, while the congested districts of 
 Cleveland report 71.7%. Of course such variations as this at once suggest what is un- 
 doubtedly the case, that the results are largely influenced by the methods employed." 
 
6 Preface 
 
 than the exception in our large cities and in many of our 
 smaller ones. However, it is true that little use is being 
 made of the great mass of information obtained from these 
 examinations. 
 
 Just what is the effect of physical abnormality on school 
 progress? No one can be quite sure. It is hoped that this 
 study will at least indicate the method to be used in finding 
 out. It will emphasize the importance of scientific analy- 
 sis of these complex relations. Though largely mathemat- 
 ical, a fact for which no apology is offered, the treatment 
 is less technical than might at first be supposed. In gen- 
 eral, the plan of treatment begun by Ayres is followed, but 
 with a much larger emphasis on the mathematical treat- 
 ment of attributes. An attempt has been made to simplify 
 the whole process to the extent of making it readable to a 
 person of reasonable mathematical ability. A knowledge 
 of simple association percentages and of correlation coeffi- 
 cients is assumed. 
 
 It is believed that the method here used is capable of 
 fruitful applications to educational fields. Students of 
 sociology have long made wide use of Pearson's association 
 formulae. Cannot the field of school administration profit 
 greatly from the development and application of a similar 
 technique? 
 
 No claim in this thesis is made to finality either in tech- 
 nique or results. It is only a beginning. May not others 
 be expected to take up the work thus begun and give it a 
 more extended application in wider fields? That is the 
 hope of the writer. 
 
INTRODUCTION 
 
 historical background for present-day move- 
 ments in health supervision 
 
 The Movement in Foreign Countries 
 
 Like a great many American institutions, this movement 
 started in Europe. 1 It was almost half of a century after 
 the French began to examine school children before it was 
 undertaken in American schools. 2 Early records mention 
 medical inspection in Paris as early as 1833, though the 
 first real inspection in Paris was begun in 1874. A more 
 noteworthy event was the establishing of a comprehensive 
 system of medical supervision in Brussels, Belgium, 1774. 
 Regular physicians were employed to visit all the schools 
 three times per month. This plan attracted so much atten- 
 tion that Antwerp, Louvain, Liege, and other cities almost 
 immediately took up the movement. The Swiss were the 
 next to borrow the Belgian idea. The Germans do not 
 claim to have gotten their scheme from the Belgians, as 
 some sort of eye examination had been in practice in Dres- 
 den three years prior to the Brussels movement. But the 
 facts are that the first real comprehensive system of phys- 
 ical examination in Germany was begun in Wiesbaden in 
 1889. This last date proved to be a landmark in the history 
 of inspection. This type of inspection, which included a 
 thorough examination of the heart, lungs, throat, spine, 
 skin, and the higher sense organs, has been widely adopted 
 throughout Europe. The child was examined on entering 
 school for the first time and reexamined each third year 
 thereafter. This was in addition to the usual routine of 
 medical inspection. 
 
 The other continental countries to fall in line were Hun- 
 gary, 1878 ; Norway, 1889, a system of three examinations 
 per year ; Sweden, 1878, a system of annual examinations ; 
 Roumania, 1899, annual examinations; Moscow, 1895, a 
 system comprising six physicians in charge of the seventy- 
 two elementary schools. 
 
 England, like her American offspring, was rather tardy 
 in contributing her share to the movement. It was not 
 until 1908 that she could claim a real system of examina- 
 tions. This was the year of the beginning of the national 
 "Society of Medical Officers," an organization formed for 
 the purpose of putting the movement over. Her sudden 
 
 •Gulick and Ayres, Medical Inspection of Schools, Chap. III. 
 -Bureau of Education Bulletin, 1919. No. 4. 
 
8 Introduction 
 
 and fitful sprint, coming late as it did, was probably due in 
 part to the influence of her French neighbors. This same 
 year marks the beginning in France of the "La Medecine 
 Scholaire," a monthly bulletin published by the "Society 
 for the Inspection of Schools." It was evidently this last- 
 named society that had much to do with the creation of a 
 similar one in England. 
 
 Other countries outside of Europe had made progress in 
 medical and physical inspection. Egypt had had a com- 
 prehensive system, with highly paid inspectors, since 1882 j 1 
 Chile, since 1888 ; Japan, since 1898 ; and America, since 
 1892. To the last-mentioned we will now turn for further 
 historical development. 
 
 The Movement in America 
 
 As stated above, medical inspection did not begin in 
 America until about the beginning of the last decade of the 
 nineteenth century. The movement is generally thought to 
 have begun in New York, under the leadership of Dr. 
 Morse, about 1892. This is disputed, however, by good 
 authority. 2 According to this authority, the first system 
 in America was inaugurated in San Antonio in 1890. It 
 is not material which of these claims is correct; for, with- 
 out question, the first permanent scheme was inaugurated 
 in Boston in 1894, with a corps of fifty inspectors — one for 
 each of the fifty districts. Chicago introduced a similar 
 system in 1895, with nine physicians. From this time on 
 other cities followed in rapid succession until prior to the 
 Great War there were more than seventy cities maintaining 
 some kind of physical examinations. This did not include 
 the thirty-two cities and three hundred and twenty-one 
 towns of Massachusetts. This state, together with six oth- 
 ers, had compulsory state-wide medical inspection. The 
 other six were Connecticut, New Jersey, Vermont, New 
 York, Utah, and California. The impetus given physical 
 training during the Great War, 1 together with the amazing 
 revelations made by the Draft Board concerning our phys- 
 ical unfitness as a nation, caused school authorities, both 
 state and local, to speed up legislation pertaining to elimi- 
 nation of physical defects and the prevention of disease. 
 The result is that at present every state in the Union main- 
 tains some kind of inspection, the same being a specific 
 requirement of law in all except a very few states. 2 
 
 ^Gralick and Ayres, Medical Inspection of Schools, page 23. 
 -Bureau of Education Bulletin, 1919, No. 13, page 28. 
 ^Bureau of Education Bulletin, 1919, No. 4. 
 ^Bureau of Education Bulletin, 1919, No. 13, page 28. 
 
Introduction 9 
 
 In 1917 the following laws were passed: 1 New Hamp- 
 shire, requiring schools to vote on the question of inspec- 
 tion ; Nevada, providing for examination of the eyes, ears, 
 teeth, and mode of breathing; North Carolina and North 
 Dakota, providing for examination by county authorities ; 
 Pennsylvania, providing for the treatment of the eyes and 
 teeth ; New Jersey, requiring dental clinic ; Rhode Island, 
 requiring treatment of the teeth ; and Virginia, authorizing 
 the county board to expend funds in providing inspectors 
 and nurses to visit the schools. These illustrate the tenden- 
 cies in legislation most prominent then and the ones that 
 have persisted to the present time. 
 
 A summary of the legislation of 1918-1919- is also sig- 
 nificant. Twenty-eight states either amended old laws or 
 passed new ones. Six of these — New Jersey, California, 
 Connecticut, Kansas, Nebraska, and North Carolina — spec- 
 ify the treatment of defectives. The others either do not 
 specify at all or specify medical inspection. The distribu- 
 tion is as follows : 
 
 Unspecified defects — North Carolina 1 
 
 Treatment of ears — South Dakota, Nebraska 2 
 
 Treatment of eyes — South Dakota, Nebraska, California 3 
 
 Treatment of nose — South Dakota 1 
 
 Treatment of throat — South Dakota 1 
 
 Mode of breathing — Nebraska 1 
 
 Providing for clinic for examination of teeth — New Jersey, Ohio, 
 
 South Dakota, California, Connecticut, Kansas, Nebraska 7 
 
 Total 16 
 
 If this table seems to put most stress on teeth, eyes, and 
 ears in the order named, it is probably due to the fact that 
 it is not known to what extent the other twenty-one states 
 passing laws this same year included only these three in 
 their program of general inspection. 
 
 Attention has already been called to the fact that often 
 no distinction is made between physical examination for de- 
 fects and medical inspection. There is a difference, and 
 there should be a distinction. The difference lies chiefly in 
 the fact that medical inspection deals primarily with pro- 
 tective measures looking to the safeguarding of the com- 
 munity against contagious diseases. This is immediate pro- 
 tection against present dangers. Physical examinations 
 are more constructive in their aim, having for their object 
 the detection of defects that prevent the proper develop- 
 ment of our coming generation and, so far as possible, elimi- 
 nation of these defects. The latter is the most profitable 
 
 1 Bureau of Education Bulletin, 1919, No. 13, page 28. 
 'Bureau of Education Bulletin, 1920. Ed. Legislation. 
 
10 Introduction 
 
 form of inspection, but is the form that has at times re- 
 ceived least attention. Ayres says in his Laggards in Our 
 Schools that a thorough examination of all the pupils is 
 rare. The laws cited above indicate that the tendency is 
 more inclined toward a constructive program of physical 
 examinations. 
 
 There is some difficulty at present, however, in that there 
 are no very reliable standards. 1 There is also noticeable 
 lack of understanding regarding the technique of the ex- 
 aminations. The specific defects are not sufficiently defined. 
 Different examiners vary widely in what is considered a 
 defective. The result is that the data obtained from dif- 
 ferent surveys are not comparable and are often meaning- 
 less to persons not familiar with the method used. Uni- 
 formity of method, producing comparable results, must be 
 brought about before the greatest good can come from this 
 kind of work. 
 
 1 Cornell says : "As a consequence, enormous figures may be quoted which are im- 
 pressive enough, but which fail to add to our medical knowledge. ... As a mat- 
 ter of fact, they have occasionally done harm by reason of their employment as a basis 
 for deduction as to the degeneracy of the race, the relation of physical to mental 
 defects. — Psychological Clinic, November 15, 1909, page 160. 
 
CHAPTER I 
 PREVIOUS OBJECTIVE STUDIES OF RELATED SUBJECTS 
 
 Prior to the introduction of standard achievement tests, 
 an objective study of the relation of physical well-being to 
 achievements was next to impossible. This, doubtless, is 
 the explanation for the fact that so little attention has been 
 given this phase of school administration. Research men 
 have been satisfied with collecting physical data, tabulating 
 them, and stating the relative percentages of defectives. 
 Most of the state and city surveys of physical defects of 
 school children have been of this type. While there has 
 been no study made from the standpoint of standard tests, 
 a few related studies have been made. 
 
 Among the men that have attempted an objective treat- 
 ment of the relation of physical defects to achievements 
 are Dr. Walter S. Cornell and Dr. S. W. Newmayer, in Phil- 
 adelphia; 1 Superintendent James E. Bryan, of Camden, 
 N. J. ; 2 a little more recently, Luther H. Gulick and Leon- 
 ard P. Ayres, in New York ;•'• and still more recently, Brad- 
 ley Ruml et al., 4 who have recently printed a psycho-phys- 
 ical study, which resembles somewhat, though not in details, 
 this study. Each of these studies will be briefly reviewed 
 before taking up the present problem. 
 
 Defects Among "Exempt" and "Nonexempt" Children. — 
 This study was made by Dr. Cornell 5 on a small group of 
 children (219) from six to twelve years of age in one school 
 in Philadelphia. He is among the early writers to under- 
 take the objective treatment of this subject. He studied 
 marks made by defective and "normal" children. 
 
 Average Per Cent 
 in Studies 
 
 Normal children 75 
 
 Average children 74 
 
 General defectives 72.6 
 
 Children with adenoids and enlarged tonsils 72 
 
 In another school he examined 907 children and classi- 
 fied them on the basis of "exempt" and "nonexempt." 
 
 ^■Psychological Clinic, January, 1908. 
 
 = Quoted from "Laggards in Our Schools," Ayres. 
 
 3 Medical Inspection of Schools, Gulick and Ayres. 
 
 *Methods and Results of Testing School Children, Dewey, Child, Ruml ; E. P. Dut- 
 ton & Co., New York. 
 
 5 Dr. Walter S. Cornell, of the Medical Department of the University of Pennsyl- 
 vania. For the original report, see Psychological Clinic of January 15, 1908. For 
 extract of same, see Gulick and Ayres. Medical Inspection of Schools, page 189. 
 
Geography 
 
 Spelling 
 
 Average 
 
 69 
 
 76 
 
 75— 
 
 71 
 
 77 
 
 73+ 
 
 70 
 
 71 
 
 69 
 
 12 A Study of the Relation of Some Physical Defects 
 
 Exempt Nonexempt 
 
 Children examined 907 687 
 
 Per cent defective 28.8 38.1 
 
 In another school he classified as "bright," "dull," and 
 "dullest" 150 children, as follows : 
 
 Bright Dull Dullest 
 
 Children Children Children 
 
 Number examined 89 32 29 
 
 Having nose or throat defects 16 9 9 
 
 Per cent 11.1 28.1 31 
 
 In another report 1 he gives percentage marks made in 
 school subjects, the children being classified on the basis of 
 "normal," "fair," and "bad" vision. 
 
 Children With — Arithmetic 
 
 Normal vision 79 
 
 Fair vision 70 
 
 Bad vision 66 
 
 These percentages were based on teachers' marks, and 
 not upon results from objective tests, as this study was 
 made before the introduction of tests in the school work. 
 They are as reliable as could be obtained at that time on 
 individual achievement. The groups were small, and are 
 valuable chiefly for the fact that they indicated the prob- 
 able truth of some association between physical defects 
 and progress and led to further study. Cornell concludes 
 that educational results in our schools suffer a discount of 
 about six per cent in the case of physically defective chil- 
 dren — this conclusion, of course, being based upon teachers' 
 marks, as stated above. He points out also that much time 
 rightfully belonging to the normal children is wasted. 
 
 Cause of Backwardness in Camden Schools. — This inves- 
 tigation was made by James E. Bryan, and included 10,130 
 children. From these, 2,020 children of excessive age were 
 selected. He considered a child overage if he were one 
 year or more behind his grade (compared with usually ac- 
 cepted standards). These were distributed according to 
 cause of overageness into seven groups. 
 
 Excessive Age Due to — Defects 
 
 Other Than 
 Sight and Mental 
 No. Age Upon Hear- Weak- 
 
 Exam. Starting Absence Slowness Dullness Health ing ness 
 
 Per Cent Per Cent Per Cent Per Cent Per Cent Per Cent Per Cent 
 
 Boys 1,081 20.2 29.4 19.8 12.1 7.4 3.6 4.6 
 
 Girls 939 22.4 27.5 22.4 11.9 12.1 4.4 2.6 
 
 Total 2,020 21.2 28.5 21.0 12.0 9.6 3.9 3.7 
 
 ^New York Medical Journal of June 1. 1907. 
 
to Achievement in the Elementary School 13 
 
 He concludes that physical defects constitute a cause, but 
 not the cause, of retardation ; secondly, that the bearing of 
 physical defectiveness on school backwardness does not ap- 
 pear to be very great. 
 
 Physical defects other than sight and hearing were as- 
 signed as reasons for excessive age in 3.6 per cent of the 
 cases of the boys and 4.4 per cent of those of the girls. 
 
 Laggards in Our Schools. 1 — This book was first printed in 
 1908. Its purpose was to throw some light on the subject 
 of retardation. Among the causes, defects is given a prom- 
 inent place, though only fourteen pages of the book are 
 devoted to this subject. Ayres made a study of 3,304 chil- 
 dren in New York City from the standpoint of the influence 
 of defects on promotion. There were no standard tests at 
 that time, so he was forced to judge school progress in 
 terms of teachers' estimates and promotions. In substance, 
 his findings are set forth in the following tables : 
 
 Table 68 — Per Cent of Dull, Normal, and Bright Pupils Suffering 
 from Each Sort of Defect. Ages, Ten to Fourteen, Inclusive. All 
 grades. 
 
 Dull Normal Bright 
 
 Defects Per Cent Per Cent Per Cent 
 
 Enlarged glands 20 13 6 
 
 Defective vision 24 25 29 
 
 Defective breathing ■ 15 11 9 
 
 Defective teeth 42 40 34 
 
 Hypertrophied tonsils 26 19 12 
 
 Adenoids 15 10 6 
 
 Other defects 21 11 11 
 
 Number examined 407 2,588 309 
 
 Defects per child 1.65 1.3 1.07 
 
 Per cent not defective 25 27 32 
 
 Per cent defective 75 73 68 
 
 Table 70 — Showi?ig Per Cent of Loss in Progress of Children Suffer- 
 ing from Each Sort of Physical Defect. 
 
 Per Cent of Loss 
 Kinds of Defects in Progress 
 
 Enlarged glands 14.9 
 
 Defective vision None 
 
 Defective breathing 7.2 
 
 Defective teeth 5.9 
 
 Hypertrophied tonsils 8.9 
 
 Adenoids 14.1 
 
 Other defects 8.5 
 
 Average 8.8 
 
 From Table 68 Ayres concludes that "in every case, ex- 
 cept in that of vision, the children rated as 'dull' are found 
 to be suffering from physical defects to a greater degree 
 
 Leonard P. Ayres, now president of Cleveland Trust Company, Cleveland, O., for- 
 merly with Russell Sage Foundation. 
 
14 A Study of the Relation of Some Physical Defects 
 
 than the normal or bright children. It is true that 75 per 
 cent of the dull children are defective, as compared with 
 73 per cent among the normal and 68 per cent among the 
 bright children." He says further: "The differences are 
 slight. But the defective dull child has, on the average, 
 1.65 defects, as against 1.07 for the bright one. In other 
 words, the number of defectives among the dull children 
 does not differ widely from the number of defectives among 
 the bright ones ; but the dull child is found to be much more 
 defective in degree." 
 
 From Table 70 Ayres draws his conclusions as to the seri- 
 ousness of the handicaps in terms of percentages. For in- 
 stance, he concludes that children suffering from physical 
 defects made, on the whole, 8.8 per cent less progress than 
 did those having no physical defects. 
 
 In his Table 67, which is not shown here for lack of space, 
 he shows data from which he concludes that physical defects 
 decrease with age. He briefly summarizes as follows : 
 
 1. "Physical defects decrease with age." 
 
 2. "It has been shown that vision does not follow the 
 same rules as do the other defects." 
 
 3. The examinations conducted in New York have shown 
 higher percentages of enlarged glands, defective breathing, 
 hypertrophied tonsils, and adenoids among dull children 
 than among the bright children. 
 
 4. It has been demonstrated that physical defectiveness 
 has a distinct and important bearing on the progress of 
 children. 
 
 Medical Inspection of Schools (Gulick* and Ayres). — This 
 entire book is given to medical inspection and physical ex- 
 aminations ; but only Chapters VII, which deals with "Phys- 
 ical Examinations for the Detection of Noncontagious De- 
 fects," and XII, which discusses "Retardation and Physical 
 Defects," are directly related to any part of this study. 
 The first-mentioned chapter deserves notice from the fact 
 that two instructive tables are given — one showing per cent 
 of vision and hearing defectives in fourteen countries, coun- 
 ties, and cities for the. sake of comparison, the other show- 
 ing the percentage distribution of defects for New York 
 and Minneapolis. The last table is quoted below : 
 
 1 Director of Physical Training, New York Public Schools. 
 
to Achievement in the Elementary School 15 
 
 Table (K) — Physical Examinations in the New York and Minneap- 
 olis 1 Schools. 
 
