-.wsi 
 
 
 UNIVERSITY OF PENNSYLVANIA 
 
 The Witmer Cylinder Test 
 
 FRANKLIN CRESSEY PASCHAL 
 
 A THESIS 
 
 PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN 
 
 PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR 
 
 THE DEGREE OF DOCTOR OF PHILOSOPHY 
 
 PHILADELPHIA; 
 
 1918 
 
UNIVERSITY OF PENNSYLVANIA 
 
 The Witmer Cylinder Test 
 
 BY 
 
 FRANKLIN CRESSEY PASCHAL 
 
 A THESIS 
 
 PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL IN 
 
 PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR 
 
 THE DEGREE OF DOCTOR OF PHILOSOPHY 
 
 HERSHEY, PA. 
 
 THE HERSHEY PRESS 
 1918 
 
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 :f3 
 
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 mn 1 
 
CONTENTS 
 
 Page 
 
 I Introduction 5 
 
 II The Standardization 12 
 
 Procedure 14 
 
 Methods of Scoring 19 
 
 Methods of Recording 21 
 
 III Treatment of Results 24 
 
 Age Distribution 24 
 
 Sex Differences 37 
 
 IV Qualitative Aspects 39 
 
 V The Relation of Cylinder Test Performance to Proficiency 43 
 
 Age-Grade Distribution 43 
 
 Adult Performances 47 
 
 Correlation with Shop Rating 49 
 
 VI Summary S^ 
 
 Bibliography 54 
 
INTRODUCTION 
 
 The differential diagnosis of the psychological clinic requires a 
 variety of "behavior" tests, tests which give the child something 
 to do, which place in his hands an article that to him is a thing to 
 play with, in order that his actions may be observed, — that we 
 may, so to speak, see his mind in action. The reactions 
 to the situations arising bring out qualitative differences 
 in the normal and feeble-minded groups, as well as be- 
 tween the various other types. A diagnosis would be of little 
 value in most cases were it not accompanied by suggestions of 
 treatment, but treatment cannot be recommended without a 
 thorough knowledge of the mental make-up of the individual, the 
 strength and weakness of the various mental traits, and an ac- 
 quaintance with the special defects that may be present and of 
 any particular adaptabilities that the individual may have. 
 
 Healy and Fernald (2) in presenting their tests, remark that, 
 "Diagnosis of mental capabilities and adaptabilities as far as this 
 might be practically possible, was seen at the outset of the work 
 of the Juvenile Psychopathic Institute to be one of the main de- 
 siderata in our study of individuals who are young members of the 
 criminalistic class or who are otherwise repeatedly delinquent." 
 For such work as this, a scale of intelligence tests alone is not 
 sufficient. The study of the perceptions, of the ability to profit 
 by experience, coordination, of psycho-motor ability, as Wallin 
 (13) calls it, demands some sort of clinical material that will per- 
 mit the study of behavior. To quote Stern (11), "We must, of 
 course, guard against the danger which is apt to arise of suppos- 
 ing that we have grasped the individuality of a pupil in its totality, 
 when we have tested his intelligence." Wallin called attention to 
 the need of a graded scale of "motor diagnostic tests" which 
 would give a differential age determination of what a normal boy 
 or girl could do industrially, or in motor performance. 
 
 5 
 
6 The Witmer Cylinder Test 
 
 Wooley and Fischer (17), in speaking of the low correlation 
 between school grade and performance with the puzzle box, call 
 attention to the fact that such a low correlation with the test re- 
 quiring "a more original mental procedure" than that of any 
 other test they used, suggests that the school is failing to recog- 
 nize certain important forms of ability. 
 
 Another work illustrating the need of such tests is that of Sten- 
 quist, Thorndike and Trabue (10), who in the mental examina- 
 tion of dependent children found that they were inferior to normal 
 children in their mechanical test, though not so much so as in the 
 more abstract abilities. Any proper estimate of these children, 
 then, should take the former as well as the latter into consider- 
 ation. 
 
 It was in response to such a demand that the formboard came 
 into clinical use, the picture puzzle tests, the Knox Moron test, 
 the Healy Instruction Box, Puzzle Box, as well as a wide variety 
 of other tests. 
 
 More recently, as a result of the inadequacy of the Binet Scale 
 in the examination of deaf children, Pintner and Patterson (8) 
 have prepared a scale of performance tests which they have stan- 
 dardized and believe will serve as a supplement to the Binet Scale, 
 being a corrective where language ability is rated too high. They 
 have pointed out that tests dependent upon the reception of com- 
 plex instructions, the comprehension of verbal directions, or in 
 which the response requires the ability to use language, places even 
 the feeble-minded "verbalist," described by Healy (3) at an ad- 
 vantage as compared with the deaf child. Though we are not 
 to consider the latter to be equal to the normal child, it must be 
 noted that his defects are confined to certain traits and others 
 must be examined without relation to those. 
 
 Whenever language difficulty is present, from use of a foreign 
 tongue in the home or the lack of educational advantages as well 
 as from the special defects, recourse must be had to performance 
 tests. Place a piece of apparatus before the subject and ask him 
 by signs to do something. His ability to comprehend is an indi- 
 cation of his intelligence; his performance with the material when 
 once it is understood, can be compared with the results of normal 
 individuals of the same age. 
 
 Such a test is the formboard, which has probably been the most 
 popular single performance test. In the Psychological Clinic of 
 
Introduction 7 
 
 the University of Pennsylvania, it has received considerable at- 
 tention, a standardization having been made by Sylvester (12) 
 and another of a revised form of the board by Young (19). But 
 while the test gave an age gradation up to the fourteenth year, 
 it did not present a real problem to be solved beyond the sixth 
 year. From that age onward, it was concluded that any normal 
 child could do the test in a comparatively short time, the speed 
 of accomplishment varying with mental development and with 
 the development of certain traits. But a more difficult piece of 
 apparatus was needed, something that would in nature approxi- 
 mate the formboard. In the search for a test of this kind. Pro- 
 fessor Lightner Witmer was attracted by statements of Dr. Mon- 
 tessori regarding certain pieces of her didactic material. 
 
 Under the heading "Sensory Education," Dr. Montessori (6) 
 presents first, "Three solid pieces of wood, in each of which is 
 inserted a row of ten small cylinders, or sometimes disks, all fur- 
 nished with a button for a handle. In the first case, there is a 
 row of cylinders of the same height, but with a diameter which 
 decreases from thick to thin. In the second, there are cylinders 
 which decrease in all dimensions, and so are either larger or smaller 
 but always of the same shape. Lastly, in the third case, the cyl- 
 inders have the same diameter but vary in height, so that, as the 
 size decreases, the cylinder gradually becomes a disk in form. 
 The first cylinders vary in two dimensions (the section); the sec- 
 ond in all three dimensions; the third in one dimension (height). 
 The order which I have given refers to the degree of ease with 
 which the child performs the exercises." 
 
 This exercise, which is the one she prefers for children of two 
 and a half to three years of age, consists in returning the blocks 
 to their recesses after they have been removed and mixed on the 
 table. In a discussion of her method. Dr. Montessori (7) states 
 that this material shows a "difference in the reaction between de- 
 ficient and normal children, in the presentation of didactic ma- 
 terial made up of graded stimuli. This difference is plainly seen 
 from the fact that the same didactic material used with deficients 
 makes education possible^ while with normal children it provokes 
 auto-education." 
 
 This set of didactic apparatus promised to be of use as a mental 
 test as it possessed these requisite qualities: 
 
8 The Witmer Cylinder Test 
 
 First: A qualitative difference in performance. Dr. Montessori 
 gives a description of the performance of a normal child and brings 
 out a number of points of diagnostic importance, such as profiting 
 by experience, spontaneous interest, evidence of perplexity when 
 face to face with an error, as contrasted with the indifference and 
 inability to correct errors on the part of the deficient child. 
 
 Second: A series of graded stimuli, which may be presented in 
 order of ease of performance. 
 