 Nei» York, Minneapolis, 
 
 1906 Per Cent 1908 Per Cent 
 
 Number examined 78,401 100 710 100 
 
 Bad nutrition 4,921 6.3 166 23.3 
 
 Anterior cervical glands _-_29,177 37.2 377 53.0 
 
 Posterior cervical glands 8,664 11.0 
 
 Chorea 1,380 1.7 2 0.2 
 
 Cardiac disease 1,096 1.4 15 2.1 
 
 Pulmonary diseases 757 .9 30 4.2 
 
 Skin diseases 1,558 1.9 12 1.6 
 
 Deformity of spine 424 .5 
 
 Deformity of chest 261 .3 
 
 Deformity of extremities 550 .7 
 
 Defective vision 17,928 22.8 170 23.9 
 
 Defective hearing 869 1.1 55 7.7 
 
 Defective nasal breathing__ll,314 14.4 
 
 Defective teeth 29,597 55.0 309 43.5 
 
 Defective palate 831 1.0 2 0.2 
 
 Hypertrophied tonsils 18,306 23.3 221 31.1 
 
 Postnasal growth 9,438 12.0 91 12.8 
 
 Defective mentality 1,857 2.3 
 
 Where treatment was nec- 
 
 sary 56,259 71.7 462 65.1 
 
 It will be observed that there are wide differences in the 
 percentages for the two cities. Ayres attributes most of 
 this to the difference in rigidity of examination. He re- 
 marks, however, that the most interesting figures of all are 
 those for "where treatment is necessary." "These per- 
 centages are 71.1 for New York and 65.1 for Minneapolis." 
 
 Chapter XII, 2 mentioned above, deals largely with the 
 distribution of defects which on the whole decrease with age. 
 He makes the statement also that from 100,000 cases ex- 
 amined among school children it has been found that from 
 66 to 72 per cent are defective. This agrees very closely 
 with the findings in this study, where 64 per cent were 
 found sufficiently defective to need treatment. Of the many 
 tables given, only one will be quoted here as being different 
 from any mentioned above. 
 
 Table (Y) — Per Cent Having Each Defect by Sexes. 
 
 Boys Girls 
 
 Defectives 78.5 79.2 
 
 Enlarged glands 32.2 20.3 
 
 Defective vision 15.7 20.8 
 
 Defective breathing 19.1 14.3 
 
 Defective teeth 48.4 53.5 
 
 Hypertrophied tonsils 33.1 24.7 
 
 Adenoids 17.4 15.6 
 
 Other defects 13.6 14.7 
 
 ^Medical Inspection of Schools, page X~. 
 
 -The data in this chapter were secured in the Manhattan Schools during Mav and 
 June, 1908. 
 
16 A Study of the Relation of Some Physical Defects 
 
 Table (Y) is interesting, inasmuch as it compares "per 
 cent defective" among boys and girls. From the examina- 
 tion of 3,301 boys and 4,305 girls, the boys were found to be 
 defective oftener than the girls with respect to enlarged 
 glands, defective breathing, and hypertrophied tonsils; 
 while the girls were oftener defective with respect to vision 
 and teeth. The latter happen to be the ones that Ayres 
 finds least apt to cause retardation. 1 This should mean 
 that boys, as a rule, are more retarded, other things being- 
 equal, than girls. As stated below, Ruml is planning to 
 make further study of this phase of the problem. 
 
 Chief among the conclusions reached by Gulick and Ayres 
 in this study is, quoting from them: "Physical defects con- 
 stitute a cause, not the cause, of retardation." 
 
 A study was made in" New York City in 1915 by Evelyn 
 Dewey, Emily Child, and Beardley Ruml for the purpose 
 of obtaining norms for a series of tests as a basis for further 
 study of the value of mental tests for improvement of 
 schoolroom procedure. The printed report of the study 
 naturally divides itself into two large divisions — the method 
 used in collecting the data and the methods used in their 
 interpretation. Ruml leaves most of the interpretation for 
 a second volume yet to appear in print. The thing that is 
 of interest in this connection about the first volume is the 
 fact that the relations between test scores and attributes are 
 touched on, though they are not treated by Pearson's for- 
 mulae. 
 
 The tests were given to 3,000 Jewish children between 
 the ages of eight and thirteen, most of whom were found in 
 a single school in New York City. Jewish children were 
 selected because of their race homogeneity. The influence 
 of race characteristics could then be eliminated from the 
 study. The tests given were Whipple's: grip, steadiness, 
 tapping, rote memory, sentence completion, cancellation of 
 A's, association of opposites, substitution, card sorting 
 (Jastrow), and certain other tests, as nail driving, needle 
 threading, fastening buttons, cart construction, narrative 
 pictures, and instruction box. Each child was given a sep- 
 arate examination and had from twenty-five to forty-five 
 minutes on each question. The data were grouped accord- 
 ing to the ages of the children. The mean, standard devia- 
 tion, and regression of score on age were found. The table 
 below will illustrate: 
 
 ^t was pointed out above that James Bryan in the Camden investigation found 
 that physical defect was the cause of average in 4.4 of the cases among the girls and 
 in only 3.6 per cent of cases among the boys. It is difficult to harmonize these two 
 conclusions. The difference may be due to local conditions in New York and Camden. 
 
to Achievement in- the Elementary School 17 
 
 Picture Completion Index 
 
 Age 9-9.9 10-10.9 11-11.9 12-12.9 13-13.9 
 
 Mean 12 ± .11 56.7 ± .36 19.1 ± .39 24.6 ± .22 25 6 .18 
 
 S. D. 54 ± .02 .59 ± .02 .50 ± .02 .53 ± .02 .53 .02 
 
 Regression equation: 9.49 .183 age Sig. = .564 
 
 Tables of this kind were worked out for each test, boys 
 and girls separately. Deviations for each sex of several 
 ages were found. These were used as the bases for deter- 
 mining the influence of sex, maturity, etc., on scores. The 
 standard deviations of the small groups were subtracted to 
 find by what amount they differed. This difference was 
 divided by the probable error of the difference. If this dif- 
 ference were less than the probable error, it was disre- 
 garded. If it were from one to three probable errors, it 
 was of "possible" significance. If it were more than three 
 times the probable error, it was of "probable" significance. 
 From these probable error differences Ruml concluded that 
 boys were stronger in picture completion. In fact, he con- 
 cluded that girls excel only in needle threading and in 
 steadiness. The standard deviations in the picture com- 
 pletion tests are given here for comparison : 
 
 Picture Completion Index 
 
 Age 9-9.9 10-10.9 11-11.9 12-12.9 13-13.9 
 
 Boys, S. D .52 .59 .50 .53 .53 
 
 Girls, S. D .33 .43 .38 .43 .41 
 
 In each of these age groups the boys seem to show a 
 larger deviation, and there is an evident difference; but as 
 the probable error of the differences is not shown in the 
 table, the extent of difference cannot be indicated here. It 
 would be interesting to have the original data from which 
 to work out the association coefficients according to the 
 Pearson formulae. 
 
 The data mentioned above do not touch upon physical 
 defects. This is to be regretted, inasmuch as the physical 
 data constitute the portion of Ruml's study which comes 
 closest to the problem being worked out in this study. But 
 as this part of it is not yet in print, except the tabulated 
 data, it can only be surmised as to the method to be used 
 in its interpretation. The usual physical examinations 
 were given, except that no notice was taken of defects of 
 the eyes, ears, nose, and throat. In fact, the only defects 
 reported that are included in this study are the defects of 
 the teeth. The data collected had to do with heights, 
 weights, blood pressure, etc. It was tabulated and the 
 means, standard deviations, and probable errors found as 
 
18 A Study of the Relation of Some Physical Defects 
 
 in the tests above. It is presumed that the standard devi- 
 ation method of comparison is to be used in its interpreta- 
 tion as with the other data. The deviations by ages and 
 sex are shown below for the number of permanent teeth : 
 
 Number of Permanent Teeth 
 
 Age 9-9.9 
 
 Boys, S. D 1.08 .08 
 
 Girls, S. D 2.87 .20 
 
 It will be noticed that, with the exception of the first and 
 fourth groups, the boys have larger standard deviations; 
 but this may not be significant, as the standard deviations 
 for the entire sex groups are not given. 
 
 10-10.9 
 
 11-11.9 
 
 12-12.9 
 
 13-13.9 
 
 3.81 .26 
 
 4.05 .34 
 
 2.25 .16 
 
 1.94 .13 
 
 3.73 .26 
 
 3.07 .21 
 
 2.86 .19 
 
 1.30 .09 
 
CHAPTER II 
 THE PURPOSE AND SCOPE OF THE PRESENT STUDY 
 
 The purpose of the study is clearly expressed in the state- 
 ment of the problem. It reads : "A Study of the Relation 
 of Some Physical Defects to Achievement in the Elementary 
 Schools." It is difficult to state a research problem of this 
 kind clearly enough to be understood alike by all. Few 
 statements are so perfect that they cannot be distorted. 
 Too much may be read into them, or too little. A prob- 
 lem should be so defined as to include the essentials of a 
 unified study and to exclude the nonessentials. Depth is 
 often more to be desired than breadth. An attempt has 
 been made to narrow the present study down to the single 
 purpose of arriving at the degree of association, if any, be- 
 tween physical defects and achievements in the elementary 
 schools. The fact that this study is based on standard test 
 scores and physical examination restricts it to the objective. 
 "Hearsay" and teachers' estimates give way to quantita- 
 tive study and objective measurements. Scores come under 
 the head of variables and physical examinations under at- 
 tributes. Either of these yield themselves readily to math- 
 ematical treatment. This, in fact, is the method used to a 
 very large extent in this study. Whenever it was possible 
 to use mathematical formulae to aid in the interpretation 
 of the data, they have been so used. 
 
 It is believed that the contributions made by the present 
 study to education are threefold. 
 
 1. The study calls attention to a wide field of research 
 dealing with the relation of physical defects to achievement 
 scores. Being one of the first to deal with achievements 
 in this way, it should influence others to take up the work 
 and to make more extended studies. 
 
 2. The study indicates the methods for applying the the- 
 ory and formulae of attributes to problems of school ad- 
 ministration, many of which cannot be studied directly from 
 the standpoint of variables. Attributes have for quite a 
 while had a very prominent place in the study of sociology. 
 This is an attempt to use similar methods in the field of 
 education. Indeed, a large part of that technique has been 
 brought over into this new field. 
 
 3. So far as it is possible to base conclusion on the results 
 of a single piece of research, this study indicates the rela- 
 tion of physical defects to achievement scores. 
 
 It is well to state, in the outset, that this study does not 
 
20 A Study of the Relation of Some Physical Defects 
 
 undertake to trace the probable effects of physical abnor- 
 malities on mental ability. Intelligence comes into consid- 
 eration only as a factor influencing association of defects 
 with achievement scores. This discussion, for this reason, 
 keeps off the psychological processes underlying the learn- 
 ing process — not that such a study would not be interesting 
 and profitable, but because such a discussion belongs to the 
 field of psychology. The real problem here is the relation 
 of physical defects to achievement scores as shown by stand- 
 ard tests. Neither is this study concerned with the under- 
 lying biological factors, such as heredity and environment, 
 that, without doubt, affect school progress. The consider- 
 ation of these would lead too far afield. Home environment 
 and its relation to standard scores would of itself make a 
 subject of much interest, and sufficiently complex for a 
 thesis. 
 
 It will be observed also that "some" of the physical de- 
 fects are to be studied. A consideration of the whole cate- 
 gory would be too extended and not so profitable as a more 
 detailed study of the most prominent ones, which include 
 defects of eyes, nose, throat, tonsils, and teeth. Ninety-five 
 per cent of all defects reported in this study come under 
 these five heads. This is further discussed in connection 
 with Table II. The ones not specifically considered have 
 been noted, however, and disposition made of them in a way 
 not to invalidate the present study. 
 
 This study has undertaken to show, first, the apparent 
 relations as indicated by percentages and as indicated by 
 association coefficients derived from fourfold and manifold 
 formulae, without considering the effect of other factors, 
 such as intelligence ; and, second, the same coefficients after 
 being freed, by the use of partial correlations, from the 
 influences of these other factors. An example here will 
 suffice for the present, as a full discussion of this phase is 
 included in Chapter III. 
 
 It will be shown later, in Table LII, that the coefficient 
 of association between defective tonsils and spelling achieve- 
 ment scores is .084. This means that in this school if a 
 child with defective tonsils is selected at random, the 
 chances are slightly in favor of his having low achievement 
 scores. But is this association of defective tonsils with 
 scores in spelling direct, or is it due to the connection that 
 both defective tonsils and scores in spelling have with gen- 
 eral intelligence? After the association has been freed 
 from the influence of intelligence, the coefficient is .08. 
 This result is not very different from the .084 first obtained, 
 
to Achievement in the Elementary School 21 
 
 but shows that the influence of defective tonsils is slightly 
 less than was first supposed. 
 
 These original coefficients and those derived from partial 
 correlations are found not only in respect to the general 
 problem — that is, the relation of defects in general to 
 achievements in general — but the effect of specific defects 
 on the general achievement, as well as specific defects on 
 individual subjects, such as reading. The results of these 
 comparisons are stated in Chapters IV and V and summa- 
 rized in Chapter VI. 
 
CHAPTER III 
 
 MATERIAL AND METHODS USED IN THIS STUDY 
 
 The data used in this study were secured by means of a 
 survey of the elementary grades in the public school of the 
 town of Humboldt, Tenn. 1 This survey included the giv- 
 ing of standard tests to all the pupils up to and including 
 the eighth grade and giving each child a thorough physical 
 examination. The physical examination was in charge of 
 Miss Sanborn, 2 a registered health nurse. The achieve- 
 ment tests consisted of a series of tests covering all the ele- 
 mentary school branches. The tests selected for this pur- 
 pose were arithmetic, Monroe and the Cleveland ; spelling, 
 Buckingham Extension of the Ayres' Scale; geography, 
 Hahn Lackey; writing, Freeman Scale; reading, Monroe 
 Silent Reading; English, Trabue Extension and Nassau 
 County Supplement of Hillegas Scales. 
 
 The Illinois intelligence test was given all grades above 
 the second. Holley's picture tests were used in the first 
 and second grades. 
 
 For the most part, the papers were scored by the direc- 
 tors of the survey. The scores were tabulated by classes 
 and the medians determined. The latter were used in de- 
 riving the percentage score shown in Table I. The details 
 of that process are explained in connection with the inter- 
 pretation of that table. As explained below, this procedure 
 made it possible to combine scores made by a child in vari- 
 ous subjects and also to combine like subjects throughout 
 the elementary school. The method of averages used is also 
 explained in the proper place below. It is sufficient here 
 simply to say that the median per cent score was taken as 
 the average achievement for each child. 
 
 x The survey was directed by J. N. Mallory, Superintendent of Student Activities, 
 Union University, Jackson, Tenn., and L. D. Rutledge, Professor of Education in the 
 same school. 
 
 -Miss Sanborn is a graduate of a nurse training school, served overseas during the 
 war, and is now regularly employed by the Red Cross and is stationed at Humboldt. 
 
to Achievement in the Elementary School 
 
 23 
 
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 6; a 
 
 CO W 
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 1-5 8 
 
 
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 s[isuox 2 
 
 S ' , JO UBipSH J- 
 
 uBipan jo % 2 
 aaoos IbuiSuo ^ 
 
 uBipaK J° j /j 3 
 aaoos iBuiai.io w 
 
 usipaH jo % w 
 aaoos IBUiSiao ^ 
 
 UEipapj jo J/, S 
 aaoos \BUi3iao J 
 
 uBipaK J° % x 
 aaobs iBuiSiao £ 
 
 uBipajft jo >>/> S 
 aaoos iBuiSiao S 
 
 uBipaw jo ' , - 
 aaoos IBUiSiaQ w 
 
 lOiOOOlOO 
 C- O !C lO -* 05 
 
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 (M (M c- oo to os 
 
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24 A Study of the Relation of Some Physical Defects 
 
 Explanation of Table I. — This table includes only the 
 first six pupils of one section of the third grade, only enough 
 of the original data being given here to illustrate the method 
 of refining and interpreting the data. The figures in the 
 first column represent the names of pupils; those in the 
 second, the ages ; the third, intelligence score ; the fourth, 
 the intelligence score reduced to per cent of the median for 
 the class ; the odd columns from 5 to 15, scores in the re- 
 spective subjects; the even columns from 6 to 16, the per 
 cent of median for the respective subjects ; column 17, 
 medians of per cents of median for each pupil ; and columns 
 18 to 21, defects. Some method of combining the achieve- 
 ment scores made by each child in the various subjects in 
 order to arrive at a measure of his general ability was to 
 be found. Any method of doing this would require that all 
 these achievement scores be reduced to a common unit. 
 The simplest method of doing this is to reduce each score to 
 per cent of the median for the class in the respective sub- 
 jects, as is done in the table, and then take the average to 
 represent general ability. This method of combining scores 
 is the one used by Dr. Joseph Peterson, of Peabody College, 
 in the Paducah Survey, and recommended by him in his 
 article in the Journal of Educational Research for April, 
 1921. The method has been used in this study in prefer- 
 ence to the more complicated method of standard devia- 
 tions. To get the per cent score, the original score was 
 divided by the class median which is shown at the bottom 
 of each column. The first score in column 5 under writing 
 is 7. When 7 is divided by 9.25, the median shown at the 
 bottom of this column, the 76 shown in column 6 is ob- 
 tained as the corresponding per cent score. In the same 
 manner the figures 111, 52, 80, 112, 75, and 195 in the first 
 'row were obtained. The 111 is the per cent intelligence 
 score, and is not combined with the others in getting the 
 average, as it is treated as a separate factor and is used as 
 such in the study of relations in Chapter V. The ones to 
 be used, therefore, in the average are 76, 52, 80, 112, 75, 
 and 195. The median 1 of the row falls halfway between 
 76 and 80, or on 78. If the second row be taken, the per 
 cent scores are 86, 56, 80, 112, 105, and 61. Here the 
 median falls halfway between 80 and 86, or on 83. 
 
 Restating what has been said above, the entire first row 
 may be read as follows: Pupil "1" is 9 years of age; his 
 scores are 25, 7, 5, 14, 54, 5, and 32 in intelligence, writing, 
 language, spelling, reading rate, reading comprehension, 
 and arithmetic, respectively ; his per cent scores are 111, 
 
 x The median was selected as the average in preference to the mean because of. the 
 mathematical objection to using the mean with so few cases (six in this class). 
 
to Achievement in the Elementary School 25 
 
 76, 52, 30, 112, 75, and 195 in the subjects in the order just 
 named ; his median of per cents is 78 ; and he has defective 
 vision. The last fact is indicated by the check "1" under 
 vision in column 20. 
 