 Third: Applicability to a wide age range, with increasing per- 
 formance with age. While its use as didactic material is limited 
 to the ages of two to four, it was to be expected that with increas- 
 ing age there would be increased ability to solve this problem. 
 
 Fourth: A uniform method of procedure could be adopted for 
 all ages. 
 
 Fifth: No instructions would be necessary that would place any 
 premium upon language. 
 
 So the Montessori cylindrical insets were adopted by Professor 
 Witmer for use in the clinic and were presented in four 
 series, the three separate pieces and the three used together. This 
 last arrangement consisted of placing the three blocks in a 
 triangular position on the table in front of the child, the third 
 block (varying in height) parallel to the edge of the table and 
 forming the base of the triangle, the second block (varying in 
 height and diameter) forming the right side and the first block 
 (varying section) forming the left side. The thirty cylinders were 
 all removed and placed within the enclosed triangle, mixed to- 
 gether, and the child was instructed to put them back in their 
 proper places. Here was a performance test of considerable diffi- 
 culty, which was of use with all ages beyond those with which the 
 single sets were useable and which promised to permit of a quanti- 
 tative standardization. 
 
 But there were certain inherent difficulties which made a satis- 
 factory standardization doubtful. In the first place, the knobs 
 on the cylinders, which were of value in the "psycho-sensory 
 training," caused many false moves and errors. The block could 
 be handled with more speed if grasped than when picked up by 
 the knob and this meant many errors through dropping the cyl- 
 inder into its correct hole knob downwards, then removing it 
 under the belief that there had been an error of position. The 
 loss of time resulting from this was often out of proportion to the 
 
Introduction 9 
 
 nature of the error. Then too, there were duplications of blocks, 
 the first blocks of the last two sets being identical, the seventh 
 blocks of the first two sets and the seventh block of the third set 
 being identical with the first block of the first set. While this was 
 not a serious drawback, it was more desirable that each cylinder 
 have but one proper recess. Another objection was that for 
 younger children especially, the cylinders represented three psycho- 
 logically different classes of objects, the greater part being cylin- 
 ders, but some being disks and others sticks. 
 
 The Witmer Cylinder Test 
 
 In the Spring of 191 5, Professor Witmer began to construct a 
 piece of apparatus based upon this material, but which would pos- 
 sess the advantages without the disadvantages above enumerated. 
 The Witmer Cylinder Test was the result. One board instead of 
 three, made of a light wood, contains eighteen blocks instead of 
 thirty, the three smallest cylinders of each set being omitted as 
 well as all duplications. There are no knobs, the ends being thus 
 interchangeable. 
 
 The cylinder board is a circular board of 11%. in. diameter and 
 i}4 in. height. The recesses are drilled about the outer edge so 
 as to form a slot which will give a side view of each recess as well 
 as facilitate the removal of the cylinder. This slot is made as 
 
10 
 
 The Witmer Cylinder Test 
 
 small as is consistent with the strength of the material, for it is 
 desired that the perception of the recess be influenced as little 
 as possible. In the center is a circular compartment of 8 in. di- 
 ameter and 2 in. depth. The cylinders will be spoken of in this 
 work as though divided into three series corresponding to the 
 original sets of Montessori. The series varying both in diameter 
 and in height (which will be called Series A) begins at the top of 
 the board with a cylinder lYs in. in each dimension. Then along 
 the right side of the board the successive cylinders are i /i6 in., 
 
 Arrangement and Designations of Cylinders 
 
 i^ in., I /i6 in,, i /§ in., iVie in. and i in. in both dimensions. For 
 convenience in identifying them, these cylinders will be spoken of 
 as numbers i, 2, 3, 4, 5, 6 and 7 respectively of Series A. The 
 series of constant height and varying diameter begins at the top 
 of the board and comes down the left side (called here Series B), 
 the height being constant at 2V8 in. while the diameters decrease 
 successively as in Series A. The one cylinder 2V8 in. in each 
 dimension serves as No. i of both Series A and Series B, then the 
 corresponding numbers of these two series have the same diameter 
 but differ in height. The last block of Series B (B7) is one of the 
 blocks corresponding to an original duplication and hence is also 
 considered as No. i of Series C, which forms the remainder of 
 
Introduction 11 
 
 the circle. Series C has a constant diameter of one inch, but the 
 height decreases as in Series A, hence corresponding numbers of 
 these two series have equal heights but differ in diameter, includ- 
 ing A7, which is logically a member of each series. 
 
 The three blocks which represent the original duplications are 
 given two designations because of the fact that in practical work, 
 a series is thought of as composed of seven cylinders, but the ex- 
 tremities are at the same time considered as members of other 
 series. The use of some system of designation will be seen to be 
 necessary since the similar character of the pieces prevents the 
 use of distinctive names. 
 
II 
 
 THE STANDARDIZATION 
 
 As soon as the final form of this board had been determined 
 upon and the preliminary experiments upon method of procedure 
 had been made, this quantitative standardization was begun. 
 The method adopted was that used by Young (19) in his work on 
 the formboard, an age distribution of a large number of unselect- 
 ed cases proportioned among different social classes. 
 
 The test was given in four of the public schools of Philadelphia, 
 one of which is located in a slum region where the population is 
 largely foreign born or native born Jewish. Another is in a sub- 
 urban manufacturing district, where a considerable proportion 
 are foreign born. In this part of the city, the living conditions 
 are much better than in the first section, almost all the popula- 
 tion living in small detached frame houses. The third is in a 
 somewhat isolated suburb, where the population is composed 
 mainly of the native born working class, with a large percentage 
 of the business class. The living conditions are quite good. The 
 fourth school is located in a part of the city occupied by the pro- 
 fessional and business class. In order to fill out certain of the 
 age groups, a number were examined in a fifth school, close to the 
 first mentioned, since the proportion of cases from that social 
 level was somewhat less than had been obtained from the others. 
 While an approximately equal number of cases were examined 
 from each of the four types of schools, they are not evenly dis- 
 tributed among the age groups. There is, however, an approxi- 
 mately equal distribution among the two social classes, the poorer, 
 represented by the first two schools, and the middle class, repre- 
 sented by the last two schools. These correspond to the two 
 groups used by Young in his standardization. 
 
 In the work with these children, there was no selection of cases 
 whatever. When the examination of the children of any room 
 was begun, they were taken one at a time according to seating 
 
The Standardization 13 
 
 order, no distinction being made in the treatment of results be- 
 tween foreign and native born, or between the feeble-minded and 
 the supernormal. Numerous cases were examined that were 
 quite evidently of defective mentality, but the discarding of any 
 of these cases would have required the same treatment of the 
 especially bright children, which would not have given a samp- 
 ling of the entire population of that age. Physical disability was 
 the only ground for discarding results, an arm paralyzed or lost, 
 sickness at the time of the examination, and one instance of pecu- 
 liar performance quite evidently due to badly fitted glasses. No 
 colored children are included. 
 
 The standardization of adult men has been taken from the two 
 mental extremes, one group composed of college students and of 
 students at one of the army aviation schools, the other group 
 being inmates of the Indiana Reformatory. A number of pris- 
 oners was included equal to the number of cases in the first group, 
 following the method of Simpson (9) who holds that the median 
 performance of two such widely varying groups should give an 
 indication of what would be the average of the entire population. 
 For adult women, we have available only the results of college 
 women. The reliability of this norm will be discussed in its 
 proper place. 
 
 There were 2230 cases used in this standardization, 1722 school 
 children, of whom 867 were boys and 855 girls, and 508 adults, 
 354 men and 154 women. For each age from eight to thirteen in- 
 clusive, a hundred boys and a hundred girls were used. For the 
 ages six, seven, fourteen and fifteen the attempt was made to 
 approximate this number, but due to certain defects in the re- 
 sults for these years, which will be brought out at a later point in 
 the discussion, this number was not considered necessary. 
 