 Physical Defects. — Every precaution was taken to make 
 the data derived from the physical examinations reliable. 
 Miss Sanborn spent almost the whole of a school month in 
 this work. Each child was examined privately and with 
 painstaking precision. 
 
 It is true, however, that only such defects as could be 
 detected without the use of the X-ray and other expensive 
 apparatus were reported. The results as reported by Miss 
 Sanborn are tabulated in Tables II and III. 
 
 Explanation of Table II. — This table is intended to show 
 the total number of defectives in the eight grades, and to 
 show how these were distributed. The Roman numerals 
 in column I indicate the grades. The Arabics in the other 
 columns indicate the frequencies. Across the top the data 
 read: In the first grade there were 34 boys and 43 girls, 
 of which 26 boys and 20 girls were without defects, while 
 17 boys and 14 girls had defects. That is to say that 31/77 
 of the first grade had such defects. The other rows are 
 read in the same manner. Reading the last row, it is found 
 that of the 515 pupils examined, 245 were boys and 270 
 were girls ; 61 boys and 103 girls had no defects, while 331 — 
 164 boys and 167 girls — had defects. It will be seen that 
 
 
 
 
 TABLE ] 
 
 [I 
 
 
 
 
 
 
 Defectives 
 
 BY 
 
 Grades 
 
 
 
 
 No. 
 
 Examined 
 
 Without Deff.cts 
 
 Wit 
 
 h Defects 
 
 Grades 
 
 Boys 
 
 Girls 
 
 Total 
 
 Boys 
 
 Girls 
 
 Total 
 
 Boys 
 
 Girls Total 
 
 I 
 
 . 43 
 
 34 
 
 77 
 
 26 
 
 20 
 
 46 
 
 17 
 
 14 31 
 
 II 
 
 40 
 
 32 
 
 72 
 
 20 
 
 20 
 
 40 
 
 20 
 
 12 32 
 
 III 
 
 29 
 
 43 
 
 72 
 
 11 
 
 16 
 
 27 
 
 18 
 
 27 45 
 
 IV 
 
 28 
 
 23 
 
 51 
 
 9 
 
 5 
 
 14 
 
 19 
 
 18 37 
 
 V 
 
 22 
 
 30 
 
 52 
 
 3 
 
 13 
 
 16 
 
 19 
 
 17 36 
 
 VI 
 
 20 
 
 17 
 
 37 
 
 5 
 
 7 
 
 12 
 
 15 
 
 10 25 
 
 VII 
 
 22 
 
 35 
 
 57 
 
 1 
 
 6 
 
 7 
 
 21 
 
 29 50 
 
 VIII 
 
 21 
 
 41 
 
 62 
 
 5 
 
 11 
 
 16 
 
 16 
 
 30 46 
 
 Mixed 18 17 35 15 6 17 12 29 
 
 Totals 243 272 515 81 103 184 162 169 331 
 
 331 515 of the total number examined were defective. 
 This is a little more than 60 per cent. Everything that was 
 thought to be serious enough to require treatment was re- 
 ported. This included the five major defects — eyes, ton- 
 sils, nose, teeth, and hearing — and, in addition, twenty-one 
 of the less frequent ailments. The twenty-one cases were 
 distributed about equally among goitre, undernourishment, 
 
26 A Study of the Relation of Some Physical Defects 
 
 undersize, breathing trouble besides obstructed nasal cavi- 
 ties, throat trouble other than tonsilitis, and deformed 
 limbs. 
 
 These twenty-one cases were found to distribute them- 
 selves so that 52 per cent of these defectives made less than 
 100 per cent achievement score, while 48 per cent made 
 above 100 per cent score. Because of this near fifty-fifty 
 distribution, these minor ailments have been disregarded 
 and the study confined to the five major defects (eyes and 
 vision counted together as one) . 
 
 Explanation of Table III. — This table is similar to the 
 one above, except that it contains only those cases having 
 defective tonsils, eyes (or vision), nasal cavities, teeth, and 
 hearing. Reading the first two rows across the top, with 
 
 TABLE III 
 
 Distribution of Physical Defects by Grades and Ailments 
 
 Defects 
 
 Vision 
 
 Eyes 
 
 Hearing 
 
 Nasal Obstruction 
 
 Tonsils 
 
 Teeth 
 
 Totals 
 Grand Total 
 
 Boys 
 Girls 
 Boys 
 Girls 
 Boys 
 Girls 
 Boys 
 Girls 
 
 Grades 
 
 Sex I 
 
 Boys 5 
 
 Girls 
 
 
 
 
 1 
 2 
 1 
 21 
 
 III IV 
 4 
 6 3 
 
 
 
 
 
 1 
 
 
 1 
 
 10 
 
 To- 
 VI VII VlII tals 
 
 1 1 1 17 
 
 2 5 7 34 
 
 3 4 
 9 12 
 
 23 13 15 11 
 
 1 
 3 
 
 4 
 1 
 3 
 5 
 4 
 13 
 
 7 
 11 
 
 8 
 15 
 14 
 23 
 73 
 66 
 
 Boys 
 Girls 
 
 8 
 1 
 
 7 
 4 
 
 11 
 13 
 
 10 
 
 9 
 
 14 
 11 
 
 24 
 
 17 
 
 17 
 16 
 
 14 
 22 
 
 102 
 
 93 
 
 Boys 
 Girls 
 
 35 
 6 
 
 15 
 13 
 
 24 
 39 
 
 20 
 25 
 
 34 
 31 
 
 43 
 
 38 
 
 30 
 43 
 
 18 
 55 
 
 219 
 250 
 
 41 28 63 45 65 81 73 73 U69 
 
 bad vision in the first grade there are 5 boys and no girls ; 
 in the second grade, 1 boy and 3 girls ; in the third grade, 
 4 boys and 6 girls ; in the fourth grade, no boys and 3 girls ; 
 in the fifth grade, 4 boys and 6 girls ; in the sixth grade, 1 
 boy and 2 girls ; in the seventh grade, 1 boy and 5 girls ; in 
 the eighth grade, 1 boy and 7 girls; total, 17 boys and 34 
 girls. For the other defects the reading is similar. The 
 last row gives the totals of grades as follows: first grade, 
 35 boys and 6 girls ; second grade, 15 boys and 13 girls ; 
 
 ^his total should not agree with the total in Table II. The total in Table II is 
 the number of defective children examined. The total, in Table III is the number of 
 "defects." Some children had several defects. 
 
to Achievement in the Elementary School 27 
 
 third grade, 24 boys and 39 girls ; fourth grade, 20 boys and 
 25 girls ; fifth grade, 34 boys and 31 girls ; etc. The grand 
 totals in the last row give the total number of pupils having 
 these defects, boys and girls combined : first grade, 41 ; sec- 
 ond grade, 28 ; third grade, 63 ; fourth grade, 45 ; etc. 
 
 Justification of Data. — The nature of this study does not 
 make it highly essential rigidly to prove that the group of 
 students here studied presents a normal distribution. It 
 is not necessary to apply the tests for soundness of random 
 selection, for the reason that the consideration of the prob- 
 lem from the standpoint of attributes only requires that in- 
 vestigation be limited to a definite time, place, and material, 
 or that the universe be determined. When the universe is 
 once establishd, the only other condition to be satisfied is 
 that the investigations go on under uniform conditions and 
 requirements throughout. If the lines of class distinction 
 are sufficiently defined to make classification certain, the 
 relative ratios of frequencies is not material. Yule makes 
 the following observation : 
 
 "The student should note that the value of Q for a given 
 table is unaltered by multiplying either a row or a column 
 by any arbitrary number — i. e., the value is independent of 
 the relative proportions of A's and a's included in the table. 
 This property is important, and renders such a measure of 
 association specially adapted to experiments in which the 
 proportions are arbitrary." It is interesting to note, how- 
 ever, that both the distribution of Illinois intelligence scores 
 and diseases show the group to conform rather closely to 
 the normal expectation for the country at large. 
 
 Distribution of Intelligence Scores. — The distribution of 
 intelligence scores is shown in Figure I. The graph, when 
 smoothed, will be seen to approach very closely the normal 
 curve. So far as intelligence can be used as a criterion, 
 this group appears to be a fair sample. The Illinois tests 
 were used above the second, while the Holley Picture Com- 
 pletion tests were used in the first and second grades. As 
 there is no method of reducing the latter to I. Q.'s, all scores 
 were reduced to percentages of the median for the class 
 instead. The per cent scores were the ones used in plot- 
 ting the graph. The distribution of intelligence is shown 
 in Figure I. 
 
 The percentages of defects are shown in Table IV. They 
 are strikingly near the averages determined from other 
 sources. It must be mentioned, however, that these aver- 
 
28 A Study of the Relation of Some Physical Defects 
 
 65 
 
 60 
 
 55 
 
 50 
 
 45 
 
 40 
 
 35 
 
 30 
 
 25 
 
 20 
 
 15 
 
 10 
 
 LQ 
 
 20 40 60 80 100 120 140 160 180 200 
 
 Distribution of intelligence scores for the grades one to eight, scores first reduced to 
 per cent of median of class. 
 
to Achievement in the Elementary School 29 
 
 ages are from Northern cities ; the data under consideration 
 are from a small Southern town. According to the Army 
 Draft Board Report, both these items must be taken into 
 consideration. For instance, these data show a total per- 
 centage of physical defectives of 64 ; while the average for 
 New York State (71 per cent), Minneapolis (65 per cent), 
 New York City (72 per cent) is a little less than 70 per 
 cent. 1 Table IV shows the comparative data. According 
 to the Army Report mentioned above, only about 88 per cent 
 as many defectives are found in the semirural districts of 
 the South as in cities of the North. Taking 88 per cent of 
 the 70 per cent would give about 62 per cent, a number very 
 near the Humboldt percentage. 
 
 In the same way it has been shown that the 13.4 per cent 
 defective vision in Humboldt data approaches very near the 
 Northern city average of 18 per cent ; 4.3 defective hearing, 
 near the 5.5 per cent average; 27 per cent defective hearing, 
 near Ayres' average of 40 to 14 per cent for extreme ages 
 of five to fourteen. The comparison is similar for nose, 
 tonsils, and teeth, as shown in Table IV. 
 
 TABLE IV 
 
 Showing the Percentages of Defectives in the Humboldt Schools 
 Compared With Certain Other Reports- 
 
 Rcports Total Eyes Ears Nose Tonsils Teeth 
 
 Humboldt 64 13.4 4.3 8 27 41.7 
 
 Other sources 703 18-t 5.55 3_236 14-40- 31-65^ 
 
 Method of Attributes. — Some students fall into the habit 
 of thinking of statistics as dealing solely with variables and 
 overlook entirely the treatment of attributes. To so re- 
 strict the meaning of statistics would leave out of consid- 
 eration a very large and important class of material. This 
 kind of data involves only the counting of those that possess 
 and those that do not possess certain characteristics. The 
 whole of any selected field of investigation, which is known 
 as "the universe," is divided into two groups, called 
 "classes." For instance, all men may be classed as "tall" 
 or "short." In this study all children are classed as "non- 
 defectives" and "defectives." The treatment of this kind 
 of data required a different method from that used in the 
 
 ^Medical inspection of Schools, Gulick and Ayres. 
 J The data are taken from Ayres' Laggards in Our Schools. 
 
 Average of finding in New York State, New York City, and Minneapolis. From 
 Medical Inspection of Schools, pages 83-87, by Gulick and Ayres. 
 4 Median of finding in fourteen cities. See - above. 
 "Ibid, Gulick and Ayres, pages 83-87. 
 "Taken from Laggards in Our Schools, page 121. 
 "Ibid. See also Chapter 1 of this study. 
 s Ibid. See also Chapter 1 of this study. 
 
30 A Study of the Relation of Some Physical Defects 
 
 study of variables ; but, on the whole, the method is not 
 more difficult. The usual procedure is to find what per cent 
 of the individuals in the universe is found in one of the 
 classes. 
 
 Sometimes it is desirable to make a study of more than 
 one attribute of the same object or person. For instance, 
 it might be a classification of garden peas into tall and 
 dwarfed vines and smooth and wrinkled pods. Some peas 
 that grow on tall vines are smooth and some are wrinkled, 
 while both smooth and wrinkled may be found on dwarfed 
 vines. It is evident that here there would be the four types, 
 or "classes" — tall smooth, tall wrinkled, dwarfed smooth, 
 and dwarfed wrinkled. This is a fourfold classification. 
 This is the way the classes used in this study are deter- 
 mined. The positive and negative attributes are high 
 achievement or low achievement, and physically sound or 
 physically defective. It can be seen that all children fall 
 into one of four groups — sound with high scores, sound with 
 low scores, defective with high scores, and defective with 
 low scores. In this study high and low scores are arbi- 
 trarily taken to mean above 100 per cent average achieve- 
 ment score and below 100 per cent average score. 
 
 It is often desirable to know what the relation of one 
 attribute is to another. It may be that if peas grow on tall 
 vines they are more apt to be wrinkled than smooth. 
 Where there exists such a cause-and-effect relation, it is 
 known as association. If peas growing on tall vines are as 
 apt to be wrinkled as smooth, then there is no association 
 between tallness of vine and smoothness of peas. This 
 study is an attempt to find if such an association exists be- 
 tween defects and ability to make high scores on tests in 
 school subjects. 
 
 The methods to be used in determining this lead to the 
 consideration of Karl Pearson's association formulae. Be- 
 fore taking up these formulae, however, methods of classi- 
 fying the data will be further considered. 
 
 Grouping the Data. — For use in the criteria of associa- 
 tion and in finding the coefficient of correlation, the data 
 must be distributed as shown in the diagram below. Start- 
 ing with the upper right-hand quadrant and going counter 
 clockwise, the first quadrant represents the group of stu- 
 dents that had no defects and were making low scores (less 
 than 100) at the same time; quadrant II (the upper left- 
 hand quadrant), the group that had no defects and were 
 making high scores (100 or above) ; quadrant III, those 
 making low grades. Pupil 1, Table I, has a median score 
 of 78 and has defective vision, so he was checked in quad- 
 
to Achievement in the Elementary School 
 
 31 
 
 rant IV; pupil 3, with a median of 115 and defective 
 tonsils and teeth, was checked in quadrant III. If he had 
 not been defective, he would have been checked in quadrant 
 II. The attribute "without defects" is designated in this 
 study as "A ;" with defects, "a ;" with high scores, "B ;" 
 with low scores, "b." Pupil 1 above is represented by "ab," 
 while pupil 3 is "aB." A pupil in the first quadrant is rep- 
 resented by "Ab ;" one in the second quadrant is indicated 
 by "AB." 
 
 Diagram Showing Distribution of Pupils into Four Groups — 
 Sound with Low Grades, Sound with High Grades, Defec- 
 tive with High Grades, Defective with Low Grades 
 
 Second Quadrant "AB" 
 >)»>> >>»>» >>>»> >>>>> 
 
 > > J T > >)!>» >>>>> >!>>> 
 
 " " ' " ' " " etc. 
 
 First Quadrant "ab" 
 **>>> nn I ? 7 7 7 7 * t > f > nm »>>>> 
 >>>>> >»>»» ?>»»» )>?»» )»>>» >>»»» 
 
 Third Quadrant "aB" 
 >>>>> >?>>> >>»>» >»>>» 
 
 9 7 7 7 7 JJJJJ ) ? J > J ! IMI 
 ,,,,, ,,,,, et( . 
 
 Fourth ( uadrant "ab" 
 
 »>»J> >J»>J ? f } 1 f t > 7 9 f )»>>> >>>J» 
 )»>>> )!>>> >>>>> )»)»> >>>?> >»>»> 
 
 " ' " " ' " " ' " ""> etc. 
 
 TABLE V 
 
 Total Defective Eyes, Ears, Nose, Teeth, and Tonsils. Fourfold 
 Distribution of Frequencies 
 
 Not Defective 
 Above 100% 
 AB 
 
 91 
 
 Not Defective 
 Below 100% 
 Ab 
 
 117 
 
 Defective 
 
 Above 100% 
 aB 
 
 97 
 
 Defective 
 Below 100% 
 ab 
 
 191 
 
 The data for Table V were taken from the distribution 
 made in the diagram above. The total defectives below 
 100 per cent in score were found to be 191 ; those defective 
 and above, 97. The sound or "not defective" below, total 
 117; the sound above 100 per cent, total 91. The total 
 number of frequencies in this distribution is known as the 
 "Universe" and is designated as "N." In this case "N" = 
 496. This is the base used in finding the percentages rep- 
 resenting the different quadrants. 
 
32 A Study of the Relation of Some Physical Defects 
 
 Per cent of pupils not defective making below 100% (quad. I) '=.562 
 
 Per cent of pupils not defective making above 100% (quad. II) =.436 
 
 Per cent of pupils defective and making above 100% (quad. Ill) =.336 
 
 Per cent of pupils defective and making below 100% (quad. IV) =.620 
 
 Quadrants I and II represent the sound pupils % of Universe =.419 
 
 Quadrants III and IV represent the defective pupils % of Universe =.581 
 
 Quadrants II and III represent High Scores % of Universe =.379 
 
 Quadrants I and IV represent Low Scores % of Universe =.621 
 
 Association. — Suppose, now, we wish to check the data 
 shown in Table V to ascertain if there is an association be- 
 tween defects and achievement score. This is easily done 
 by reducing each second-order frequency to percentage of 
 the Universe and comparing the percentages, or by com- 
 paring these second-order frequencies with the correspond- 
 ing first-order frequency. By a first-order frequency is 
 meant the number of individuals possessing a single attri- 
 bute, as Soundness (A) or Defectiveness (a). By a second- 
 order frequency is meant the number of individuals pos- 
 sessing simultaneously two attributes, as sound bodies and 
 high scores (AB), or sound bodies and low scores (Ab). 
 They are represented by two letters. These percentages 
 would be difficult to interpret without the aid of some kind 
 of measure of association, or else have certain criteria for 
 judging. Karl Pearson has devised formulae adapted to 
 both of these methods. 
 
 Testing the Data by Association Formulae. — If there is 
 an association between defective bodies and low scores, the 
 following inequalities must hold : 
 
 A? - A_ . AB B AB^Ab. AB.aB 
 
 B " N ' A > N ' B b ' A " a 
 
 The first of these says that the per cent of sound pupils 
 among those making a high score should be greater than 
 the per cent of sound pupils in the Universe. In simple 
 language, the number of sound children with high scores di- 
 vided by the total number of children with high scores should 
 be greater than the number of sound children in the school 
 divided by the number of pupils in school, if there is a posi- 
 tive association. The second formula requires that the 
 number of sound pupils with high scores divided by the 
 number of sound pupils be greater than the number of pu- 
 pils with high scores examined divided by the number ex- 
 amined, if there is to be a positive association. The third 
 requires that the number of sound pupils with high scores 
 divided by the number of pupils with high scores' in the 
 school be greater than the sound pupils with low scores 
 divided by the total number with low scores for positive 
 association. The fourth requires that the sound pupils 
 
to Achievement in the Elementary School 33 
 
 with high scores divided by the number of sound pupils in 
 the Universe be greater than the defective pupils with high 
 scores divided by the defective pupils examined. Any one 
 of these would indicate an association, but the application 
 of the four is further proof of it. 
 