 All the grade school cases were tested by the writer, as were the 
 men in the aviation school, but the college men and women, all 
 of whom were graduate or undergraduate students in the course 
 in General Psychology at the University of Pennsylvania, were 
 tested by members of an advanced psychology course, under the 
 direction of the writer. The Indiana Reformatory cases used in 
 the standardization proper, were tested by Mr. C. P. Stone,* pys- 
 
 *The writer wishes to express his appreciation of the cooperation of Mr. Stone 
 in the gathering of this material. 
 
14 The Witmer Cylinder Test 
 
 chologist of that institution, while a large part of the cases from 
 that institution used in a later table were examined by the writer. 
 
 Procedure 
 
 In view of the emphasis that all authors have laid upon identity 
 of procedure, it should be unnecessary to say that in order that 
 the results of other examiners may be interpreted on a basis of this 
 investigation, the same rules of procedure must be adhered to. 
 For this reason, it is desirable that the procedure be as simple as 
 possible. Owing to the variety of possible errors, however, and 
 the fact that, contrary to the opinion of Dr. Montessori, the ap- 
 paratus is not "self-correcting," the instructions have been 
 made quite exact and a careful consideration of the various possi- 
 bilities is necessary in order that an examiner may be ready to 
 cope with all the situations that may arise. 
 
 In testing a subject, a room should be used in which he may be 
 alone with the examiner and may be free from all outside inter- 
 ference. Ask the subject to stand before a table in a well lighted 
 spot, the height of the table used being proportionate to the 
 height of the subject. It must not be so low as to require him 
 to stoop, nor so high as to interfere with arm movements. A table 
 of the usual height gives an adult of five feet nine inches perfect 
 freedom of movement, yet it seems to bring the board too far be- 
 low him to permit it to be seen to the best advantage. For this 
 reason, the distance of the board from the near edge of the table 
 cannot be definitely set, but it may be said roughly that when the 
 subject is standing erect at the edge of the table, the line of sight 
 to the center of the board should make an angle of about sixty 
 degrees with the plane of the table. 
 
 The board is placed with the series of one inch cylinders. Series 
 C, adjacent to the subject, with the largest one, Ai, directly op- 
 posite him. The solution of Series C is facilitated by having it 
 where it may be seen, while it is of less advantage to see the larger 
 recesses. The board must be kept turned in this way at all times, 
 as it gives the subject a point of orientation. 
 
 First Trial. Before giving the instructions, it is necessary 
 that the attention of the subject be upon the board, but placing 
 him at the table in this position and moving the board before him 
 has always been sufficient so that no further remarks were neces- 
 sary before beginning the formal instructions. The aim in this 
 
The Standardization 15 
 
 first trial is to require the subject to perform a new task with the 
 least possible instruction. Therefore, the trial is carried where 
 necessary, beyond the original instruction through a series of 
 steps of training until he has completed the task satisfactorily. 
 
 Having drawn his attention to the board, say, "I am going 
 to take these blocks out and place them in the center and 
 I want you to put them back as quickly as you can." As 
 the directions are being completed, begin to remove the cylinders 
 with both hands, tossing them at random into the cenral com- 
 partment, the small ones first, then working up the opposite 
 sides of the board at the same time so that the large cylin- 
 ders will lie on top of the pile. If the small ones are permitted 
 to remain on the top, there results a loss of time either in digging 
 out the large ones, or in digging out the remaining small ones before 
 going on to the larger, which introduces a variant that is better 
 eliminated. Having done this, add, "You may use both hands. 
 Begin when you are ready and do it as quickly as you can." 
 
 Take the time to the nearest second, preferably with a stop- 
 watch, from the moment the first block is touched until the last 
 block is placed in the correct recess. 
 
 Questions may be asked, especially by older subjects, but we 
 have avoided answering all these, giving evasive replies, except 
 in a few cases with aviators, who have asked whether the blocks 
 taper, when the response was made that they were cylinders. 
 Urging is in order should the subject begin to lag or lose interest, 
 but no evidence should be given as to the correctness of place- 
 ments. The questioning look of a child as he is in doubt may be 
 best answered with the suggestion, "Hurry on!" 
 
 Should the subject quit with an error remaining on the board, 
 whether from oversight or due to his conclusion that placing 
 them by diameter, regardless of height, is sufficient, or should he 
 give up the attempt with some unplaced, record the time at which 
 he stops. This completes the first step; we are then ready to 
 begin the steps of education, the instructions for which are: 
 
 Second Step: "Is that alright?" 
 
 Third Step: "That is not right." 
 
 Fourth Step: "Fix it so that they will be level with the top." 
 
 Each step ends when the subject ceases work either believing 
 himself through, or being unable to complete the task. The 
 watch should not be stopped before the end of the trial, but the 
 
16 The Witmer Cylinder Test 
 
 time of the completion of each step should be recorded, not that 
 it is of use as a quantitative measure, but for its descriptive value. 
 
 This question in the second step should be asked in an off-hand 
 manner, as though merely to remark, "Are you through already?" 
 With adults, this bare question is sufficient in most cases to cause 
 them to turn their attention again to the board and to begin to 
 make corrections or ask about the correctness of their performance. 
 Questions resulting directly from this instruction, as "Should they 
 be level with the top?" may be answered where a simple affirma- 
 tive or negative will suffice. With many older children, especial- 
 ly those who have merely stopped to see whether or not they are 
 correct, or as we say, "quit for a decision," this instruction will 
 be all that will be necessary. But with most young children, this 
 question brings out either an affirmative answer or none whatever. 
 A more definite instruction as in the third step must then be given 
 them. 
 
 With normal individuals above the age of eleven, this third step 
 is the last that is necessary. With young children or with cases 
 of mental deficiency this may not be sufficient to suggest to them 
 the right solution. Except in a few cases in the sixth or seventh 
 years, normal grade school children require no more than the 
 fourth step of instruction. When told that the cylinders must be 
 level with the top, a child of school age will usually make the nec- 
 essary corrections. 
 
 If this is not enough, point to some that are correct, rubbing the 
 hand over them to indicate that they are level with the top. The 
 next step would be to point to one that is wrong and require him 
 to hunt for its correct recess until it is found. The purpose here 
 is to give by small steps, the teaching that will enable the child 
 to place the cylinders with his own hands. Whenever the subject 
 has completed the task successfully, we are ready for the second 
 trial. 
 
 In this standardization, it was considered necessary to set a five 
 minute limit, when if the trial was not completed, even though 
 but one or two steps of instruction had been given, the child was 
 credited with a failure and was dismissed. Young set a three 
 minute limit on the formboard. A time limit is needed in under- 
 taking such an investigation as this, and it has been found that 
 with grade children, none but those of low mental level require 
 
The Standardization Yl 
 
 more time than this other than in the ages of six, seven and eight. 
 The question of failures will be taken up again in connection with 
 the data. 
 
 Second Trial. After declaring the work to have been satis- 
 factory and giving some encouragement, as is advisable in all 
 testing of children, remove the blocks in the same manner as be- 
 fore, saying as it is being done, "Now I am going to take them 
 out again and I want to see if you can put them back even more 
 quickly." Should the subject have used but one hand during the 
 greater part of the time, it is well to add, "Use both hands this 
 time." If he cannot work with both, this will not confuse him 
 as he will soon cease to work with one of them. Take the time as 
 in the first trial. 
 
 The second and third trials are not qualitative trials and no 
 attempt at education is made, except in one instance. Should 
 an error remain which is evidently an oversight rather than a 
 failure to understand when the test is satisfactorily performed, re- 
 quire the subject to correct it but count that trial a failure. The 
 reversal of an adjacent pair of blocks in Series C, or of A2 and B2 
 may be considered an oversight, or even an error further removed 
 in the case of a younger child. Correction is never permitted ex- 
 cept where the error has been quite evidently but an oversight, and 
 it is allowed only as a caution for the next trial Should a more 
 serious error be made, the entire test is considered a failure. 
 