 If the data from Table V be used to illustrate the method 
 described above, then A = 208 (sound) ; B (with high 
 scores) = 188; a (defective) =388; b (low scores) = 308; 
 N (Universe) =496; AB (sound with high scores) =91; 
 Ab (sound with low scores) = 117; ab (defective with low 
 scores) = 191. These numbers substituted in the formulae 
 give: 
 
 91' 208 .„, , in 91 188 ,„„ n „ n 
 
 188 > 496' -484 .419; ^ ^ ; .436 .379 
 
 91 117 AOA or7ft 91 97 
 
 188 > 308 : - 484 - 379 = 208 > 288' -436 >. 336 
 
 The inequalities all prove true. This means, then, that 
 the per cent of bright pupils in the sound group is greater 
 than the per cent of pupils with high scores in the whole 
 group ; that the per cent of sound pupils among those with 
 high scores is greater than the per cent of sound pupils 
 among the whole group ; that the per cent of sound among 
 those with high scores is greater than the per cent of sound 
 among the pupils with low scores ; and that the per cent of 
 those with high scores among the sound is greater than 
 the per cent of high scores among the defectives. Since 
 these all agree and the left-hand member in each inequality 
 is greater than the right, the conditions between defects 
 and low scores are all met. Therefore it must be concluded 
 that there is a positive association between these two traits. 
 
 Testing the Degree of Association. — If the inequalities 
 were noticeably large when determined as above, the degree 
 of association would probably be large; but when the per- 
 centages are nearly equal, it is difficult to estimate the de- 
 gree of association. To aid in the interpretation of the 
 results, another formula is used. If A, B, a, and b have 
 the same meaning as above and if the coefficient of correla- 
 tion is indicated by Q, the formula below will give the degree 
 of association. This formula is such that as the association 
 increases, the value of Q increases from to +1 ; and as the 
 disassociation, or negative association, increases, Q de- 
 creases from to — 1. 
 
34 A Study of the Relation of Some Physical Defects 
 (AB) (ab) — (Ab) (a B) 
 
 Q = 
 
 (AB) (ab) + (Ab) ■ (a B) 
 
 When the data from Table V is substituted, the equation 
 becomes : 
 
 Q 
 
 (91) (191) — (117) (97) 
 (91) (191) + (117) (97) 
 
 17381 _ 11344 5937 
 
 17381 + 11344 ~ 18725 
 
 21 
 
 This result shows positive association, because the prod- 
 uct of the sound with high scores and the defective with 
 low scores is greater than the product of the sound with 
 low scores and the defective with high scores. This is the 
 same as saying that if the product of the second and fourth 
 quadrants is greater than that of the first and third, the 
 association is a positive one. A glance at Table V will make 
 this fact clear. As the product of the first and third quad- 
 rants approaches zero, the value of Q approaches 1, since 
 the numerator and denominator of the fractions are then 
 equal, each being the product of the second and fourth quad- 
 rants. As the product of the second and fourth quadrants 
 approaches zero, Q approaches — 1, since the numerator and 
 denominator are then equal, each being the product of the 
 first and third quadrants. This coefficient, then, is the 
 ratio of this excess or deficit to the sum of the products of 
 the two pairs of opposite quadrants. 
 
 This coefficient of .21 indicates that if a single child were 
 selected at random from this school, the chances favor its 
 being one with high scores, if it be one without physical de- 
 fects. This is especially true, since the probable error of 
 this coefficient is small, as will be seen from the application 
 of the probable error formula : 
 
 iP. E. = .67449x1 — r 2 
 
 /N 
 
 Here r — .21 and N = 496. Putting these values in the 
 formula, 
 
 i or-' Q^Q 
 
 P.E. = .67449 J^ - .67449 ^jgL : ± .«, 
 
 Then r = .21 ± .03 
 
 ^ugg, Statistical Method Applied to Education, page 273. 
 
to Achievement in the Elementary School 35 
 
 This interpreted means that the coefficient of association 
 lies between .18 and .24 in half of the cases, or with a prob- 
 ability of 1 : 1. 
 
 While the probable errors shown in Table VII, Chapter 
 IV, were derived by the above formula, they should be con- 
 sidered only as near approximations. In a strictly math- 
 ematical sense, probable error formulas that apply to vari- 
 ables do not apply to attributes. 1 An absolute correction 
 can be obtained by using Pearson's Formula- for a fourfold 
 table as follows: 
 
 P.E. 
 
 .67449 
 
 /N A - r J / 1 — ( sin"" 1 r)- 
 
 ( 90 )-' 
 
 h ( 1 -a ) h( 1 + a) / |il -a ) ( 1 -a) 
 H K 
 
 Here N and r have the same meaning as in the formula 
 on page 34; sin ' can be found by finding an angle whose 
 sine is "r" ; J (1 — a), \ (la), \ (l_ a ,), and \ (l + a 2 ) 
 are percentages representing the relative areas included 
 under the normal curve as shown by Sheppard's tables (see 
 footnote, page 37). H and K are the values of Z for col- 
 umns and rows, respectively, and can be read from Shep- 
 pard's tables. 
 
 The data from Table V substituted in this formula give : 
 
 ■67449 /i .21-' 1 12i J /.621 .379 
 
 .419 x .581 
 .38022 
 
 (90)-' .39104 
 
 P. E. = .043 
 
 This shows an increase over the probable error found 
 above of .01. 
 
 If access is had to Sheppard's Tables, Miss Gibson's Ta- 
 
 67449 
 bles :! for 1 , and Everitt's Tables of Tetrachoric Func- 
 
 /N 
 tions, 4 this formula should be used for fourfold tables in- 
 stead of the ordinary formula. Without Sheppard's tables, 
 
 ^ule, Introduction to the Theory of Statistics, page 352. 
 
 -Blometrika, Vol. IX, page 22. 
 
 3 Biometrika, Vol. IX, page 25. 
 
 <Biometrika, Vol. VII, page 436, and Vol. VII, page 385. 
 
36 A Study of the Relation of Some Physical Defects 
 
 it cannot be used; and, with them, the amount of work 
 required is extreme unless Gibson's and Everitt's tables are 
 also accessible. 
 
 A Method of Correlation that is Adapted to a Variable 
 and an Attribute. — The method used above does not take 
 advantage of the fact that one of the attributes was a meas- 
 urable quantity. The scores yield themselves most readily 
 to this kind of treatment. Pearson 1 has given us a formula 
 for utilizing this property and at the same time making it 
 possible to correlate with a nonmeasurable attribute. 2 
 
 At first sight the formula seems complex, because it is 
 derived from the equation of the normal curve and con- 
 tains integral signs. It is as follows : 
 
 ly 2 
 
 N /~00 2 o--r 
 
 W^f J y ye ' dy 
 
 N /»oo y 
 
 2 n a-> J y e 2 *? dy 
 
 (1) 
 
 r^=- - i (y>--0- 
 '2n . e 2 Ky/ 
 
 1 ,oo 1 ., I (1 — a) 
 
 '2lf J y/0-2 e 2 y dy 
 
 (2) 
 
 But p = r en ± .'. p == r <n* j ( i - a) 
 
 , p Z o-i HI — a) p (£ , 
 andr=— ! =- -— — 7 = — ^ — = — —, (4) 
 
 0"! 
 
 (1 — a) _Z o-i Z 
 
 (1-a) 
 
 In these equations p and q are the coordinates from a 
 point on the regression line, r the coefficient of correlation ; 
 o-i and o-i are the standard deviations for the two variables ; 
 e-^y 2 is the logarithmic function that gives the normal 
 
 J Karl Pearson A New Method of Determining Correlation Between a Measured 
 Character A and' a Character B, of which Only the Percentage of Cases Wherein B 
 Exceeds a Given Intensity is Recorded for Each Grade of A.—Biometrika, Vol. Vll, 
 page 98. 
 
 -See note, page 46. 
 
to Achievement in the Elementary School 
 
 37 
 
 curve ; Z is an abbreviation for the numerator of the right- 
 hand side of equation 2 above; .] (1 — a) is the denomina- 
 tor of the same fraction. Sheppard has worked out the 
 values of the last two expressions — Z and -\ (1 — a) — and 
 has made a table to be used in finding the area under the 
 normal curve. p can be found by subtracting the mean 
 of the whole distribution from the mean of one array. The 
 standard deviations of the whole distribution and that of 
 the single array can be found. Z and \ (1 — a) can be 
 taken from Sheppard's tables. 1 Thus everything needed in 
 the solution of equation 4 above is easily obtainable. 
 
 The application of this formula to a specific set of data 
 will help to clear it up. It is desired to find the correlation 
 betv/een defective tonsils and scores in spelling. The data 
 in the table on the following page were used to represent 
 the method. The first column is the scores ; the second, the 
 frequencies for the group without defects ; the third, the 
 frequencies for the group with defects ; the fourth, the to- 
 tals, d, fd, fd-, columns were used in finding the standard 
 deviation of the whole distribution ; the last two columns 
 were used for finding the mean of the array of defectives. 
 These, with the values of Z and \ (1 — a) from the tables, 
 enable us to solve for r. 
 
 TABLE VI 
 
 Correlation Between Scores in Spelling and Defective Tonsils 
 
 Per Cent Sound Defective Total 
 
 fd 
 
 id? 
 
 d 
 
 df 
 
 10 
 
 7 
 
 2 
 
 9 
 
 —8 
 
 —73 
 
 576 
 
 —8 
 
 —16 
 
 20 
 
 6 
 
 2 
 
 8 
 
 —7 
 
 —56 
 
 392 
 
 —7 
 
 —14 
 
 30 
 
 7 
 
 2 
 
 9 
 
 —6 
 
 —54 
 
 324 
 
 —6 
 
 —12 
 
 40 
 
 8 
 
 6 
 
 14 
 
 —5 
 
 —70 
 
 350 
 
 —5 
 
 —30 
 
 50 
 
 20 
 
 5 
 
 23 
 
 —4 
 
 —92 
 
 368 
 
 —4 
 
 —20 
 
 60 
 
 19 
 
 4 
 
 23 
 
 —3 
 
 —67 
 
 307 
 
 — 3 
 
 —12 
 
 70 
 
 18 
 
 11 
 
 29 
 
 —2 
 
 —56 
 
 116 
 
 —2 
 
 —22 
 
 80 
 
 38 
 
 8 
 
 46 
 
 —1 
 
 —46 
 
 46 
 
 —1 
 
 — 8 
 
 90 
 
 15 
 
 17 
 
 32 
 
 
 
 
 
 
 
 
 
 
 
 100 
 
 29 
 
 9 
 
 38 
 
 1 
 
 38 
 
 38 
 
 1 
 
 9 
 
 110 
 
 44 
 
 13 
 
 57 
 
 2 
 
 114 
 
 238 
 
 2 
 
 26 
 
 120 
 
 28 
 
 5 
 
 33 
 
 o 
 
 o 
 
 99 
 
 397 
 
 3 
 
 15 
 
 130 
 
 14 
 
 2 
 
 16 
 
 4 
 
 64 
 
 256 
 
 4 
 
 8 
 
 140 
 
 8 
 
 5 
 
 13 
 
 6 
 
 65 
 
 325 
 
 5 
 
 25 
 
 150 
 
 O 
 
 o 
 
 3 
 
 6 
 
 6 
 
 36 
 
 216 
 
 6 
 
 18 
 
 160 
 
 1 
 
 
 
 1 
 
 7 
 
 7 
 
 49 
 
 7 
 
 
 
 170 
 
 6 
 
 2 
 
 5 
 
 8 
 
 30 
 
 320 
 
 8 
 
 16 
 
 180 
 
 
 
 1 
 
 1 
 
 9 
 
 9 
 
 81 
 
 9 
 
 9 
 
 190 
 
 1 
 
 
 
 1 
 
 10 
 
 10 
 
 100 
 
 10 
 
 
 
 200 
 
 5 
 
 
 
 5 
 
 11 
 
 55 
 
 605 
 
 11 
 
 
 
 Totals 
 
 314 
 
 95 
 
 409 
 
 
 20 
 
 4895 
 
 
 8 
 
 
 pard's 
 
 Tables, B 
 
 ometrika. 
 
 Vol. II. page 
 
 182. 
 
 
 
 
 'Shep 
 
 
38 A Study of the Relation of Some Physical Defects 
 
 Mean of total distribution, 97.885 ; mean for defectives, 
 94.158. Standard deviation for the total distributions, 
 
 .0025 = 3.341 
 
 409 
 
 P 3 797 
 
 Then ^—^ = (94.158 — 97.885) -^ 33.41 
 
 33.41 "" x -■•— , . ~~.^- 3341 
 
 £(1 _ a) = -r£ = .2322 ; then i (1+a) = 1 —.2322 =.7678 
 From Sheppard's tables this gives Z — .3056. Then 
 
 3.727 .2322 = .865409 = 
 r 33.41 .3655 10.210096 
 
 It will be noted that the result shows a negative correla- 
 tion between defects and high scores which would give a 
 positive correlation between defects and low scores. 
 
 A table of similar results is shown in the next chapter 
 for each defect with specific subjects. 
 
 It will be remembered that it was the aim of this study, 
 as set forth in the outset, to get the apparent correlations 
 and then to free them from the influence of certain factors 
 that might affect these coefficients. This has been done, 
 and the following is an extract of the process as applied to 
 the correlation between tonsils and spelling. The formula 
 used is Pearson's and is taken from Yule's Introduction to 
 the Theory of Statistics, page 238. 1 
 
 v _ ^12,34 . . , (n — 1) ' Pin 34 . . . . (n -1) •^2n.34 . . . . (n - 1) 
 
 * 12.34. n— /-, _ 2 W1 _ 2 ; rf~ 
 
 V- 1 - x ln34 . . . .(n — 1)) K*- 1 2n.34. . . .(n—\)) 
 
 The formula for three variables is : 
 
 y ^12 ^13 ' ^23 
 
 123 = " (l-ryMi-r!) 4 
 
 In another place in this report the correlation of sound 
 tonsils with Illinois intelligence scores gave a coefficient of 
 
 ^t should be remembered here that these partial coefficients of association might 
 have been found in a way similar to that for testing for simple associations. Yule 
 discusses this method and furnishes criteria for testing for partial association, but the 
 method is complex and is less refined than the regular correlation formula used here. 
 The latter is far better here, because in each case one of the traits is expressed as a 
 variable, and in case of intelligence and scores both are variables. 
 
to Achievement in the Elementary School 39 
 
 .04 ; of Illinois intelligence and median achievement scores, 
 .32 ; tonsils and spelling scores, .10. Substituting these val- 
 ues in the formula, we have : 
 
 ru = .04; rss .32; ta .10, 
 
 where the figures 1, 2, 3 stand for the variables and attri- 
 butes, tonsils, achievement scores, and intelligence scores, 
 respectively. 
 These give : 
 
 .10 (.04) (.32) 
 ri2 3 (1 .0016) • (1 .1024) » 
 
 .057200 noo 
 Tl2 " .943000 ~ ' 0J2 
 
CHAPTER IV 
 
 PRELIMINARY ANALYSIS, USING PERCENTAGES AND 
 ASSOCIATION COEFFICIENTS 
 
 This chapter deals with the tabulated data derived by the 
 methods outlined in Chapter III. Tables VII to XII, inclu- 
 sive, show the distribution of the data according to the va- 
 rious traits. Table XIII is a summary of these. Tables 
 XIV to LIII contain the data from which the coefficients of 
 association between each defect and the specific subjects 
 are derived. These forty coefficients are summarized in 
 Table LIV. These are the coefficients as they appear before 
 being freed, by the formula for partial correlations, from 
 the influence of other factors. 
 
 Defects Correlated with General Ability 
 
 table VII 
 
 All Defects Correlated with General Ability 
 
 
 Scores Above 100% 
 
 Scores Below 100% 
 
 Totals 
 
 Without Defects 
 
 AB, 91 
 
 Ab, 117 
 
 208 
 
 With Defects 
 
 aB, 97 
 
 ab, 191 
 
 288 
 
 Total 
 
 188 
 
 308 
 
 496 
 
 In Tables VII to XII the following notation should be 
 observed : 
 
 N — Total number of observations, the "Universe." 
 
 A — Number of individuals without defects. 
 
 a — Number of individuals with defects. 
 
 B — Number of individuals scoring above 100% of class 
 median. 
 
 b — Number of individuals scoring below 100% of class 
 median. 
 
 AB — Number of individuals without defects making 
 above 100%. 
 
 Ab — Number of individuals without defects making be- 
 low 100%. 
 
to Achievement in the Elementary School 41 
 
 aB — Number of individuals with defects making above 
 100%. 
 
 ab — Number of individuals with defects making below 
 100%. 
 
 A full explanation of the formulae used in testing the 
 association is made in Chapter III, page 43. It is suffi- 
 cient here to state that the left-hand members of the fol- 
 lowing inequalities must be greater than the right-hand 
 members and to repeat enough of the process to visualize 
 the results : 
 
 AB A 
 
 AB B AB Ab . AB . 
 
 aB 
 
 B N 
 
 ' A N ' B b ' A 
 
 a 
 
 Q 
 
 (AB ab) (Ab aB) 
 
 
 (AB ab) + (Ab aB) 
 
 
 These give : 
 
 _91>208 484 :> i419 
 108 496 
 
 I>1«'« - 379 
 
 
 _9K HZ 
 
 108 308 
 
 _9i^ jn 
 
 208 288 
 
 or .484 .379 
 
 or .436 > .336 
 
 Which show there is positive association. If the left- 
 hand members were smaller than the right, a negative asso- 
 ciation would be indicated. To find the degree of associ- 
 ation, as was done on page 34 of this study, the following 
 substitution is made in the formula for Q : 
 
 (91 191) — (117x97) 5937 __ n 
 
 M " (91 191) + (117x97) 18725 _ 
 
 In Chapter III the probable error of this coefficient was 
 found to be == .03. This indicates a rather significant de- 
 gree of association between general ability as shown by 
 scores and physical soundness. 1 
 
 'Karl Pearson interprets a coefficient of association of .076 between good tonsils 
 and weight as significant.— Iiiometrika. Vol. VII, page 103. 
 
42 A Study of the Relation of Some Physical Defects 
 
 TABLE VIII 
 
 Tonsils Correlated with General Ability 
 
 
 Scores Above 100% 
 
 Scores Below 100% 
 
 Totals 
 
 Without Defects 
 
 AB, 144 
 
 AB, 218 
 
 362 
 
 With Defects 
 
 aB, 44 
 
 ab, 88 
 
 132 
 
 Total 
 
 188 
 
 306 
 
 494 
 
 Substituting in the formula above 
 
 144 362 . 
 
 188 ^ 494 • 766 ^ ' 732 
 
 144 ^ 188 
 36 ^ 496 
 
 144 ^ 218 
 494 > 132 
 
 : .398 > .380 
 : .766 > .712 
 
 These inequalities indicate a positive correlation the de- 
 gree of which is shown by : 
 
 Q 
 
 (144x88) — (218x44) 
 (144x88) + (218x44) 
 
 ,138 ± .044 
 
 This coefficient is also large enough to show that sound 
 tonsils and general achievement are related significantly. 
 
 TABLE IX 
 Eyes (Vision and Eyes) Correlated with General Ability 
 
 
 Scores Above 100% 
 
 Scores Below 100% 
 
 Totals 
 
 Without Defects 
 
 AB, 170 
 
 Ab, 276 
 
 446 
 
 With Defects 
 
 aB, 18 
 
 ab, 31 
 
 49 
 
 Total 
 
 188 
 
 307 
 
 495 
 
to Achievement in the Elementary School 
 
 43 
 
 From the formula the data in this table give : 
 
 170 188 
 
 446 ' 505 
 
 170 446 
 
 188 505 
 
 p= : .381 .372 
 
 .904 
 
 Q 
 
 170 
 
 276 
 
 188 
 
 307 
 
 170 
 
 18 
 
 446 
 
 49 
 
 (170 31) 
 
 
 .904 .899 
 
 .381 .367 
 
 (276 18) 
 
 (170 31) + (276 18) 
 
 ,029 
 
 .(»: 
 
 There is but slight indication of a positive association 
 between sound eyes and high scores. As will be shown 
 later, this coefficient varies with different subjects, some 
 showing a negative correlation. As stated in the introduc- 
 tion, Ayres and Cornell report negative or slight positive 
 correlation between sound eyes and teachers' marks. 
 
 TABLE X 
 Correlation of Defective Nasal Cavities with Achievement 
 
 
 Scores Above 100' , 
 
 Scores Below 100' , 
 
 Totals 
 
 Without Defects 
 
 AB. 185 
 
 Ab, 280 
 
 465 
 
 With Defects 
 
 aB, 2 
 
 ab, 27 
 
 29 
 
 Total 
 
 187 
 
 307 
 
 494 
 
 It follows that 
 
 185 
 187 
 185 
 465 
 185 
 187 
 185 
 465 
 
 465 
 494 
 187 
 494 
 280 
 307 
 _2 
 29 
 
 .989 .941 
 
 .397 .378 
 
 .987 .912 
 
 .397 > .069 
 
 _ (185x27) -(280 x2) 
 H ~ (185x27) - (280x2) '' yy ~ >UiD 
 
44 A Study of the Relation of Some Physical Defects 
 
 This is is by far the most significant coefficient found. 
 There is evidently a high degree of association between 
 mouth breathing or nasal obstruction and backwardness in 
 subjects. This conclusion is also supported by Ayres in 
 his study of promotions in his Laggards in Our Schools. 
 It will be noticed that all pupils, except two, with nasal 
 obstructions made less than 100% as an average achieve- 
 ment score. 
 
 TABLE XI 
 
 Correlation of Soundness of Teeth with Achievement Scores 
 
 
 Scores Above 100% 
 
 Scores Below 100% 
 
 Totals 
 
 Without Defects 
 
 AB, 134 
 
 Ab, 184 
 
 318 
 
 With Defects 
 
 aB, 53 
 
 ab, 136 
 
 189 
 
 Total 
 
 187 
 
 320 
 
 507 
 
 134 318 . 
 
 187 507 • 
 
 .627 
 
 134 . 184 . 
 
 187 '' 320 * 
 
 .593 
 
 134 
 318 
 
 187 
 507 
 
 .421 
 
 .362 
 
 134 
 
 318 
 
 _53 
 
 189 
 
 .421 
 
 .280 
 
 Q = 
 
 (134x136) — (184x53) 
 (134x136) + (184x53) 
 
 .302 ± .02 
 
 The degree of positive association of sound teeth with 
 achievement is larger than might have been expected. This 
 is probably due in part to the fact that a large number of 
 those having defective teeth also have other defects. 
 
to Achievement in the Elementary School 45 
 
 TABLE XII 
 Correlation of Hearing with High Scores 
 
 
 Scores Above 100% 
 
 Scores Below 100' < 
 
 Totals 
 
 Without Defects 
 
 AB, 180 
 
 Ab, 284 
 
 464 
 
 With Defects 
 
 aB, 7 
 
 ab, 23 
 
 30 
 
 Total 
 
 187 
 
 307 
 
 494 
 
 These data indicate positive association. The inequali- 
 ties are: 
 
 180 464 . 
 
 187 494 • ,aW •* W 
 
 1 1 : - 903 > - 398 
 
 1 i ■■ - 9037 - 398 
 
 ISO 7 
 
 ii -35 : - 903 - 233 
 
 _ (180x23) -(284x7) 
 y " (180x23) + (284 x 7) "^ - UaJ 
 
 Next to obstructed breathing, this is the largest coeffi- 
 cient of association found between defects and general 
 achievement. There is probably some relation between ob- 
 structed breathing and defective hearing; but to what 
 extent, this study does not undertake to determine. 
 
 TABLE XIII 
 
 Summary of Data Showing Relation of Specific Defects to 
 Achievement Scores 
 
 Defects Ab AB aB ab Q P.E. 
 
 Hearing 284 180 7 23 .351 .059 
 
 Tonsils 218 144 44 88 .138 .044 
 
 Nasal Obstruction 280 185 2 27 .799 .016 
 
 Eyes and Vision 276 170 18 31 .029 .0.44 
 
 Teeth - 184 134 33 136 .302 .02 
 
 General Defects 117 91 97 191 .21 .03 
 
46 A Study of the Relation of Some Physical Defects 
 
 Table XIII, Summary. — If the probable effect of other 
 factors is ignored, it is evident that there is indication of a 
 positive association between each of the defects mentioned 
 in Table XIII and general ability. Nasal obstruction, which 
 usually results in mouth breathing and is often accompa- 
 nied by defective hearing, appears to be a greater handicap 
 than either of the others tabulated. The high coefficient of 
 .799, with a probable error of : .016, would justify the 
 statement that should an individual with defective tonsils 
 be selected from the Humboldt School, he would very prob- 
 ably be one that would be low on tests. The same could be 
 said of hearing, except that the probability would be less, 
 though the coefficient .351 ± .059 is not a low correlation. 
 That for teeth with Q = .302 ± .04 shows the next highest 
 indication of a positive relation. Defective tonsils show a 
 negligible correlation with scores, .138 ± .044. This, at 
 the most, can only be taken as a slight indication of positive 
 association. Defective eyes and vision give almost a zero 
 correlation, .029 ± .044. In fact, it will be shown later 
 that with some subjects this coefficient becomes negative. 
 
 Relation of Defects to Special Abilities 
 
 The discussion immediately above was based upon the 
 average ability of the child as represented by the median of 
 his per cent scores. In order to see if certain defects are 
 a greater handicap than others in relation to special sub- 
 jects, or if a particular defect affects progress in one sub- 
 ject more than in another, the subjects will be dealt with 
 separately. In this process the frequencies are smaller and 
 the range is often as great as for the whole distribution. 
 For this reason a formula that utilizes the influence of this 
 wide range is substituted for the fourfold association for- 
 mula. It is based on a decile distribution. As a full and 
 complete discussion of this formula may be found on page 
 36, Chapter III, the discussion will be omitted here. 1 
 
 TABLE XIV 
 
 Correlation of Hearing with Trabue Completion Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 
 
 Total 
 
 S 
 D 
 
 3 4 4 9 9 32 19 47 106 40 36 19 13 3 4 2 
 . 11222 1 2 2 1 1 . 
 
 1 
 
 2 
 
 353 
 15 
 
 
 
 
 
 
 T 
 
 3 __ 4 4 10 10 34 21 49 107 42 33 20 14 3 4 2 
 
 1 
 
 2 
 
 368 
 
 S, nondefective ; D, defective; T, total distribution. 
 
 1 The coefficients of mean square contingency deduced from such tables will be 
 comparable among themselves, but possibly 30 to 50 per cent below the true value of 
 the correlation coefficient. Tables worked out by the fourfold table method show, on 
 am average, 40 per cent increase on the contingency values. It is only needful to 
 bear this in mind when considering the absolute importance of the contingencies in- 
 vestigated. — Biometrika, Vol. VII, page 223. 
 
to Achievement in the Elementary School 47 
 
 Mean of total distribution, 88.33; mean of defectives, 
 93.66. 
 
 Standard deviation of total distribution, 27.20. 
 
 £ (1 — a) = .0402, \ (1 + a) = .9598, Z = .0863 
 
 5.33 .0402 
 
 27.20 .0863 
 
 .092 
 
 Thus children are somewhat more likely to make high 
 scores on the Trabue Completion Test if they do not have 
 defective hearing. 
 
 TABLE XV 
 
 Correlation of Eyes and Vision with Trabue Completion Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 Total 
 
 S 
 D 
 
 3 —348 8 33 17 44 100 40 32 19 11 3 3 2 
 1 _.. 2 2 1 4 5 7 2 E 1 3 1 
 
 1 
 
 1 332 
 1 36 
 
 T 
 
 3 __ 4 4 10 10 34 21 49 107 42 38 20 14 3 4 2 
 
 1 
 
 2 368 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 93.665 ; mean of defectives, 
 95.833. 
 
 Standard deviation of total distribution, 27.20. 
 
 -J (1 + a) =.9020, HI — a) =.0980, Z = .1725 
 
 2.168 .0980 
 
 27.20 .1725 
 
 .045 
 
 This coefficient indicates that there is a negative asso- 
 ciation between sound eyes and ability, as measured by the 
 Trabue Tests. This probably means that the more studious 
 develop defective eyesight. 
 
 TABLE XVI 
 
 Correlation of Nasal Obstruction with Trabue Completion Test 
 
 
 Achievement Scores Expressed as Per Cent of 
 
 Median 
 
 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 
 
 150 
 
 160 
 
 170 
 
 180 Total 
 
 s 
 
 D 
 
 3 _ 4 4 X 10 32 19 44 98 41 36 19 13 3 
 2 __ 2 2 5 9 1 2 1 1 __ 
 
 3 
 1 
 
 2 
 
 1 
 
 2 342 
 
 2(i 
 
 T 
 
 3 _. 4 4 10 10 34 21 49 107 42 38 20 14 3 
 
 4 
 
 2 
 
 1 
 
 2 368 
 
 S, nondefective; D, defective; T, total distribution. 
 
 'In keeping with Pearson's practice, r is used to represent the coefficient of asso- 
 ciation when derived by the above formula. As indicated in note, page 46, these 
 r's must be increased about 40% to make them comparable with the Q's. 
 
48 A Study of the Relation of Some Physical Defects 
 
 Mean of total distribution, 93.665 ; mean of defectives, 
 92.308. 
 
 Standard deviation of total distribution, 27.20. 
 
 i (1 _ a ) = .0708, HI + a) =.9292, Z = .1354 
 1.357 .0708 
 
 27.2 .1354 
 
 .026 
 
 While this coefficient is small, it is large enough to indi- 
 cate that there is a positive association between nasal ob- 
 struction and ability as shown by the Trabue Tests. 
 
 TABLE XVII 
 
 Correlation of Teeth with Trabue Completion Test 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 Total 
 
 S 
 D 
 
 3 2 3 9 8 23 8 25 68 25 20 15 10 2 4 1 
 2 1 1 2 11 13 24 39 17 18 5 4 1- __ 1 
 
 1 
 
 2 318 
 50 
 
 T 
 
 3 _. 4 4 10 10 34 21 49 107 42 38 20 14 3 4 2 
 
 1 
 
 2 368 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 93.665 ; mean of defectives, 
 92.5. 
 
 Standard deviation of total distribution, 27.20. 
 
 i (1 — a) =.1866, $ (1 + a) = .8134, Z = .2684 
 
 1,165 ,1866 
 27.20 .2684 ' 
 
 Thus defective teeth and low scores are slightly, but 
 probably significantly, associated. 
 
 TABLE XVIII 
 
 Correlation of Sound Tonsils with Trabue Completion Test 
 
 Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 
 
 10 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 200 Total 
 
 s 
 
 D 
 
 2 
 1 
 
 . 2 
 __ 2 
 
 4 7 9 22 15 35 82 30 27 15 8 2 3 2 __ 2 
 3 1 12 6 14 25 12 11 5 6 1 1 1 
 
 261 
 101 
 
 T 
 
 3 
 
 . 4 
 
 4 10 10 34 21 49 107 42 38 20 14 3 4 2 1 2 
 
 362 
 
 S, nondefective; D, defective; T, total distribution. 
 
to Achievement in the Elementary School 49 
 
 Mean of total distribution, 93.665 ; mean of defectives, 
 93.81. 
 
 Standard deviation of total distribution, 27.20. 
 
 i (1 — a) =.2790, HI + a) =.7210, Z = .1988 
 
 .145 .2790 
 
 27.20 .1988 
 
 = .0062 
 
 There is a positive association between sound tonsils 
 and high scores on the Completion Tests, but it is so slight 
 as to make it negligible. 
 
 TABLE XIX 
 
 Correlation of Nasal Obstruction with Low Scores in Reading 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 1 
 
 3 4 12 15 21 31 20 29 41 43 29 15 S 15 6 1 1 
 -246135_1 1. 
 
 5 
 
 3 330 
 24 
 
 
 
 
 
 T 
 
 1 
 
 3 4 12 17 25 37 21 32 46 43 30 15 1 16 6 1 1 
 
 5 
 
 3 359 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 100.363 ; mean of defectives, 
 83.75. 
 
 Standard deviation of total distribution, 36. 
 
 i (i _ a) = .0727, 4 (1 + a) = .9273, Z = .1374 
 
 16.613 .0727 
 
 36 .1374 
 
 = .244 
 
 This coefficient of association between nasal obstructions 
 and low scores deserves special mention, as it is the most 
 significant of any found between defects and ability in spe- 
 cial subjects. A child's ability to read rapidly seems to be 
 closely associated with his soundness as to nasal breathing. 
 
 TABLE XX 
 
 Correlation of Tonsils with Reading Rate Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 3 
 2 
 
 3 
 
 4 9 13 11 28 18 22 34 29 31 11 5 12 5 1 1 
 __ 3 4 14 9 3 10 12 14 9 4 3 4 1 __ __ 
 
 4 
 
 1 
 
 3 237 
 93 
 
 T 
 
 5 
 
 :; 
 
 4 12 17 25 37 21 32 46 43 40 15 8 16 6 1 1 
 
 5 
 
 3 330 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 100.363 ; mean of defectives, 
 98.118. 
 
 Standard deviation of total distribution, 36.04. 
 
50 A Study of the Relation of Some Physical Defects 
 i (1 — a) =.2818, i (1 + a) =.7182, Z = .3362 
 
 2.245 .2818 
 
 36.04 .3362 
 
 .044 
 
 This coefficient indicates that there is at least some asso- 
 ciation between defective tonsils and reading rate. 
 
 TABLE XXI 
 Correlation of Defective Teeth with Reading Rate Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 3 
 2 
 
 1 
 2 
 
 1 7 9 9 20 11 20 23 32 14 11 5 9 3 1 1 
 3 5 8 16 17 10 12 23 11 16 4 3 7 3 __ __ 
 
 4 
 1 
 
 2 186 
 1 144 
 
 T 
 
 5 
 
 3 
 
 4 12 17 25 37 21 32 46 43 30 15 8 16 6 1 1 
 
 5 
 
 3 330 
 
 S, nondef ective ; D, defective; T, total distribution. 
 Mean of total distribution, 100.563 ; mean of defectives, 
 95.7638. 
 
 Standard deviation of total distribution, 36.04. 
 
 i (1 — a) =.4363, | (1 + a) =.5637, Z = .3935 
 
 _ 4.7992 .4363 _„ 
 
 " 36.04 .3935 ' 
 
 There is quite a sensible correlation between defective 
 teeth and low scores, much of which is probably due to in- 
 fluence of bad teeth on general health. 
 
 TABLE XXII 
 
 Correlation of Hearing with Reading Rate Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 5 
 
 
 
 3 
 
 
 4 12 15 23 25 19 31 42 41 28 15 8 16 6 1 1 
 0022221422000000 
 
 5 
 
 
 3 313 
 17 
 
 T 
 
 5 
 
 3 
 
 4 12 17 25 27 21 32 46 43 30 15 8 16 6 1 1 
 
 5 
 
 3 330 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 100.563; mean of defectives, 
 98.118. 
 
 Standard deviation of total distribution, 36.04. 
 
to Achievement in the Elementary School 51 
 
 I (1— a) == .05151, \ (1 + a) = .94849, Z = .10567 
 
 9.0920 .05151 12 „ 
 36.04 .10567 
 
 This coefficient is large enough to indicate quite a positive 
 association of hearing with rate of reading. 
 
 TABLE XXIII 
 Correlation of Eyes with Reading Rate Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 1G0 170 180 
 
 190 
 
 200 Total 
 
 S 
 L> 
 
 5 
 
 
 
 3 
 
 
 3 12 15 23 33 17 26 42 37 27 11 8 16 5 1 1 
 1022446463400100 
 
 4 
 
 1 
 
 2 291 
 1 39 
 
 T 
 
 5 
 
 3 
 
 4 12 17 25 37 21 32 46 43 30 15 8 16 6 1 1 
 
 5 
 
 3 330 
 
 S, nondefective ; D, defective; T, total distribution. 
 Mean of total distribution, 100.060 ; mean of defectives, 
 104.717. 
 
 Standard deviation of total distribution, 36.09. 
 
 J (1 — a) =.1121, i(l + a) =.8879, Z = .19070 
 
 _ 4.657 .1121 _ 75g 
 
 r " ~36^9~ 719070 — 0758 
 
 As might have been expected from what is known of the 
 relation of defective eyes to other subjects, as shown in the 
 above tables, good vision shows a negative association with 
 scores. 
 
 TABLE XXIV 
 Correlation of Hearing with Reading Comprehension Scores 
 
 Achievement Scores Expressed as Per Cent op Median 
 
 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 
 
 ISO 
 
 L90 
 
 200 Total 
 
 s 
 l) 
 
 2 
 
 
 8 
 
 
 a 
 i 
 
 8 15 17 25 40 23 28 35 14 22 13 8 14 10 5 
 110130033211001 
 
 3 
 
 
 5 
 
 
 5 306 
 18 
 
 T 
 
 •J 
 
 8 
 
 9 
 
 9 16 17 26 43 23 28 38 17 24 14 9 14 10 6 
 
 3 
 
 5 
 
 5 324 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 96.697; mean of defectives, 
 97.777. 
 