 Third Trial. The instructions this time are, "Now once more. 
 Let's see if you can do it even faster this time." The time is 
 taken as in the preceding trials. No corrections need be permit- 
 ted as this is the last trial. Final errors on the three trials would 
 class the test as a failure, but no instances of this have been seen 
 in cases who have completed the first trial within the five minute 
 limit even with instruction. 
 
 It was discovered early that the time of the performance was 
 affected more by the chance position of cylinders A2 and B2 than 
 by any other variable. If A2 happened to be thrown on the right 
 side of the compartment, it would probably be picked up with 
 the right hand and hence would be placed in its own recess, while 
 if it were thrown on the left hand side, it would be picked up in 
 most cases with the left hand and then would ensue a period de- 
 voted to straightening out the difficulty. For that reason, a 
 
18 The Witmer Cylinder Test 
 
 definite order of placement of the three largest blacks was de- 
 termined upon. 
 
 Trial 1 Trial II Trial III 
 
 Position of Large Cylinders in Compartment 
 
 In each trial, the largest cylinder, Ai, is placed in the median 
 line, at the top in the first trial, in the center in the second trial 
 and at the base in the last trial. Blocks A2 and B2 are removed 
 at the same time and in the first trial are thrown on the side ad- 
 jacent to their recesses. The second time, these blocks are placed 
 in the median line, which gives the child an equal chance of pick- 
 ing up a cylinder with the correct hand. On the last trial, Ai is 
 placed at the near side of the compartment, to vary its position, 
 while A2 and B2 are thrown to the opposite sides, thus requiring 
 the child to accept the more difficult situation. Perhaps for 
 practical purposes, it would be better to place these three in dif- 
 ferent positions on the median line in each trial. At least, it is 
 necessary to eliminate variables so far as is possible and exper- 
 ience has shown that the chance placements of these cylinders 
 by the examiner is the most important one. 
 
 When this test was first used, the procedure adopted included 
 instructing the subject to put the cylinders "back where they be- 
 long" and in case errors were left, immediately telling him that 
 they must be level with the top. But this procedure had two 
 weak points; first, a time record made on the first trial with this 
 additional information is not comparable to one made without 
 this assistance; second, the equivalent instruction cannot be 
 given to one who lacks the use of language, whether from deaf- 
 ness or from insufficient knowledge of our tongue. In order to 
 avoid these difficulties and at the same time to make the test more 
 of a problem, the instructions were changed to those now in use. 
 
The Standardization 19 
 
 the subject being merely told to "put them back." The pro- 
 cedure as then used provided that in case final errors were left, 
 the examiner was to make the corrections himself, without calling 
 attention to them, the assumption being that this should 
 be sufficient to suggest to the subject that his performance 
 had not been satisfactory and to indicate the nature of the correct 
 solution. But when given to a university class of a hundred and 
 three students in this manner, there were three individuals who 
 made observational errors (failed to observe that two cylinders 
 were reversed) and each of these profited by the instruction; 
 there were seventeen students, one-sixth of the class, who replac- 
 ed the cylinders by diameter only, regardless of height, and of 
 these, but five profited by this silent correction made by the ex- 
 aminer. Of the remaining twelve, four did the test correctly on 
 the last trial but the other eight assumed that as nothing had been 
 said, their performance has been satisfactory and they completed 
 it in the same manner in each of the three trials. When less than 
 a third of a university group draw the desired conclusion from the 
 movements of the examiner, it is hardly to be expected that grade 
 school children should profit by the corrections made before them 
 and to which attention is not called. In order that a quantitative 
 comparison may be made between the results of different subjects, 
 it is necessary that at the end of the first trial all should have 
 learned the nature of the problem. 
 
 Some experimenters may find that the method of least possible 
 steps of instruction on the first trial makes too much of a demand 
 upon their time when examining a group. Perhaps the chief 
 consideration that has induced us to adopt a form of first trial re- 
 quring the test to be satisfactorily finished by the child himself, 
 is that we believe our records may be made use of without loss of 
 reliability by anyone who will adopt this principle. It is but nec- 
 essary that the child shall start the second trial knowing definitely 
 from previous performance, just what he is to do. A deaf child, 
 or one unable to use the English language, may complete the first 
 trial, instructed only by. signs, and is then ready to begin the 
 quantitative trials on a level with the subjects that we have used 
 in this investigation. 
 
 Methods of Scoring 
 
 There are five possible methods of scoring, — the time on the 
 first, the second or the third trials, the average time, or the time 
 
20 The Witmer Cylinder Test 
 
 of the shortest trial. As to the first trial, enough has been said 
 to show that it will not permit of quantitative standardization. 
 
 At the beginning of this investigation, it was thought that the 
 second trial should be used, on the theory that after the individual 
 had learned what was required of him, a single trial would give a 
 valid time index. However, the precedent of three trials used in so 
 many tests was followed pending an investigation into the validity 
 of the various scoring devices. It was soon found that too often 
 some single trial would show a slow time due to chance errors fol- 
 lowed by mental confusion, or due to varying the method or order 
 of placement, which would completely destroy the value of that 
 trial. This was particularly true of bright children who, after 
 making a fast record on one trial, would give a poor performance 
 on the next due to excessive haste. Our records, even with col- 
 lege students and aviators, show that some one trial, usually the 
 second, has a slow time because of too much haste or misfortune 
 in making placements. What has been said of the second trial 
 applies equally to the third trial, the children in the higher grades 
 more often than adults using excessive haste on this trial. 
 
 The average of three trials cannot be used because of the im- 
 possibility of treating the first trial quantitatively. Certainly 
 the time of completion of a trial in which there were three steps of 
 instruction should not be brought into comparison with the time 
 made with but the original instruction. Hence an average must 
 be an average of two trials, the second and the third. This like- 
 wise is affected by any chance slow trials, though the excess is 
 halved, but that there should be some penalty is not 
 unreasonable. It may be that the best method of scoring this 
 test would be found to be the giving of four trials and using the 
 average of the last three. However, the time required and the 
 fatigue induced are important elements in a clinical examination 
 and would seem to suggest that even three trials is a little long 
 in working with younger children. 
 
 In the shortest trial, chance plays less part. It is true that in 
 certain instances a series of chance placements have given a final 
 result much shorter in time than the other performances seemed 
 to warrant, but there were fewer cases misplaced by this method 
 than by any of the others. There are so many possibilities of 
 error to be avoided in the cylinder test that luck will assist an 
 individual much less than it will retard him. With the exception 
 
The Standardization 21 
 
 of the few cases mentioned, the shortest trial has seemed to give 
 us a more satisfactory determination when applied to individual 
 cases than did any other scoring method. It is a better indica- 
 tion of what the child can do. 
 
 Sylvester (12) tested experimentally the various scoring de- 
 vices as applied to the form board and came to these conclusions; 
 First Trial, the performance is too irregular to be of value; Third 
 Trial, "Bright children often fall back through over-hurrying, 
 change of method of handling the blocks or bad luck in fitting 
 them into the recesses;" Shortest Trial, This is the most regular 
 and has the lowest variability, hence statistically is the most re- 
 liable; Average of Three Trials, seems the most satisfactory 
 with individual cases, probably due to the fact that it gives weight 
 to the first trial. 
 
 Our own investigation gave less concrete results than that of 
 Sylvester. In the first school that was tested, each of the teach- 
 ers from the first to the sixth grade inclusive was asked to place 
 the members of each of her classes in a rank order, boys and girls 
 separate. The instructions were given them in such a way as to 
 endeavor to get a ranking on a basis of intelligence or general 
 ability rather than upon school performance. There was a great 
 variation in the resulting material, the personal element being very 
 large, so that the results do not warrant presentation. However, 
 an investigation into the lists which showed marked correspond- 
 ence or marked diflPerence between the teacher's rank order and 
 the rank order of cylinder test performance was the basis of the 
 conclusions that have been drawn above. It leads us to agree 
 with Sylvester, except that the shortest trial instead of the aver- 
 age of three trials proves the most satisfactory in individual cases. 
 