 Standard deviation of total distribution, 42.5. 
 
52 A Study of the Relation of Some Physical Defects 
 
 i (1 — a) = .0555, HI + a) =.9445, Z = .1127 
 1.080 .0555 ni1 
 
 r= ~m~ ^127 =- 011 
 
 The indications are that comprehension in reading is not 
 associated to any appreciable extent with defective hearing. 
 What association there is, is probably negative. 
 
 TABLE XXV 
 
 Correlation of Teeth with Reading Comprehension Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 s 
 
 D 
 
 2 
 
 
 
 6 
 2 
 
 3 
 6 
 
 4 8 4 15 24 12 14 21 7 15 10 6 6 5 4 2 
 
 5 6 13 11 14 11 14 17 10 9 4 3 8 5 2 1 
 
 4 
 1 
 
 5 177 
 147 
 
 T 
 
 -1 
 
 8 
 
 9 
 
 9 14 17 26 38 23 28 38 17 24 14 9 14 10 6 3 
 
 5 
 
 5 324 
 
 S, nondef ective ; D, defective; T, total distribution. 
 Mean of total distribution, 96.697; mean of defectives, 
 92.347. 
 
 Standard deviation of total distribution, 42.5. 
 
 £ (1 — a) =.4851, 1(1 + a) =.6149, Z = .10567 
 
 4.35 .4851 
 
 42. 5 . 3896 
 
 .124 
 
 The association of sound teeth with high reading com- 
 prehension scores is large enough to be significant. 
 
 TABLE XXVI 
 
 Correlation of Freedom from Nasal Obstructions with Reading 
 Comprehension Scores 
 
 Achievement Scores Expressed as Per Cent op Median 
 
 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 s 
 1) 
 
 •1 
 
 8 
 
 8 
 1 
 
 7 12 15 23 40 20 25 35 16 24 13 9 13 10 6 3 
 222333331 1 1 
 
 5 
 
 5 299 
 25 
 
 
 
 
 
 T 
 
 ■1 
 
 8 
 
 SI 
 
 9 14 17 26 43 23 28 38 17 24 14 9 14 10 6 3 
 
 5 
 
 5 324 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 96.697; mean of defectives, 
 93.4. 
 
 Standard deviation of the total distribution, 42.50. 
 
to Achievement in the Elementary School 53 
 
 I (1 — a) =.07716, HI + a) =.92284, Z = .14453 
 3.297 .07716 
 
 36.04 .14453 
 
 .042 
 
 This coefficient indicates that there is at least a slight 
 negative association between nasal breathing and compre- 
 hension scores in reading. 
 
 TABLE XXVII 
 
 Correlation of Sound Tonsils with Reading Comprehension 
 
 Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 !90 
 
 200 Total 
 
 s 
 I) 
 
 2 
 
 7 
 1 
 
 8 
 1 
 
 8 9 13 19 33 13 20 24 10 17 6 4 12 7 5 3 
 1 5 4 7 10 10 8 14 7 7 8 5 2 3 1 ._ 
 
 5 
 
 3 22S 
 2 96 
 
 T 
 
 ■1 
 
 8 
 
 9 
 
 9 14 17 26 43 2:5 28 38 17 24 14 9 14 10 6 3 
 
 5 
 
 5 324 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 96.697 ; mean of defectives, 
 100.833. 
 
 Standard deviation of the total distribution, 42.50. 
 
 I (1 — a) = .2960, HI + a) =.7040, Z = .3457 
 
 r = " 4 - 14 - 2960 - = _071 
 
 42.50 .3457 
 
 This coefficient shows a slight negative association be- 
 tween sound tonsils and reading comprehension scores. 
 
 TABLE XXVIII 
 Correlation of Eyes and Vision with Reading Comprehension 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 
 
 10 
 
 ■jo 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 
 n 
 
 ■1 
 
 8 
 
 1 
 
 9 14 14 24 35 21 23 31 15 21 12 9 13 10 6 3 
 3 28257232 1 
 
 5 
 
 4 287 
 1 37 
 
 
 
 
 
 T 
 
 ■1 
 
 8 
 
 9 
 
 9 14 17 26 43 23 28 38 17 24 14 9 14 10 6 3 
 
 5 
 
 5 324 
 
 S, nondefective; D, defective; T, total distribution. 
 Mean of total distribution, 96.097 ; mean of defectives, 
 95.54. 
 
 Standard deviation of total distribution, 42.91. 
 
54 A Study of the ReloMon of Some Physical Defects 
 i(l_ a) =.1142, £ (1 + a) =.8858, Z = .19302 
 
 r= __557_ ^142_ = .o076 
 42.91 .19302 
 
 The association between good eyes and vision and reading 
 comprehension, while positive, is negligible. 
 
 TABLE XXIX 
 
 Correlation of Hearing with Geography Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 
 
 S 2 _ 8 6 6 16 26 35 46 37 20 18 9 4 3 7 3 246 
 
 D 1—1 3 3 3 2 4 3 2 __________ — — — 22 
 
 T 3~T. 1 8 6 6 19 29 38 48 41 23 20 9 4 3 7 3 268 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 95.222; mean of defectives, 
 86.819. 
 
 Standard deviation of total distribution, 30.67. 
 
 i (1 — a) =.0820, -I (1 + a) =.9180, Z = .1508 
 
 8.403 .0820 14g 
 
 " 30.67 .1508 ' 
 
 It is evident from this correlation that progress in the 
 Humboldt schools in geography is rather highly associated 
 with acuteness of hearing. It will be observed from the 
 summary at the close of the chapter that defective hearing 
 is more highly associated with geography than with any 
 other subject in the curriculum. 
 
 TABLE XXX 
 
 * Correlation of Eyes and Vision with Geography Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 
 
 S 2 __. 1 7 6 4 17 26 33 42 37 19 19 8 4 3 6 • - 3 238 
 
 D 1 1 __. 2 2 3 5 6 4 4 __ 1 __ __ 1 ______ __ 30 
 
 T 3 __. 1 8 6 6 19 29 38 48 41 23 19 9 4 3 7 . 3 268 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 95.52 ; mean of defectives, 
 89.33. 
 
 Standard deviation of total distribution, 30.67. 
 
to Achievement in the Elementary School 55 
 
 HI — a) =.1119, |(1 + a) =.8881, Z = .1977 
 6.2167 .1119 
 
 30.67 .1977 
 
 .114 
 
 Contrary to what has been observed between soundness of 
 vision and other subjects, this coefficient indicates a rather 
 high association between vision and geography scores. 
 
 TABLE XXXI 
 Correlation of Nasal Obstruction and Low Scores in Geography 
 
 Achievement Scores Expressed as Per Cent of Median 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 
 
 S 3 _.. 1 7 6 6 15 24 35 42 39 18 20 9 4 3 7 3 242 
 
 D 1 4 5 3 6 2 5 __ __ __ __ __ __ __ __ __ 26 
 
 T 3 _.. 1 8 6 6 19 29 38 48 41 23 20 9 4 3 7 . 3 268 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 95.222 ; mean of defectives, 
 87.693. 
 
 Standard deviation of total distribution, 30.67. 
 
 |(1 — a) =.097, 1(1 a) =.903, Z = .17136 
 
 7.529 .097 
 
 r " 30.67 .17136 
 
 This coefficient indicates a rather high degree of associ- 
 ation between nasal obstructions and low scores in geogra- 
 phy. 
 
 TABLE XXXII 
 Correlation of Teeth with Geography Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 
 
 10 20 
 
 30 40 50 60 70 «0 90 100 110 120 130 140 150 160 170 180 190 
 
 2"" Total 
 
 S 
 
 3 
 
 1 
 
 3 3 3 9 13 17 25 15 15 14 3 3 3 5 . 
 
 5 3 3 10 16 21 23 26 8 6 6 1 2 
 
 2 137 
 1 131 
 
 
 
 
 
 T 
 
 3 
 
 1 
 
 8 6 6 19 29 38 48 41 23 20 9 4 3 7 
 
 3 268 
 
 S, nondefective; D, defective; T, total distribution. 
 Mean of total distribution, 95.522 ; mean of defectives, 
 94.7. 
 
 Standard deviation of total distribution, 30.67. 
 
56 A Study of the Relation of Some Physical Defects 
 i (1 — a) = .4888, i (1 + a) =.5112, Z = .3987 
 
 _ L 822_ ^4888 . _ 
 ' 30.67 .3987 
 
 It can only be said that there is a positive association be- 
 tween sound teeth and high scores in geography, slight 
 stress being put on the degree of association owing to the 
 smallness of the coefficient. 
 
 TABLE XXXIII 
 Correlation of Tonsils with Geography Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 
 
 S . 1 ... 1 4 5 5 13 20 33 34 27 16 16 7 3 1 5 . 3 193 
 
 D 2 4 1 1 6 9 5 14 14 7 4 2 1 2 2 __ __ __ 1 75 
 
 T 3 _.. 1 8 6 6 19 29 38 48 41 23 20 9 4 3 7 . 4 268 
 
 S, nondef ective ; D, defective; T, total distribution. 
 Mean of total distribution, 95.52 ; mean of defectives, 
 97.666. 
 
 Standard deviation of total distribution, 30.67. 
 
 \ (1 — a) = .2798, 4. (1 + a) =.7202, Z = .3312 
 
 r _ -2.116 .2798 _ 05g 
 r - 30.67 73312 — - 068 
 
 There appears to be a negative association between the 
 sound tonsils and geography scores. This fact is not clearly 
 understood, as the association of other subjects has been 
 positive. 
 
 TABLE XXXIV 
 
 Correlation of Nasal Obstructions with Written Composition 
 
 Achievement Scores Expressed as Per Cent of Median 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 Total 
 
 S 1 _ .. 1 2 2 3 12 5 41 57 16 26 9 3 5 1 3 3 _ 190 
 D 6 6 2 2 __ __ __ __ __ __ __ 16 
 
 T 1 _.. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 3 . 206 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.23 ; mean of defectives, 95. 
 Standard deviation of total distribution, 24.37. 
 
to Achievement in the Elementary School 57 
 
 I (1 — a) = .0776, £U + a) = .9224, Z = .14453 
 2. 23 . 0776 
 
 24.37 .14453 
 
 .049 
 
 The association of nasal obstructions with written com- 
 position scores, while positive, is less than that shown with 
 other subjects. This may be due to the fact that only the 
 students above the fourth grade took this test. Ayres says 
 that defective tonsils decrease with age. 
 
 TABLE XXXV 
 Correlation of Eyes and Vision with Written Composition 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 Total 
 
 S 
 D 
 
 1 _.. 1 2 2 3 11 4 42 58 17 25 7 2 5 . 3 
 115 5 1321 1 
 
 3 
 
 __ 186 
 20 
 
 
 
 
 T 
 
 1 _. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 
 
 3 
 
 206 
 
 S, nondef ective ; D, defective; T, total distribution. 
 Mean of total distribution, 97.23 ; mean of defectives, 
 106.5. 
 
 Standard deviation of total distribution, 24.37. 
 
 4 (1_ a) =.0979, Ml + a) =.9021, Z = .17248 
 
 _. -8.27 .0979 _ 102 
 
 24.37 .17248 ' 
 
 There is obviously a very high degree of negative associ- 
 ation between sound vision and written composition. 
 
 TABLE XXXVI 
 Correlation of Teeth with Written Composition 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 Total 
 
 S 
 D 
 
 1 1 _.. 1 .. 8 3 27 38 8 18 3 . 3 13 
 
 2 1 3 4 2 20 25 10 10 6 3 2 __ __ 
 
 1 
 2 
 
 118 
 
 88 
 
 T 
 
 1 ... 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 
 
 3 
 
 206 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.23 ; mean of defectives, 
 96.93. 
 
 Standard deviation of total distribution, 24.37. 
 
58 A Study of the Relation of Some Physical Defects 
 i (1 — a) =.1271, $ (1 + a) =.5729, Z = .392 
 
 . 30 . 4271 
 
 24. 37 . 392 
 
 = .012 
 
 Consistent with what has been found with other subjects, 
 the association of teeth and composition is positive, but 
 slight. 
 
 TABLE XXXVII 
 
 Correlation of Hearing with Written Composition 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 Total 
 
 S 
 D 
 
 1 _.. 1 2 1 3.12" 4 44' 60 15 25 8 2 5 1 3 
 
 1 13-33311 
 
 3 
 
 190 
 16 
 
 
 
 
 
 T 
 
 1 _.. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 
 
 3 
 
 206 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.23 ; mean of defectives, 
 98.75. 
 
 Standard deviation of total distribution, 24.37. 
 
 i (1 — a) = .0776, J (1 + a) =.9224, Z = .14453 
 
 -1.52 .0776 
 
 24.37 .14453 
 
 -.033 
 
 This is relatively a small coefficient, but is positive, and 
 indicates some degree of association between hearing and 
 composition. 
 
 TABLE XXXVIII 
 
 Correlation op Tonsils with Written Composition 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 
 
 170 
 
 180 Total 
 
 S 
 D 
 
 1 _. 1 1 2 3 10 4 31 47 16 23 5 1 5 1 2 
 1 2 1 16 16 2 5 4 2 . 1 
 
 1 
 2 
 
 154 
 52 
 
 T 
 
 1 _.. 1 2 2 3 12 5 47 63 18 28 9 3 5 1 3 
 
 3 
 
 206 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.23 ; mean of defectives, 
 98.26. 
 
 Standard deviation of total distribution, 24.37. 
 
to Achievement in the Elementary School 59 
 
 I (1 — a) = .4, h (1 + a) = .6, Z = .279 
 
 1_ 24T37 .279 " -° 68 
 
 Except in the case of arithmetic and reading comprehen- 
 sion, this is the largest coefficient of association shown with 
 tonsils. 
 
 TABLE XXXIX 
 Correlation of Eyes and Vision with Arithmetic Scores 
 
 
 
 
 
 Achievement Scores 
 
 Expressed as Per Cent 
 
 of Median 
 
 
 
 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 
 
 100 110 120 130 140 
 
 150 
 
 160 170 
 
 180 
 
 190 
 
 200 Total 
 
 s 
 D 
 
 1 
 
 2 
 1 
 
 9 
 
 16 11 16 23 28 31 29 
 
 113 8 4 2 7 
 
 24 26 24 12 11 
 3 2 13 1 
 
 1 
 
 4 7 
 2 
 
 4 
 1 
 
 4 
 1 
 
 7 297 
 1 43 
 
 T 
 
 1 
 
 3 
 
 9 
 
 17 12 19 31 32 33 3G 
 
 27 28 25 15 12 
 
 8 
 
 6 7 
 
 5 
 
 5 
 
 8 340 
 
 S, nonclef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.44 ; mean of defectives, 
 97.79. 
 
 Standard deviation of total distribution, 42.54. 
 
 j (1 — a) =.1264, HI + a) =.8736, Z = .2071 
 
 _=_35 .1264 
 
 r - 42.54 72071 -— 005 
 
 The association of sound vision with ability in arithmetic 
 is both negative and negligible. 
 
 TABLE XL 
 Correlation of Tonsils with Arithmetic Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 il 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 1 
 
 2 
 1 
 
 5 
 3 
 
 1 7 15 27 24 18 26 16 18 19 10 9 5 4 7 3 
 9 5 4 4 8 15 10 11 10 6 5 3 3 2 2 
 
 3 
 2 
 
 2 231 
 6 109 
 
 T 
 
 1 
 
 3 
 
 B 
 
 17 12 19 31 32 33 36 27 28 25 15 12 8 6 7 
 
 5 
 
 8 340 
 
 S, nondef ective ; D, defective; T, total distribution. 
 Mean of total distribution, 97.441 ; mean of defectives, 
 90.138. 
 
 Standard deviation of total distribution, 42.54. 
 
60 A Study of the Relation of Some Physical Defects 
 i (1 — a) = .3206, i (1 + a) =.6794, Z = .358 
 
 7.203 .3206 _ 1Fn 
 
 r- ~ 42.45 .358 " ' 
 
 This coefficient shows a rather high degree of positive 
 association between sound tonsils and arithmetic scores — 
 much higher than the corresponding coefficients with other 
 subjects. 
 
 TABLE XLI 
 
 Correlation of Nasal Obstructions with Low Scores in 
 Arithmetic 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 2 
 1 
 
 9 
 
 16 12 15 30 27 28 34 24 27 25 15 12 8 6 7 5 
 1 4 15 5 2 3 1 
 
 5 
 
 8 317 
 23 
 
 
 
 
 
 T 
 
 __ 3 
 
 9 
 
 17 13 19 31 32 33 36 27 28 25 15 12 8 6 7 5 
 
 5 
 
 8 340 
 
 S, nondefective ; D, defective; T, total distribution. 
 Mean of total distribution, 97.41 ; mean of defectives, 
 77.2. 
 
 Standard deviation of total distribution, 42.54. 
 
 £ (1 — a) = .0676, i( + a)=.9324, Z = .130492 
 
 ,2021 .0676 _ 
 
 " 42.54 .130492 
 
 There is a very significant association between nasal ob- 
 struction and low grades. If a pupil has such defects, he is 
 probably poor in arithmetic. 
 
 TABLE XLII 
 
 Correlation of Teeth with Arithmetic Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 1 2 
 __ 1 
 
 6 
 
 4 
 
 12 8 9 13 20 18 21 15 11 16 8 6 3 5 5 3 
 5 4 10 18 12 15 15 12 17 9 7 6 5 1 2 3 
 
 2 
 3 
 
 5 209 
 3 131 
 
 T 
 
 1 3 
 
 10 
 
 17 12 19 31 32 33 36 27 28 25 15 12 8 6 7 6 
 
 5 
 
 8 340 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.441 ; mean of defectives, 
 98.046. 
 
 Standard deviation of total distribution, 42.54. 
 
to Achievement in the Elementary School 61 
 
 HI — a) = .4441, HI + a) =.5559, Z ,= .395 
 
 .605 .4441 Ma 
 
 Y= -&M T395" -° 16 
 
 This is the only negative association of teeth with sub- 
 jects found thus far. It is too small to be of much signifi- 
 cance. 
 
 TABLE XLIII 
 Correlation of Hearing with Arithmetic Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 
 I) 
 
 1 3 9 16 12 18 28 30 28 36 26 27 24 13 12 S 5 7 5 
 1 1325 1112 _1 
 
 5 
 
 8 322 
 18 
 
 
 
 
 
 T 
 
 1 3 9 17 12 19 31 32 33 36 27 28 25 15 12 8 6 7 5 
 
 5 
 
 8 340 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.441 ; mean of defectives, 
 91.111. 
 