 In connection with the investigation of the relation between 
 cylinder test performance and shop ability, presented in Chapter 
 V, the question of the value of the various methods of scoring is 
 again taken up and from another angle. It will suffice here to point 
 out that Table 8, page 50, indicates that the shortest trial is the 
 most satisfactory index, followed closely by the average of two 
 trials, while the first trial and the average of three trials are much 
 less suitable. 
 
 Method of Recording 
 
 The method of recording any test must not be so complicated 
 as to detract the attention of the examiner during the progress of 
 
22 The Witmer Cylinder Test 
 
 the test, yet it must adequately portray the important points. 
 The examiner employing this test for the first time may find it 
 difficult to report his results, particularly of the first trial with its 
 complex possibilities, without missing much of the subject's per- 
 formance. For this reason, sample records will be given to illus- 
 trate the system used in this investigation and to demonstrate 
 some of the short cuts of reporting that have been worked out. 
 
 Case 251 Name, A. D. Age, Adult Sex, M 
 
 (i) 48-6 Diameter; approximate positions. 
 
 62 "Are they supposed to be level?" 
 
 (2) 42 
 
 (3) z(^* 
 
 In this case, the blocks were returned in 48 seconds with six 
 errors remaining, the subject placing them by diameter only, ex- 
 cept that they were close to the correct position. In response to 
 the question, "Is that right?" he responded, "Are they supposed 
 to be level?" An affirmative answer was given as this question 
 had been enough to suggest to him the correct solution. He is 
 therefore credited with two steps on the first trial, requiring a 
 total time of 62 seconds. The second and third trials were pre- 
 formed in 42 and 36 seconds respectively, a star being placed after 
 the time of the third trial to indicate that it is the shortest trial. 
 
 Case 2047 Name L. R. Age, 8 yr. 4 mo. Sex F 
 
 (i) 125-10 By diameter only; Ai in compartment. 
 Yes 
 
 183-8 Meaning not understood. 
 205-2 C 6, 7. 
 214 
 
 (2) 109* 
 
 (3) 74-2 AB 2. 
 
 In this instance, the child returned the blocks to some recess 
 without regard to height, but stopped work as though through with 
 the largest block still lying in the central compartment. At this 
 time, 125 seconds, there were ten errors remaining. In response 
 to the question of the second step, she answered, "Yes," so the 
 third step was given her, the statement, "That is not right." 
 This time she placed every cylinder in some recess, finally stop- 
 
The Standardization 23 
 
 ping with eight incorrect placements. It was evident that she 
 did not yet understand what should be done. She was told to fix 
 them so that they would be level with the top and then began to 
 understand what was wanted, with the result that at the end of 
 205 seconds, all had been correctly returned with the exception of 
 the reversal of C6 and C7, an observational error. A fifth step 
 was necessary, in this case it being enough to tell her that she was 
 not yet through. She then found her error and corrected it, the 
 total time consumed in the entire trial being 214 seconds. As 
 several seconds are required to be sure that the child has stopped 
 work and to give the additional instructions, it is evident that the 
 last correction was quickly made. Her second trial required 109 
 seconds and the third 75 seconds, but this time she left two final 
 errors, A2 and B2 being reversed. This trial being thrown out 
 because of final errors, the time used as the index is that of the 
 second trial, 109 seconds. 
 
 This simple combination of the numbers of two blocks had been 
 found very convenient to represent a reversal, thus AB3 indicates 
 that the third blocks of series A and B have been reversed, or C 4,5 
 indicates a reversal of the fourth and fifth cylinders in Series C. 
 
Ill 
 
 TREATMENT OF RESULTS 
 
 For this standardization, an effort was made to obtain fifty 
 cases of each sex for each half year group. But it was found that 
 for the sixth and seventh years, the test is too difficult to be per- 
 formed within the five minute limit allowed for the first trial. 
 Less than a half of the boys and even a smaller proportion of the 
 girls completed the trial within this period and it was therefore 
 considered that the determination of the performances for these 
 ages is a separate task, for the proper solution of which, any 
 amount of time necessary must be given in order that the first 
 trial may be completed. The greater part of the successful trials 
 given in the tables for the seventh year were from children who 
 were in the latter half of that year. The material for these ages 
 is included in the data simply to give an indication of what some 
 children of that age can do and in order that it might be utilized, 
 should it fit in with any further investigation of these ages. 
 
 Beginning with the eighth year, the percentage of those who 
 fail to complete the test within the time limit is not large. Those 
 who have been placed in our poorest group through failure to com- 
 plete the first trial would fall quite generally in the poor group 
 even if sufficient time were allowed for them to complete it, as will 
 be shown later. So then, for the ages from eight to thirteen in- 
 clusive, the results are complete for fifty boys and fifty girls ot 
 each half year group, one hundred for each year. The results for 
 the fourteenth year are satisfactory, although the range of ability 
 represented is probably not what might be desired. In the first 
 place, the greater part of the cases come within the first half of 
 this year, fifty of each sex as compared with thirty-two girls and 
 forty-four boys in the last half of the year. Then the children of 
 this age are in the seventh or eighth grades, mainly the latter. 
 While in the preceding ages we have had the brightest as well as 
 the poorest, the pedagogically advanced as well as the pedagogic- 
 
 24 
 
Treatment of Results 25 
 
 ally retarded, in this age we have the pedagogically "at age" and 
 the retarded, but the brightest and the pedagogically advanced 
 are out of the grades. This is particularly true of the girls. 
 
 That this is not a serious drawback is indicated by the fact that 
 the resulting curve corresponds with what other investigators have 
 found. There is a steady decrease in time for both sexes up to the 
 age of fourteen, when there is a slight increase for boys, while for 
 girls it remains the same except for an increase in the minimum. 
 The same tendency at the fourteenth year was found by Pintner 
 and Patterson (8) in most of their performance tests and by Syl- 
 vester (12) and Young (19) on the formboard. None of these 
 has explained this rise on the basis of insufficient distribution of 
 the mental grade of this year, which is probably the cause. The 
 fact that this is a performance test rather than an intelligence test 
 suggests that this lack of distribution is not as serious as it would 
 prove for tests more dependent upon language ability. As the 
 half-yearly increments of mental growth are not as large as in 
 earlier ages, a fewer number of cases can be of as much value in 
 constructing the curve of normal distribution, nor would the slight 
 excess of cases in the first half of the year greatly affect the final 
 curve. 
 
 The fifteen year group is not satisfactory for either sex as all 
 the cases are over-age for their grade and cannot be considered 
 as typical of the age. Neither sex surpasses the thirteen year 
 group in performance, and the girls of this age do poorer work. 
 The high percentage of cases requiring over fifty seconds on the 
 shortest trial, as shown in Table 2, is due to two things, the nerv- 
 ousness of girls of this age when facing a test, resulting in quali- 
 tative performances that would be poor for girls several years 
 younger, and the fact that girls of this age quite generally perform 
 the test because they have been asked to, seem satisfied if they do 
 it at all, and seldom show competetive spirit. 
 
 There is a considerable age range in the adult group. Among 
 the university students are included a number of men and women 
 who are graduates students or who are registered in the College 
 Course for Teachers and are older than the usual college students. 
 The aviator group runs from twenty-three to twenty-eight years 
 of age, most of them being college graduates. The Indiana Re- 
 formatory receives men between the ages of sixteen and thirty at 
 the time of commitment, the mean age being twenty-two. The 
 
26 
 
 The Witmer Cylinder Test 
 
 records of this group were obtained at the time of the mental ex- 
 amination about a month after admittance. One hundred seventy- 
 seven consecutive cases have been used in which the cylinder test 
 was given, the only source of error being that the test was not given 
 to everyone, being in some cases omitted for lack of time, where 
 the things that this test brings out had been determined in other 
 ways. This tends to eliminate the men of better mentality and 
 to give us figures from a more uniformly poor group. 
 
 Unfortunately our distribution for women contains only the 
 picked group, university students, and because of this it cannot be 
 said to be representative of the range of adult women. 
 
 TABLE I 
 
 Distribution of Shortest Time Trials — 1221 Boys 
 
 F. 
 
 D N. C. 
 
 29 20 
 
 13 
 
 ^9S 
 186 
 167 
 152 
 144 
 1 40 
 139 
 137 
 132 
 124 
 121 
 117 
 114 
 112 
 III 
 
 108 
 107 
 106 
 105 
 104 
 103 
 102 
 lOI 
 
 100 
 
 99 
 98 
 
 97 
 9(> 
 95 
 94 
 93 
 92 
 
 91 
 
 Age 
 
 6 7 
 
 10 II 12 13 14 15 Adult 
 
Treatment of Results 
 TABLE I — Continued 
 
 27 
 
 90 
 
 I 
 
 
 
 I 
 
 
 
 
 89 
 
 
 
 
 
 
 
 
 88 
 
 
 
 
 
 
 
 
 87 
 
 
 
 
 
 
 
 
 86 
 
 
 
 I 
 
 
 
 
 
 85 
 
 
 
 
 
 
 
 
 84 
 
 
 
 
 
 
 
 
 83 
 
 
 
 I 
 
 
 
 
 
 82 
 
 
 
 I 
 
 
 
 
 
 81 
 
 
 
 I 
 
 
 
 
 
 80 
 
 
 
 
 
 
 I 
 
 
 79 
 
 
 
 I 
 
 I 
 
 
 
 
 78 
 
 
 3 
 
 
 
 
 
 
 77 
 
 
 
 I 
 
 
 
 
 
 76 
 
 
 
 I 
 
 
 
 
 
 75 
 
 
 
 
 I 
 
 
 
 
 74 
 
 
 3 
 
 
 I 
 
 
 
 
 73 
 
 
 
 2 
 
 3 
 
 
 
 
 72 
 
 
 
 3 
 
 
 2 
 
 
 
 71 
 
 
 
 3 
 
 2 
 
 
 
 
 70 
 
 I 
 
 
 3 
 
 
 I 
 
 
 
 69 
 
 I 
 
 
 2 
 
 
 
 
 
 68 
 
 
 
 . . • 
 
 I 
 
 
 
 
 67 
 
 2 
 
 
 3 
 
 3 
 
 I ] 
 
 
 
 66 
 
 
 
 2 
 
 I 
 
 2 
 
 I 
 
 
 65 
 
 
 3 
 
 3 
 
 2 
 
 
 I 
 
 
 64 
 
 
 
 2 
 
 I 
 
 
 I 
 
 
 (>3 
 
 
 
 I 
 
 2 
 
 
 I 
 
 
 61 
 
 2 
 
 2 
 
 4 
 
 I 
 
 I 
 
 I 
 
 
 61 
 
 2 
 
 2 
 
 3 
 
 2 
 
 2 C 
 
 I I . . . I 
 
 
 60 
 
 I 
 
 
 I 
 
 I 
 
 3 •• 
 
 
 I 
 
 59 
 
 
 
 2 
 
 I 
 
 2 
 
 
 2 
 
 58 
 
 I 
 
 2 
 
 2 
 
 3 
 
 2 ^ 
 
 ^ I ... I 
 
 
 57 
 
 I 
 
 
 I 
 
 I 
 
 I : 
 
 X 2 I 
 
 I 
 
 56 
 
 I 
 
 
 3 
 
 3 
 
 3 
 
 
 
 55 
 
 
 3 
 
 3 
 
 2 
 
 I ] 
 
 I I 
 
 
 54 
 
 
 
 
 I 
 
 6 .. 
 
 I ... I 
 
 I 
 
 Si 
 
 
 2 
 
 4 
 
 5 
 
 6 
 
 [ 3 •■• I 2 
 
 2 
 
 52 
 
 
 
 4 
 
 I 
 
 5 •• 
 
 4 I .. I 
 
 2 
 
 51 
 
 
 
 2 
 
 3 
 
 3 
 
 J 2 2 I . . 
 
 
 50 
 
 
 
 2 
 
 3 
 
 4 - 
 
 I ... 3 3 I 
 
 
 49 
 
 
 
 3 
 
 4 
 
 6 
 
 t 2 3 I I 
 
 
 48 
 
 
 
 I 
 
 5 
 
 5 : 
 
 } 2 ... I 
 
 5 
 
 47 
 
 
 
 I 
 
 3 
 
 3 < 
 
 5 2 I 4 I 
 
 I 
 
 46 
 
 
 
 2 
 
 3 
 
 I ^ 
 
 ^ 2 5 5 •• 
 
 6 
 
 45 
 
 
 
 I 
 
 2 
 
 I 
 
 3 2 I 6 . . 
 
 8 
 
 44 
 
 
 
 I 
 
 4 
 
 4 
 
 J 7 2 6 3 
 
 9 
 
 43 
 
 
 2 
 
 2 
 
 4 
 
 6 
 
 7 5 4 4 I 
 
 5 
 
 42 
 
 
 
 2 
 
 
 3 
 
 77442 
 
 5 
 
 41 
 
 
 
 
 4 
 
 I 
 
 ? 6 5 2 2 
 
 12 
 
 Age 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 I 
 
 12 13 14 15 ^ 
 
 \dult 
 
28 
 
 The Witmer Cylinder Test 
 TABLE I — Continued 
 
 40 
 
 2 
 
 I 
 
 I 
 
 4 
 
 5 
 
 9 
 
 8 
 
 2 
 
 17 
 
 Z9 
 
 I 
 
 2 
 
 2 
 
 3 
 
 3 
 
 
 7 
 
 2 
 
 13 
 
 38 
 
 
 2 
 
 2 
 
 3 
 
 6 
 
 5 
 
 4 
 
 I 
 
 II 
 
 37 
 
 I 
 
 2 
 
 5 
 
 4 
 
 5 
 
 6 
 
 2 
 
 ? 
 
 17 
 
 36 
 
 
 
 3 
 
 3 
 
 2 
 
 2 
 
 3 
 
 2 
 
 18 
 
 2S 
 
 
 2 
 
 
 6 
 
 3 
 
 3 
 
 3 
 
 3 
 
 18 
 
 34 
 
 
 I 
 
 2 
 
 
 3 
 
 7 
 
 7 
 
 I 
 
 21 
 
 22, 
 
 
 
 I 
 
 3 
 
 2 
 
 5 
 
 3 
 
 3 
 
 14 
 
 32 
 
 
 
 3 
 
 2 
 
 4 
 
 8 
 
 3 
 
 ? 
 
 26 
 
 31 
 
 
 I 
 
 
 
 I 
 
 2 
 
 2 
 
 
 22 
 
 30 
 
 
 
 
 I 
 
 3 
 
 5 
 
 I 
 
 I 
 
 21 
 
 29 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 I 
 
 24 
 
 28 
 
 
 
 
 
 I 
 
 ^ 
 
 2 
 
 
 II 
 
 27 
 
 
 
 
 
 
 
 2 
 
 
 13 
 
 26 
 
 
 
 
 I 
 
 3 
 
 
 2 
 
 
 9 
 
 25 
 
 
 
 
 I 
 
 
 
 
 
 16 
 
 24 
 
 
 
 
 
 
 
 I 
 
 
 4 
 
 23 
 
 
 
 
 
 
 
 I 
 
 
 7 
 
 22 
 
 
 
 
 
 
 
 
 
 4 
 
 21 
 
 
 
 
 
 
 
 
 
 4 
 
 20 
 
 
 
 
 
 
 
 
 
 2 
 
 19 .. . 
 
 
 
 
 
 
 
 
 
 
 18 .. . 
 