 Standard deviation of total distribution, 42.54. 
 
 i (1 — a) = .05294, |( + a) = .04706, Z = .1118 
 
 6.330 .05294 
 
 42.54 .1118 
 
 = .0704 
 
 Thus there is a positive association between acuteness of 
 hearing and arithmetic scores. A child that hears well is 
 more likely to make high scores than one that does not. 
 
 TABLE XLIV 
 Correlation of Tonsils with Writing 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 200 Total 
 
 S 
 D 
 
 1 6 6 26 47 45 63 56 30 27 7 9 2 7 4 
 1 2 9 14 20 24 15 11 6 1 2 4 2 __ 1 
 
 4 310 
 2 114 
 
 T 
 
 1 7 8 35 61 65 87 71 41 33 8 11 6 9 . 
 
 6 421 
 
 S, nondef ective ; D, defective; T, total distribution. 
 Mean of total distribution, 98.561; mean of defectives, 
 99.396. 
 
 Standard deviation of total distribution, 29.08. 
 
62 A Study of the Relation of Some Physical Defects 
 H — a) =.2681, | (1 + a) = .7319, Z = .3302 
 
 .175 .2681 _ <0()4 
 
 29.08 .3302 
 
 It will be seen from this table and those that follow that 
 the association of writing with defects is slight ; for tonsils 
 it is negative. 
 
 TABLE XLV 
 
 Correlation op Eyes and Vision with Writing 
 
 
 Achievement Scores 
 
 Expressed as Per Cent 
 
 of Median 
 
 
 
 30 40 50 GO 70 80 90 
 
 100 110 120 
 
 130 140 
 
 150 
 
 160 170 
 
 180 
 
 190 200 Total 
 
 s 
 
 D 
 
 1 7 7 30 57 59 79 
 : 15 4 6 8 
 
 66 36 30 
 5 5 3 
 
 8 11 
 
 6 
 
 2 11 
 
 4 
 1 
 
 6 384 
 40 
 
 
 
 
 
 T 
 
 1 7 8 35 61 65 87 
 
 71 41 33 
 
 8 11 
 
 6 
 
 9 __ 
 
 5 
 
 6 424 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 98.561 ; mean of defectives, 
 98.5. 
 
 Standard deviation of total distribution, 29.08. 
 
 i (1 — a) = .0943, £ (1 + a) =.9057, Z = .1692 
 
 r= ^061 ^943 = . 001 
 
 29.08 .1692 
 
 The association of sound vision with writing is positive, 
 but so small that it is negligible. 
 
 TABLE XLVI 
 
 Correlation of Nasal Obstruction with Low Writing Ability 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Total 
 
 S 
 D 
 
 1 7 8 32 58 62 78 64 39 32 7 11 6 9 __ 5 •_ 6 395 
 33397211 . 29 
 
 
 
 T 
 
 1 7 8 35 61 65 87 71 41 33 8 11 6 9 . 5 _ 6 424 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 98.561 ; mean of defectives, 95. 
 Standard deviation of total distribution, 29.08. 
 
to Achievement in the Elementary School 63 
 
 \ (1 — a) =.0683, 4(+a)=.9307, Z = .1315 
 
 _ _ 3.561 .0683 _ nrQ 
 
 29.08 .1315 -• 0W 
 
 This coefficient of association, though small, is sufficiently 
 large to indicate that a child with defective nasal breathing 
 is likely to make lower scores than one that has no nasal 
 defects. 
 
 TABLE XLVII 
 Correlation of Hearing with Writing Ability 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 200 Total 
 
 S 
 D 
 
 1 7 8 34 60 63 83 64 39 30 7 11 6 9 5 
 11247231 
 
 5 402 
 22 
 
 
 
 
 T 
 
 1 7 8 35 61 65 87 71 41 33 1 11 6 9 5 
 
 6 424 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 98.561; mean of defectives, 
 102.72. 
 
 Standard deviation of total distribution, 29.08. 
 
 i (1 — a) = .0518, 4(1 + a) =.9482, Z = .1057 
 
 4.159 .0518 
 
 29.08 .1057 
 
 —.07 
 
 This coefficient indicates a negative association between 
 hearing and writing. 
 
 TABLE XLVIII 
 Correlation of Sound Teeth with Writing Ability 
 
 Achievement Scores Expressed as Per Cent op Median 
 
 
 30 40 50 60 70 SO 90 100 110 120 130 140 150 160 170 180 
 
 190 200 Total 
 
 S 
 D 
 
 1 6 5 19 42 40 49 47 23 22 6 9 4 8 . 4 
 __ 1 3 16 19 25 38 24 18 11 2 2 2 1 __ 1 
 
 5 260 
 1 164 
 
 T 
 
 1 7 8 35 61 65 87 71 41 33 8 11 6 9 . 5 
 
 6 424 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 98.561; mean of defectives, 
 96.463. 
 
 Standard deviation of total distribution, 29.08. 
 
64 A Study of the Relation of Some Physical Defects 
 i (1 — a) =.3868, ± (1 + a) =.6132, Z = .3826 
 
 2^098 .3868 ._ 074 
 
 ~ 29.08 .3836 " 
 
 This coefficient indicates a positive association between 
 sound teeth and writing ability, and probably means that a 
 child with sound teeth is slightly more likely to write well 
 than one with defective teeth. 
 
 TABLE XLIX 
 Correlation of Teeth with Spelling Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 5 
 
 4 
 
 6 
 2 
 
 9 10 13 16 20 22 41 25 36 22 11 8 6 1 5 _ 
 _ 4 10 7 9 24 31 13 21 11 5 5 1 
 
 1 
 
 5 261 
 __ 148 
 
 T 
 
 9 
 
 8 
 
 9 14 23 23 29 46 72 38 57 33 16 13 6 15 1 
 
 1 
 
 5 409 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.885 ; mean of defectives, 
 93.717. 
 
 Standard deviation of total distribution, 33.41. 
 
 x (1 — a) =.3518, £ (1 + a) =.6482, Z = .3711 
 
 4,168 .3518 __ 
 
 " 33.41 .3711 " ' 
 
 This coefficient shows that there is a slight positive asso- 
 ciation between sound teeth and spelling scores, but is too 
 small to be very significant. 
 
 TABLE L 
 
 Correlation of Nasal Obstructions with Low Spelling Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 9 
 
 8 
 
 8 11 22 19 27 44 64 38 54 31 16 13 6 1 5 1 
 1314228 3 2 
 
 1 
 
 5 283 
 26 
 
 
 
 
 
 T 
 
 9 
 
 8 
 
 9 14 23 23 29 46 72 38 57 33 16 13 6 1 5 1 
 
 1 
 
 5 309 
 
 S, nondef ective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.885 ; mean of defectives, 
 83.10. 
 
 Standard deviation of total distribution, 33.41. 
 
to Achievement in the Elementary School 65 
 
 £ (1 — a) =.0635, | (1 + a) =.9365, Z = .1237 
 
 _ 14.785 .0635 __ 22? 
 33.41 .1237 " 
 
 This coefficient indicates rather a high degree of associ- 
 ation between nasal obstruction and low scores. 
 
 TABLE LI 
 
 Correlation of Eyes and Vision with Spelling Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 9 
 
 8 
 
 9 10 21 20 25 42 63 32 49 29 15 12 6 1 3 1 
 _423449 6 8 4 1 1____ 2 „ 
 
 1 
 
 4 360 
 1 49 
 
 T 
 
 9 
 
 8 
 
 9 14 23 23 29 46 72 38 57 33 16 13 6 1 5 1 
 
 1 
 
 5 409 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.885 ; mean of defectives, 
 99.625. 
 
 Standard deviation of total distribution, 33.41. 
 
 I (1 — a) =.1198, H 1 + a)=.8802, Z = .1988 
 
 1.74 .1198 
 
 33.41 .1988 
 
 = —.031 
 
 This coefficient shows a negative association between 
 vision and high spelling scores. It is probably large enough 
 to be significant. 
 
 TABLE LII 
 Correlation of Tonsils with Spelling Scores 
 
 
 
 
 Achievement Scores 
 
 Expressed as Per Cent of Median 
 
 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 
 
 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 s 
 
 D 
 
 7 
 2 
 
 6 
 2 
 
 7 8 20 19 18 38 55 
 2 6 3 4 11 8 17 
 
 29 44 28 14 8 3 1 3 __ 
 9 13 5253 __21 
 
 1 
 
 5 314 
 95 
 
 T 
 
 9 
 
 s 
 
 9 14 23 23 29 46 72 
 
 38 57 33 16 13 6 1 5 1 
 
 1 
 
 5 409 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.885; mean of defectives, 
 94.158. 
 
 Standard deviation of total distribution, 33.41. 
 
66 A Study of the Relation of Some Physical Defects 
 i(l _a) =.2322, i(l + a) =,7678, Z = .3056 
 3.727 .2322 
 
 r = 
 
 33.41 
 
 .3056 
 
 .0837 
 
 There is a relatively significant association between sound 
 tonsils and high spelling scores. 
 
 TABLE LIII 
 Correlation of Hearing with Spelling Scores 
 
 Achievement Scores Expressed as Per Cent of Median 
 
 
 10 
 
 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 
 
 200 Total 
 
 S 
 D 
 
 9 
 
 8 
 
 8 13 22 21 28 45 67 36 54 32 15 13 6 1 4 1 
 11121152 31 1_„ 1 
 
 1 
 
 5 389 
 20 
 
 T 
 
 9 
 
 8 
 
 9 14 23 23 29 46 72 38 57 33 16 13 6 1 5 1 
 
 1 
 
 5 409 
 
 S, nondefective ; D, defective ; T, total distribution. 
 Mean of total distribution, 97.885 ; mean of defectives, 
 94.5. 
 
 Standard deviation of total distribution, 33.41. 
 
 i (l_a) = .0489, £.(1 + a) =.9511, Z 
 
 3.385 .0489 
 
 .1005 
 
 r = 
 
 33.41 
 
 .1005 
 
 .055 
 
 This coefficient shows a positive association between 
 acuteness of hearing and high spelling scores. 
 
 TABLE LIV 
 
 Summary of Coefficients of Association Between Each Physical 
 Defect and the Various Subjects 
 
 -Defects- 
 
 Subjects 
 
 Tonsils 
 
 Eyes, 
 Vision 
 
 Nasal 
 Defects 
 
 Teeth Hearing 
 
 Trabue Completion ___ 
 
 Reading Rate 
 
 Reading Compr'ension. 
 
 Spelling 
 
 Geography 
 
 Writing 
 
 Arithmetic 
 
 Composition 
 
 .0962 
 .044 
 -.071 
 .08 
 -.058 
 -.004 
 .151 
 .068 
 
 .045 
 
 .0758 
 
 .0076 
 
 .031 
 
 .114 
 
 .001 
 
 .005 
 
 .192 
 
 .026 
 .244 
 .043 
 .227 
 .139 
 .063 
 .246 
 .049 
 
 .029 
 .157 
 .124 
 .011 
 .032 
 .074 
 .016 
 .0122 
 
 .090 
 .123 
 
 —.011 
 .055 
 .148 
 
 —.070 
 .070 
 
 —.033 
 
 Summary of Indicated Associations of Defects with Spe- 
 cial Subjects. — From Table LIV it can be clearly seen that, 
 on the whole, a positive association exists between defects 
 
to Achievement in the Elementary School 67 
 
 and special abilities. The one noticeable exception is the 
 negative association of sound vision with five of the eight 
 subjects mentioned. The subjects least affected by phys- 
 ical defects are Trabue completion and writing. Writing 
 is more or less mechanical, and it was observed that there 
 was considerable uniformity in the answers to the sim- 
 plest tests in composition, while comparatively few tried the 
 more difficult ones except in the higher grades. It seems 
 from the table that the five major defects, in order of their 
 positive association with low scores, or, stated in the oppo- 
 site way, in order of their negative association with high 
 scores, are nasal defects, hearing, teeth, tonsils, and vision. 
 
CHAPTER V 
 
 other factors 
 
 Final Analysis Using the Formula for Partial 
 Correlation 
 
 The preceding chapters have been concerned with the ap- 
 parent association of physical defects with achievement 
 scores, without raising the question of partial associations. 
 It is the purpose of the present chapter to consider the influ- 
 ence of such factors, as intelligence, attendance, and re- 
 tardation on the association of defects with school prog- 
 ress, as indicated by achievement scores. The coefficients 
 tabulated in Chapter IV are to be freed from the influences 
 of these factors by the use of Karl Pearson's formula. The 
 application of this formula to partial correlations is fully 
 explained in Chapter III, page 38. The Illinois tests were 
 used to measure intelligence. These were given to all chil- 
 dren above the third grade. In the first and second grades 
 the Holly completion tests were used. All intelligence scores 
 were reduced to per cents of class medians, as explained 
 in Chapter III. One hundred per cent was arbitrarily 
 taken as the dividing line between those making high scores 
 and those making low scores. Almost any other percentage 
 score might have been the dividing point used in the four- 
 fold classification. As may be seen from Table LV, the 
 distribution of both the defectives and nondefectives is suf- 
 ficiently normal to prevent a marked change of results 
 should the dividing line be shifted. 
 
 table lv 
 Correlation op General Defects with Intelligence Scores 
 
 Intelligence Scores Reduced to Per Cent op Medians 
 
 
 
 
 10 20 
 
 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
 
 190 200 Total 
 
 s 
 
 D 
 
 2 
 1 
 
 1 1 
 
 2 __ 
 
 3 2 12 14 13 32 36 31 21 11 6 1 3 1 1 2 
 2 1 6 22 25 40 65 31 28 14 3 4 2 1 1 
 
 4 197 
 248 
 
 
 
 T 
 
 3 
 
 3 1 
 
 5 3 18 36 38 72 101 62 49 25 9 5 5 2 2 2 
 
 4 445 
 
 S, nondefective ; D, Defective ; T, total distribution. 
 
 r = .054 
 
 For use in partial correlations Q is more nearly com- 
 parable than r, with the data shown in Table XIII. It may 
 
to Achievement in the Elementary School 
 
 69 
 
 foe found from the fourfold classification shown in Table 
 LVI. If 100% be taken as the dividing line between high 
 and low scores, Q is found to equal .139. 1 
 
 TABLE LVI 
 Correlation of General Defects with Intelligence Scores 
 
 
 Scores Abort 100 1 < 
 
 Scores Below 100% 
 
 Totals 
 
 Without Defects 
 
 AB, 81 
 
 Ab, 116 
 
 197 
 
 With Defects 
 
 aB, 84 
 
 ab, 162 
 
 246 
 
 Total 
 
 165 
 
 178 
 
 443 
 
 Q = .139 
 
 TABLE LVII 
 Correlation of Special Defects with Intelligence Scores 
 
 Defects Ab 
 
 Hearing 189 
 
 Nasal Obstruction 193 
 
 Vision 193 
 
 Teeth 130 
 
 Tonsils 156 
 
 General Defects 116 
 
 AB 
 
 aB 
 
 llli 
 
 192 
 
 8 
 
 17 
 
 .36 
 
 192 
 
 13 
 
 16 
 
 .10 
 
 175 
 
 24 
 
 16 
 
 —.246 
 
 131 
 
 66 
 
 78 
 
 .08 
 
 153 
 
 47 
 
 52 
 
 .04 
 
 81 
 
 84 
 
 162 
 
 1.39 
 
 For the sake of brevity, Table LVII is made to include 
 the association coefficients between intelligence and each of 
 the five major defects. 
 
 Partial correlations also require coefficients of correla- 
 tions between intelligence scores and achievement scores. 
 When worked out by the Pearson formula, the correlation 
 between intelligence and achievement was found to be .24 ± 
 .03. Again, for the sake of comparison, Q is used instead 
 of r, and is found to be .32. Table LVIII shows the origi- 
 nal Q's in column 1, while the same coefficients, after being 
 freed from the influence of intelligence as a factor, are 
 shown in column 2. The method of deriving these partial 
 coefficients has already been fully explained in Chapter III, 
 page 38. 
 
 'To test the effect of taking some other line of division between high and low 
 scores, in the fourfold classification, 95% was taken instead, with a result that Q 
 varied only in the third decimal place, being .134. 
 
70 A Study of the Relation of Some Physical Defects 
 
 TABLE LVIII 
 
 Showing Original and Partial Correlations Obtained by Freeing 
 the Former from the Influence of Intelligence as a Factor 
 
 • Q Freed from 
 Defects Correlated with General Achievement Original Q Intelligence 
 
 Tonsils .138 .122 
 
 Vision .029 .0102 
 
 Nasal Obstructions .799 .811 
 
 Teeth .302 .294 
 
 Hearing .351 .266 
 
 General Defects .210 .175 
 
 It will be noticed that the changes brought about by par- 
 tial correlations are relatively slight. Only one — that of 
 association of nasal obstructions with achievement scores — 
 is increased. The latter coefficient is extremely large, indi- 
 cating a high probability that even an intelligent child ad- 
 dicted to mouth breathing will be backward in school work. 
 The association between vision and achievement is still 
 shown to be small ; in fact, it is negligible. 
 
 The second factor to be considered before arriving at a 
 final conclusion concerning the influence of physical defects 
 on achievement scores is that of retardation. The measure 
 of retardation used in this study is the educational quotient. 
 This coefficient is obtained by dividing the normal age of 
 the grade in which the child is found by the chronological 
 age of the child. These are expressed as percentages and 
 distributed according to the scheme for fourfold classifica- 
 tion. For this grouping, educational quotients of 100 or 
 above were considered high, and below 100 low. The four 
 classes, then, were: high educational quotients without de- 
 fects, high educational quotients with defects, low educa- 
 tional quotients without defects, and low educational quo- 
 tients with defects. From these fourfold classifications the 
 quotients shown in Table LX, column 1, were derived. 
 Before these coefficients can be used with those of column 
 2, Table LVIII, they must be freed from the influence of 
 intelligence. This is done by the use of the same formula 
 referred to in the last section, with results shown in column 
 2 of Table LX. It will be observed from these coeffi- 
 cients that there is a positive association between physical 
 defects and retardation in every case, except that of eyes, 
 or vision. Here the association is negative and sufficiently 
 large to be significant. This probably means that retarded 
 children have stronger vision than normal or accelerated 
 children, while other defectives are more often retarded 
 than are the normal children. Thus it becomes necessary 
 
to Achievement in the Elementary School 
 
 71 
 
 to consider these facts in connection with the problem of 
 defects and achievement scores. 
 