 
 
 
 
 
 
 
 
 I 
 
 No. 
 Age 
 
 58 75 
 6 7 
 
 TABLE II 
 
 Distribution of Shortest Time Trials — 1009 Girls 
 
 100 100 100 100 100 100 94 40 354 
 8 9 10 II 12 13 14 15 Adult 
 
 F. 
 D.N. 
 
 C. 
 
 27 
 
 31 
 
 18 
 
 I 
 
 10 
 
 8 
 
 3 
 
 I 
 
 
 I 
 
 2 
 
 
 205 
 188 
 
 
 
 I 
 I 
 
 
 
 
 
 
 
 
 
 
 177 
 136 
 
 
 
 I 
 I 
 
 
 
 
 
 
 
 
 
 
 107 
 106 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 105 
 104 
 
 03 
 102 
 
 
 • 
 
 I 
 
 2 
 
 
 
 
 
 
 
 
 
 lOI 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 Age 
 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 II 
 
 12 
 
 13 
 
 14 
 
 15 
 
 Adult 
 
Treatment of Results 
 TABLE II— Continued 
 
 29 
 
 ICXD . . . 
 
 99 ■■ • 
 
 98 
 
 97 .. . 
 
 96 ... 
 
 95 •• • 
 94 ... 
 
 93 I ■ 
 
 92 
 
 91 
 
 I I 
 
 I I ... I I 
 
 I ... . . 
 
 I 
 
 I I 
 
 I I I 
 
 I I . . 
 
 I 3 I 
 
 90 . . 2 
 
 89 . . I I 
 
 88 I 2 
 
 87 .. I 
 
 86 I 
 
 85 .... 2 I I ... I 
 
 84 .... I I 
 
 83 I I I 
 
 82 .. 2 I 
 
 81 .. I I I 
 
 80 I I I . . 
 
 79 •• I I I 
 
 78 I 3 I I I ... 
 
 77 I ■■ I I I ... 
 
 76 . . I I I 
 
 75 ..3 3 2 I I I I ... 
 
 74 .. ■- I 3 I .. I ... 
 
 73 I I ••■ I I 
 
 72 . . 3 • • ■ I 2 I 
 
 71 . . 2 2 2 I I 
 
 70 .... 2 2 ... I 
 
 69 I .. 3 I I I 
 
 68 I . . 2 2 5 
 
 67 . . I 2 4 I 
 
 66 21... I 4 2 I I 
 
 65 ..2 I 4 I 2... 4 I 
 
 64 .. I I I I ... I ... 
 
 63 . . 2 I I . . . I I 2 I 
 
 62 . . I 5 3 I . . . I I 
 
 61 .... 4 I . . . I I I I 
 
 60 
 
 59 
 
 58 I . 
 
 % •. . 
 
 55 I • 
 
 54 ... 
 
 53 
 
 52 ... 
 
 51 
 
 i I 4 3 
 
 I 4 5 2 2 I 3 I I... 
 
 4 I 3 2 I 
 
 I 2 2 3 6 I I I 
 
 4 I 4 2... I 2... 
 
 3 3 2 5 I I 2 .. I 
 
 I 4 I 2 3 ■■■ 2 
 
 I 2 2 I 2 2 4 I I 2 
 I 5 2 2 3--- 4.. I 
 
 r 4 2 3 6 2 2 2.. 2 
 
 Age 
 
 13 
 
 14 15 Adult 
 
30 
 
 The Witmer Cylinder Test 
 TABLE II— Continued 
 
 50 
 
 49 
 48 
 
 46 
 
 45 
 44 
 43 
 42 
 
 41 
 
 
 I 
 I 
 
 I 
 I 
 3 
 
 I 
 
 2 
 
 2 
 
 5 2 
 
 1 I 
 
 2 5 
 
 3 4 
 
 6 5 
 I 8 
 
 4 I 
 3 
 
 I 3 
 
 I 2 
 
 6 3 3 2 2 ... 
 
 I 2 5 3 I 3 
 
 243324 
 6727.. I 
 
 4 3 4 I 3 I 
 3 3 2 I I 3 
 
 443224 
 
 I 5 3 3 •• I 
 
 ..76437 
 612625 
 
 40 
 39 
 38 
 37 
 
 35 
 34 
 2,Z 
 32 
 31 
 
 
 
 
 I 4 4 5 8 4 I 4 
 
 2356312 
 I 3 I 2 4 2 3 6 
 
 I ... 3 4 5 3 ••• 
 I 2 4 ... 9 5 I 5 
 I • I 2 2 ... 3 I 5 
 
 2251128 
 I ... 3 I ... 3 .. 9 
 
 I I 4 3 I I I4 
 3 2 I . . 12 
 
 30 
 29 
 
 28 
 
 27 
 26 
 
 25 
 24 
 23 
 22 
 21 
 
 
 
 
 
 I . . . I 2 2 7 
 .. 3 I I I 7 
 
 2 . . 2 7 
 
 I I .. 8 
 
 I 6 
 
 I .. .. 4 
 
 2 
 
 2 
 
 2 
 
 20 
 19 
 18 
 
 
 
 
 
 I 
 
 2 
 
 No. 
 
 43 
 
 83 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 100 
 
 82 
 
 47 
 
 154 
 
 Age 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 II 
 
 12 
 
 13 
 
 14 
 
 15 
 
 Adult 
 
 The distribution of the shortest time trials from 1221 men and 
 boys is given in Table i and from 1009 women and girls in Table 
 1. The total number of cases examined for each age is stated 
 and the cases are then distributed by seconds. At the top of the 
 column, under the heading D. N. C. (Did Not Complete) is given 
 the number who were credited with failures through inability to 
 complete the first trial within the five minute limit. Above that, 
 under the heading F. (Failure) are placed those who after com- 
 
Treatment of Results 
 
 31 
 
 pleting the first trial, failed to give a completed trial on either the 
 second or the third trial. One boy comes within this group who 
 finished the first trial with several steps of instruction but upon 
 the second trial he had shown no evidence of ability to complete 
 the task at the end of five minutes. There are also included a 
 boy and a girl who had required several steps of instruction on 
 the first trial and then on both the second and third trial left ob- 
 servational errors. Those who succeeded on the first trial with 
 only the original instructions would be credited with this time as 
 their shortest if final errors were left on both the second and the 
 third trials, as happened in one instance. 
 
 TABLE III 
 QuiNTiLE Distribution — Boys 
 
 Age 
 
 No. 
 
 F. 
 
 30 
 
 Mean 
 
 S. D. 
 
 Min. 
 
 20% 
 69 
 
 40% 
 103 
 
 Med. 
 
 60% 
 
 80% 
 
 Max. 
 
 6 
 
 58 
 
 82.4,1 
 
 26.57 
 
 46 
 
 DNC 
 
 DNC 
 
 DNC 
 
 DNC 
 
 7 
 
 75 
 
 21 
 
 73 
 
 98 
 
 29.69 
 
 41 
 
 58 
 
 69 
 
 76.0 
 
 87 
 
 DNC 
 
 DNC 
 
 8 
 
 lOO 
 
 8 
 
 66 
 
 54 
 
 23.36 
 
 3:\ 
 
 50 
 
 59 
 
 63 
 
 5 
 
 68 
 
 88 
 
 DNC 
 
 9 
 
 IOC 
 
 13 
 
 52 
 
 48 
 
 11.98 
 
 26 
 
 43 
 
 49 
 
 52 
 
 9 
 
 57 
 
 72 
 
 DNC 
 
 lO 
 
 IOC 
 
 4 
 
 49 
 
 49 
 
 10.00 
 
 32 
 
 41 
 
 48 
 
 49 
 
 8 
 
 52 
 
 58 
 
 DNC 
 
 II 
 
 I GO 
 
 6 
 
 45 
 
 26 
 
 11-73 
 
 25 
 
 37 
 
 42 
 
 43 
 
 5 
 
 46 
 
 55 
 
 DNC 
 
 12 
 
 IOC 
 
 I 
 
 43 
 
 16 
 
 11.48 
 
 26 
 
 35 
 
 40 
 
 41 
 
 6 
 
 43 
 
 51 
 
 DNC 
 
 13 
 
 ICO 
 
 I 
 
 3« 
 
 66 
 
 8.40 
 
 23 
 
 32 
 
 3S 
 
 37 
 
 7 
 
 40 
 
 46 
 
 DNC 
 
 14 
 
 94 
 
 
 
 39 
 
 60 
 
 7-43 
 
 23 
 
 33 
 
 39 
 
 39 
 
 7 
 
 43 
 
 46 
 
 61 
 
 15 
 
 40 
 
 
 
 3« 
 
 «7 
 
 (>-3S 
 
 29 
 
 33 
 
 36 
 
 37 
 
 3 
 
 39 
 
 44 
 
 ^3 
 
 Ad. 
 