 TABLE LIX 
 Educational Quotient Correlated with General Ability 
 
 
 Scores Above 100% 
 
 Scores Below 100% 
 
 Totals 
 
 Educational Quotient 
 above 100% 
 
 AB, 90 
 
 Ab, 41 
 
 131 
 
 Educational Quotient 
 below 100% 
 
 aB, 135 
 
 ab, 80 
 
 215 
 
 Total 
 
 225 
 
 121 
 
 346 
 
 Q = .131 
 
 Q with intelligence eliminated, 
 
 Q = .095 
 
 TABLE LX 
 Correlation of Educational Quotients with Physical Soundness 
 
 Q Freed from 
 Original Q Intelligence 
 
 Tonsils .142 .138 
 
 Vision —.181 —.154 
 
 Nasal Obstruction .169 .158 
 
 Teeth .509 .535 
 
 Hearing .099 .055 
 
 General Defects .379 .126 
 
 TABLE LXI 
 
 Original and Derived Correlation Coefficients with Physical 
 Defects and Achievement 
 
 Original Q 
 
 Tonsils .138 
 
 Vision .029 
 
 Nasal Obstructions .799 
 
 Teeth .302 
 
 Hearing .351 
 
 General Defects .210 
 
 Q with Influence Q with Influence 
 of Intelligence of Retardation 
 
 Eliminated 
 
 Eliminated 
 
 .222 
 
 .110 
 
 .010 
 
 .024 
 
 .811 
 
 .814 
 
 .294 
 
 .289 
 
 .266 
 
 .262 
 
 .175 
 
 .126 
 
72 A Study of the Relation of Some Physical Defects 
 
 Table LXI, column 3, is a summary of results obtained 
 after this factor had been eliminated. On the whole, the 
 changes made in the coefficients are not very great, the 
 most noticeable one being that of the association of general 
 defects with achievement scores, which drops from .175 to 
 .126. The association coefficients are now all positive and 
 sufficiently large to be significant. The least significant of 
 all is the association of vision with defects. The most sig- 
 nificant is the association of nasal obstructions with 
 achievement. It may be observed that the latter has in- 
 creased with every elimination and finally reaches a maxi- 
 mum of .814. This indicates the extreme necessity of med- 
 ical treatment for this class of students if results are to be 
 expected from their school work. Teeth and hearing are 
 of about equal importance as handicaps to progress, the 
 former having slight ascendency over the latter. Both co- 
 efficients are large enough to indicate a serious problem 
 for the physical supervisor. 
 
 The third factor that should be mentioned in connection 
 with the association of defects with scores is that of attend- 
 ance. It is usually conceded that there is a high degree of 
 association between attendance and promotion, which leads 
 to retardation. Ayres makes the statement that an attend- 
 ance of less than three-fourths full time usually means a 
 failure of promotion. 1 Strayer and Thorndyke 2 say that, 
 on the whole, the effect of absence is small until very large 
 amounts of absence are reached. Reavis 3 considers it a 
 subject of prime importance to the school administrator. 
 
 The correlation of days attended by the Humboldt chil- 
 dren with standard test scores has been worked out from 
 the distributions shown in Table LXII below. It may be 
 seen from this distribution that the average number of days 
 attended per child is high. In fact, the median is 163.9 
 out of a total of 176. This high attendance is explained by 
 the fact that the data for this study were collected during 
 the last two weeks of the school term. The children that 
 were there at that time were those that had been regular in 
 attendance. 
 
 1 Ayres, L. P., Laggards in Our Schools, page 136. 
 
 2 Strayer and Thorndyke, Educational Administration, Macmillan Company, 1914, 
 page 42. 
 
 3 Reavis, G. H., Factors Controlling Attendance in Rural Schools. 
 
to Achievement in the Elementary School 
 
 73 
 
 TABLE LXII 
 Attendance Correlated with Scores 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 1 80 1 90 
 
 100 
 
 110 
 
 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 T 
 
 0- 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 2 
 
 3 
 
 10— . - 
 
 20 
 
 30 _ 
 
 1 
 1 
 
 1 
 
 1 
 1 
 
 
 
 1 
 1 
 
 
 2 
 3 
 
 1 
 
 1 
 
 1 
 
 1 
 1 
 
 1 
 
 3 
 
 1 
 
 1 
 3 
 
 1 
 
 
 2 
 
 1 
 4 
 4 
 4 
 9 
 5 
 2 
 2 
 2 
 
 1 
 
 1 
 
 1 
 1 
 
 6 
 10 
 
 10 
 21 
 10 
 
 7 
 5 
 
 1 
 
 1 
 
 5 
 
 8 
 
 10 
 
 23 
 
 22 
 
 20 
 
 11 
 
 7 
 
 4 
 
 1 
 
 1 
 
 1 
 
 1 
 
 3 
 
 12 
 
 14 
 
 23 
 
 37 
 
 23 
 
 27 
 
 5 
 
 3 
 2 
 
 1 
 1 
 2 
 
 1 
 4 
 
 40 — 
 
 50 
 
 60 
 
 70 
 
 1 
 1 
 
 1 
 1 
 3 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 1 
 3 
 
 2 
 3 
 1 
 1 
 
 3 
 11 
 35 
 43 
 
 80 
 
 70 
 
 90 _ 
 
 100 
 
 102 
 63 
 
 110 
 
 1 1 
 1 
 
 49 
 
 120 
 130 
 
 27 
 
 7 
 
 140 
 
 5 
 
 150 _. 
 
 4 
 
 160 
 
 3 
 
 170 
 
 1 
 
 180 — _ 
 
 1 
 
 Above 180 
 
 
 
 
 ■ 
 
 3 
 
 Totals ! 3| 3j lj 0| 2| 2| 6| 7| 1] 7| 6| 5| 13| 36] 74] 112] 157|435 
 
 This uniformity in the group as to attendance almost 
 eliminates attendance as a factor. The coefficient of cor- 
 relation, worked out from Table LXII, is found to be — .01, 
 which is really negligible. The coefficient of association 
 between attendance and defects for the group was found to 
 be only .08. If these coefficients are used with the one for 
 defects and scores, Table LXI, a partial coefficient with 
 the factor of attendance eliminated may be found. If 1, 2, 
 and 3 represent achievement scores, defects, and attendance, 
 respectively, 
 
 then Qv> = .126; Qk 
 
 and Qi-.-o = 
 
 126 
 
 01 
 
 01; Qas 
 
 ,08) 
 
 08 
 
 (1 .0001) *(1— .0064) 
 
 127 
 
 Thus the coefficient of .127 is found to differ from the 
 original .126 in the third decimal place only, which is really 
 a negligible difference. None of the coefficients shown in 
 Table LXI were found to be materially changed by the elim- 
 ination of attendance as a factor. In view of this fact, it 
 has been deemed expedient, for the sake of brevity, to disre- 
 gard attendance as a factor. So the final conclusions drawn 
 from this study are to be based on the results tabulated in 
 column 3, Table LXI. 
 
CHAPTER VI 
 SUMMARY AND CONCLUSIONS 
 
 Summary. — In the introductory chapter it was pointed 
 out that while for almost a century medical and physical 
 inspection had been practiced in Europe, they did not be- 
 come very frequent in America until about the beginning of 
 the present century. It was also pointed out that much 
 confusion has from the first resulted from a lack of agree- 
 ment as to the purpose, the technique, and the interpreta- 
 tion of the results of these examinations. The need for 
 uniform and concerted action has been stressed along with 
 the need of objective interpretation. It was shown that 
 this is now made possible by the introduction of standard 
 tests and measures, but that it had been difficult to make 
 objective a method that was based to so large an extent upon 
 teachers' estimates. Objective tests not only make testing 
 scientific, but make results comparable for the country at 
 large. 
 
 Chapter I has briefly outlined those studies that by their 
 nature form a background for the present one. Chapter II 
 emphasizes the importance of the problem and points out 
 the three aims of the study as, first, calling attention to 
 the relation of physical defects to school progress as a wide 
 field for fruitful research ; second, application of the math- 
 ematical technique of attributes to problems of school ad- 
 ministration ; and, third, the interpretation of the results 
 obtained from the data used in the study by means of coeffi- 
 cients of association. The first of these has been realized 
 by pointing out the lack of objective literature on the sub- 
 ject and by calling attention to the indicated association of 
 defects with successful school work. The second has been 
 demonstrated by concrete application of the fourfold, mani- 
 fold, and mean square contingency formulae to the data used 
 in this study. In Chapter III especially has particular 
 pains been taken to emphasize and visualize each step, so as 
 to give the reader not only a reading knowledge of the for- 
 mulae, but a working knowledge as well. The third pur- 
 pose — namely, the interpretation of the results of this 
 study — has been carried out in part by a brief interpreta- 
 tion of each association quotient as soon as derived, and in a 
 general way in the conclusions following this summary. 
 
 In addition to indicating the probable association of gen- 
 eral defects with general ability, Chapter IV has under- 
 
to Achievement in the Elementary School 75 
 
 taken to indicate the association of each defect with each 
 subject included in the elementary school. These results 
 are shown in separate tables and summarized in tabular 
 form at the close of the chapter. 
 
 Chapter V undertakes to account for the influence of at- 
 tendance, intelligence, and retardation as factors in achieve- 
 ment and to eliminate the influence of these factors from 
 the coefficients of association. This has been done by means 
 of partial correlations in the case of each of the major de- 
 fects. These factors have also been eliminated from the 
 coefficient of general defects with general ability. The final 
 results, together with the original coefficients, are shown in 
 tabular form in Table LXI. 
 
 Conclusions. — Physical defects are directly associated 
 with low scores 1 Physical defects constitute "a" cause of 
 retardation. 2 It has been shown that retardation consti- 
 tutes a cause of backwardness in achievement. 3 Then 
 physical defects both directly and indirectly constitute a 
 cause of backwardness in achievement. 
 
 All defects do not constitute handicaps to progress to the 
 same degree. In this respect they should probably be 
 ranked in the following order: 4 nasal obstruction and mouth 
 breathing with which it is accompanied, defective teeth and 
 the resulting maladies, defective hearing, defective tonsils, 
 and defective eyes, which includes both defective eyes and 
 defective vision. The last named appears to be only slightly 
 associated with low scores or backwardness in subjects. In 
 fact, in connection with many subjects the association is 
 shown to be negative. 5 In other words, it can hardly be 
 said that vision follows the same rules as do other defects. 
 But, in general, the defective child is somewhat more liable 
 to make low scores than is the physically sound one under 
 the same conditions. 
 
 The objective evidence presented in the early part of 
 this study shows that physical defects are widespread ; 6 in 
 the latter part it is shown that these materially affect school 
 work, 7 while the two lead to the conclusion that there would 
 be a gain — financial, social, and otherwise — by the elimina- 
 tion of such defects as are capable of prevention or removal 
 by medical science. 
 
 The application of the theory of attributes, together with 
 the association formulae, to an administrative problem of 
 
 1 This statement is based upon Table LXI. 
 
 2 See Table LX. 
 
 3 See Table LIX. 
 
 4 See Table LXI. 
 
 5 See Table LIV. 
 
 °See Tables II and III. 
 
 7 See Table LXI. 
 
76 A Study of the Relation of Some Physical Defects 
 
 this kind, is both scientific 1 and desirable as an aid to the 
 method of variables usually employed. That it is practica- 
 ble is demonstrated by its application to the present study. 
 
 Figures, while having distinct values as revealing general 
 tendencies, must not be interpreted as showing with abso- 
 lute precision either the sum total effect of physical handi- 
 caps or, in the case of individual defects, the exact relative 
 retarding force of each. But the indication may be taken 
 as significant. It is very probable that there are complex 
 associations among the various defects themselves, the exact 
 nature or degree of which is not yet known. Neither is it 
 known to what extent or with what ratio, constant or vary- 
 ing, the retarding force of a defect increases as the defect 
 becomes more serious. These offer themselves as field for 
 further study. Factors not dealt with here, such as home 
 environment or heredity, without doubt play an important 
 part both in explaining the cause of defects and in the force 
 with which they impede progress. These, too, are problems 
 full of promise to the research student. 
 
 From the results of this study it is evident that the field 
 open to the health supervisor of the school is full of oppor- 
 tunities to serve humanity by conserving the physical sound- 
 ness of the rising generations. He can greatly increase the 
 possibilities of many pupils in his charge. He can at least 
 make their work easier and their lives happier and more 
 successful by insistent and persistent discharge of his duty. 
 And yet he, too, has his limitations. Doubtless, Ayres 2 is 
 correct when he so forcefully says: "The long-yearned-for 
 royal road to learning is not always to be found through 
 the surgeon's knife. 'It has not been demonstrated that if 
 you cut out a child's tonsils, fit him with a pair of eyeglasses, 
 and clear him of adenoids, the school term will be cut in 
 half, the general level of education will surge up, and the 
 city will save millions of dollars.' The old-fashioned vir- 
 tues of industry, application, intelligence, and regularity still 
 hold sway, and among the reasons for poor scholarship are 
 still to be found such old stand-bys as age upon starting, 
 absence, laziness, and stupidity." 
 
 Suggested Further Studies 
 
 1. The influence of heredity on the association of physical 
 defects with achievement scores. 
 
 2. The influence of environment on the association of 
 physical defects with achievement scores. 
 
 3. The influence of the personal equation on the reliabil- 
 ity of the physical examiner's report. 
 
 4. The interrelation of the physical defects and the prob- 
 able effect of multiplicity of defects in a single individual. 
 
 ^Yule, Chapter I. 
 
 -Laggards in Our Schools, Ayres. 
 
to Achievement in the Elementary School 77 
 
 BIBLIOGRAPHY 
 
 I. On Method: 
 
 1. Biometrika, Volume II : 
 
 a. Correlation Tables: Correlation in Lesser Celondine. 
 
 These tables illustrate unequally the best forms for 
 representing- data, page 154. 
 
 b. Sheppard's Tables: W. F. Sheppard. These tables are 
 
 indispensable in the use of Karl Pearson's formula for 
 one variable and, one attribute, page 182. 
 
 c. Also many other illustrations and applications of va- 
 
 rious formulae for attributes. 
 
 2. Biometrika, Volume VII : 
 
 a. Karl Pearson's formula? for correlating one variable 
 
 with an attribute, page 97; correlation of physical de- 
 fects and weight, page 102; also his interpretation of 
 a coefficient as "significant," page 103. 
 
 b. Karl Pearson: A New Method, with one variable given 
 
 by alternative and the other by multiple categories, 
 page 248. 
 
 c. Elderton, Ethel M. Galton, Eugenics Laboratory: Asso- 
 
 ciation of Drawing with Other Capacities in School 
 Children. Gives coefficients and makes statement that 
 Q is not comparable with r unless the latter is in- 
 creased 40% to 60%. 
 
 3. Peterson, Dr. Joseph: Method of Interpreting Results in the 
 
 Cleveland Arithmetic Tests. Contains an explanation 
 of grouping data by means of average percentages, 
 enabling the score from several tests to be combined 
 into a general ability score. 
 
 4. Rugg, H. O. : Statistical Method Applied to Education. 
 
 Formulae for mean square contingencies. 
 
 5. Yule, G. U.: Introduction to the Theory of Statistics. This 
 
 is probably the most helpful reference on use of at- 
 tributes. Chapters I to III, inclusive. Griffity & Co., 
 London. 
 
 II. Previous Objective Studies: 
 
 1. Gulick and Ayres: Medical Inspection of Schools. Russell 
 
 Sage Foundation Publication. Fuli of valuable infor- 
 mation on method and results of physical and medical 
 examinations. 
 
 2. Ayres, L. P.: Laggards in Our Schools. Russell Sage Foun- 
 
 dation Publication. Full of information on causes of 
 retardation, using teachers' estimates and promotions 
 as basis of study. Physical defects one cause of re- 
 tardation. 
 
 3. Cornell, W. S.: Defects Among Exempt and Nonexempt 
 
 Children. Psychological Clinic, January 15, 1908. 
 Based on teachers' marks. 
 
 4. Allpors, Frank, Chairman of Committee on Conservation of 
 
 Vision, Chicago. Pamphlet entitled, School Children's 
 Eyes. This is not an objective study, but a report. 
 
 5. Albert E. Taussig, M.D., Clinic St. Louis County, Mo.: 
 
 Physical Examination of Public School Children. 
 Very good objective report of percentages of defec- 
 tives and relation to teachers' reports. 
 
78 A Study of the Relation of Some Physical Defects 
 
 6. Bureau of Education Bulletin, No. 4, 1919: A Manual of 
 
 Educational Legislation. Contains valuable mention 
 of history of medical examinations and laws in differ- 
 ent states. 
 
 7. Bureau of Education Bulletin, No. 13, page 28, 1919: Review 
 
 of Educational Legislation. Contains valuable men- 
 tion of the history of the movement and state laws. 
 
 8. Ruml et al. : Methods and Results of Testing School Chil- 
 
 dren. E. P. Dutton Company, New York. Gives data 
 on defects and Whipple tests, but does not work out 
 association coefficients for same. A second volume is 
 promised. 
 
 9. Cornell, W. S. : Classification of pupils on the bases of "nor- 
 
 mal," "fair," "bad" vision in relation to school sub- 
 jects, showing difference in percentages based on 
 teachers' marks. 
 
 III. Related Subjects: 
 
 Berkowitz, J. H. : The Eyesight of School Children. Defective 
 vision as related to environment. Bureau of Education Bul- 
 letin, 1919, No. 65. 
 
 Heilman, J. D. : A Clinic Examination Blank for Backward 
 Children in the Public Schools. Psychological Clinic, De- 
 cember 15, 1907. 
 
 Newmayer, S. W. : The Trained Nurse in the Public Schools 
 as a Factor in Education of the Children. American Journal 
 of Nursing, December, 1906. 
 
 Tyler, John N. : Abstract of Eight Lectures on the Physical 
 Basis of Education. Twentieth-Century Club, Boston, 1906. 
 
 Effect of Study on the Eyesight. Popular Scientific Monthly, 
 Volume XXII, page 74. 
 
 Effect of Student Life Upon Eyesight. Circular No. 6, Bu- 
 reau of Education, page 29. 
 
 Psychological Clinic, Volume I, No. 1, March 15, 1907. (Most 
 scientific exponent of the work for backward and mentally 
 retarded children.) 
 
 Terman, L. M. : Hygiene of School Children. Houghton, Mifflin 
 & Co., New York. 
 
 Dressier, F. B., and Kinsley, S. C. : Open-Air Schools. Rather 
 complete history of the movement from Germany to America. 
 On page 228 is also found a quotation from Ayres as to the 
 number of failures among defectives. 
 
 Englis: Principles of Secondary Education, Chapters I to IV. 
 Thinks there is high correlation between physical well-being 
 and achievements. 
 
 Cubberley: Public-School Administration, Chapter XX. 
 
 Dutton and Sneddon: Administration of Public Education in the 
 United States, pages 96, 394, 439, 47. 
 
 Dressier, F. B., United States Commissioner of Education, Bul- 
 letin, 1913, Volume I, pages 415-434. 
 
 Baker, Josephine: Physical Condition of Retarded Children. 
 Fourth International Congress on School Hygiene, Volume 
 IV, 1913. Twenty-five per cent of retarded due to personal 
 illness; eighty-nine per cent of children defective. Does 
 not correlate. 
 
mSESL!* egress 
 
 I 111 , 
 
 019 599 477 8 #