 354 
 
 
 
 34.20 
 
 7-34 
 
 18 
 
 28 
 
 32 
 
 33-S 
 
 3S 
 
 40 
 
 69 
 
 TABLE IV 
 
 QuiNTiLE Distribution — Girls 
 
 Age 
 
 No. 
 
 F. 
 
 Mean 
 
 S. D. 
 
 Min. 
 
 20% 
 
 40% 
 DNC 
 
 Med. 
 
 60% 
 
 80% 
 
 Max. 
 
 6 
 
 43 
 
 27 
 
 75-75 
 
 14-23 
 
 55 
 
 77 
 
 DNC 
 
 DNC 
 
 DNC 
 
 DNC 
 
 7 
 
 83 
 
 31 
 
 80 
 
 79 
 
 31-58 
 
 44 
 
 65 
 
 80 
 
 89.0 
 
 177 
 
 DNC 
 
 DNC 
 
 8 
 
 100 
 
 18 
 
 65 
 
 77 
 
 14-79 
 
 41 
 
 55 
 
 62 
 
 68.0 
 
 75 
 
 lOI 
 
 DNC 
 
 9 
 
 100 
 
 II 
 
 58 
 
 51 
 
 13-56 
 
 33 
 
 47 
 
 54 
 
 58-9 
 
 65 
 
 74 
 
 DNC 
 
 10 
 
 100 
 
 8 
 
 52 
 
 07 
 
 12.53 
 
 32 
 
 42 
 
 47 
 
 50.5 
 
 56 
 
 67 
 
 DNC 
 
 II 
 
 100 
 
 3 
 
 49 
 
 50 
 
 10.97 
 
 30 
 
 40 
 
 47 
 
 49-7 
 
 51 
 
 58 
 
 DNC 
 
 12 
 
 100 
 
 I 
 
 47 
 
 06 
 
 13-50 
 
 29 
 
 37 
 
 42 
 
 44-5 
 
 47 
 
 54 
 
 DNC 
 
 13 
 
 100 
 
 
 
 45 
 
 88 
 
 12.29 
 
 25 
 
 36 
 
 40 
 
 42.3 
 
 46 
 
 53 
 
 94 
 
 14 
 
 82 
 
 I 
 
 44 
 
 10 
 
 10 -43 
 
 27 
 
 36 
 
 41 
 
 42.2 
 
 46 
 
 51 
 
 DNC 
 
 15 
 
 47 
 
 2 
 
 45 
 
 71 
 
 14.81 
 
 26 
 
 3S 
 
 40 
 
 42.4 
 
 46 
 
 56 
 
 DNC 
 
 Ad. 
 
 154 
 
 
 
 3S 
 
 41 
 
 9.29 
 
 18 
 
 28 
 
 32 
 
 33-2 
 
 35 
 
 42 
 
 66 
 
 This material is presented in Tables 3 and 4, distributed by 
 quintiles and accompanied by means, standard deviations and 
 
32 The Witmer Cylinder Test 
 
 medians. These tables are identical in construction with those 
 of Young (19) on the formboard and Humpstone (4) on the mem- 
 ory span. The first column lists the ages, the second the total 
 number of cases examined, the third the number of failures, in 
 this case the term including both those listed as D. N. C. and the 
 failures in the previous tables. The mean has but little value in 
 a work such as this as it places undue emphasis upon the extreme 
 cases, particularly the slow ones. The median, on the other hand, 
 gives equal weight to all the cases. The time values of the mini- 
 mum, the maximum and the intervening quintiles are given, with 
 the cases of failure to complete the first trial (the D. N. C. group) 
 included in the distribution as the poorest group. 
 
 In an effort to determine whether we were warranted in placing 
 these failures in the upper quintiles, six control cases were used. 
 These were children whose qualitative performances were such as 
 to suggest that they were among the best of those who failed to 
 come within the time limit. We might expect that they would 
 profit most by a removal of the limit. These six were permitted 
 to complete the first trial and were then given the second and third 
 trials. A quintile distribution was then made for each sex on a 
 basis of the number completing the test, omitting all failures. 
 Placing these control cases in this new distribution, four of the 
 six children still fell in the fifth, or poorest, quintile, the other 
 two being raised to the second quintile. 
 
 Of those children requiring from 260 to 30c seconds to complete 
 the first trial, just within the limit, we find that for those below 
 the age of nine, three are in the first quintile, six in the second, 
 two in the third, two in the fourth and eleven m the fifth; of those 
 nine years of age or more, there are two whose shortest trial places 
 them in the first quintile, two in the second, three in the third, 
 five in the fourth and six in the fifth. These two control groups 
 give distributions which lead to the following conclusions: 
 
 (i) Had sufficient time been given to complete the first trial, 
 our failures of the ages six, seven and eight would have been dis- 
 tributed throughout the scale but would tend to fall largely in 
 the poorest half. 
 
 (2) This disposition does not do justice to the failures in the 
 ages of six and seven, for which years the standardization can 
 only be made by extending the time limit to such a point as will 
 permit almost the entire number to complete the first trial. 
 
Treatment of Results 33 
 
 (3) The distribution for the eighth year is not so seriously 
 affected, owing to the much smaller proportion of the failures, for 
 here we find that but few would fall in the higher quintiles. 
 
 (4) Above the age of eight the number of failures is quite small 
 and the evidence shows that they would fall almost entirely in 
 the last two quintiles. 
 
 (5) Such a completion of our material, then, might raise the 
 median and the sixty percentile slightly, but the proportion of 
 this change to the range of distribution would be small. The 
 boundary between the fourth and fifth quintiles would suffer the 
 greatest increase. 
 
 (6) The assignment of the failures to the upper end of the dis- 
 tribution is therefore justified. It gives a more reliable result 
 than would be obtained from the only alternative, a distribution of 
 successful cases, the failures being discarded. 
 
 A graphical representation of the material of Tables i and 2 is 
 given in Graphs i and 2, distributed by quartiles. These curves 
 show with increasing age a steady decrease in time of performance 
 and a decrease in the range of the quartiles. The minimum line 
 has this same tendency but is subject to the influence of individ- 
 ual exceptional cases. The line of the lower quartile shows a 
 steady decrease and a smooth curve in each table. The displace- 
 ment in the median line at ten years for boys and eleven years 
 for girls is probably due to a greater proportion of children from 
 the poorer social group. The quota of boys in the last half of 
 the tenth year and of the giris in the first half of the eleventh 
 year had not been filled when the examination of the other ages 
 had been completed, so the remaining cases were taken 
 from the school then being used, which was one of those described 
 as being of the poorer class. The rise in the median and upper 
 quartile of fourteen year old boys has been explained as has the 
 rise in the upper quartile for fifteen year old giris. The maximum 
 curve is not drawn because of the inclusion of the D. N. C. cases 
 
 at this end. 
 
 The most comprehensive graphical representation of any dis- 
 tribution is given by the percentile curve. The grouping of the 
 curves for the various ages as is done in Graphs 3 and 4, permits a 
 comparison of the results of any individual with those of the other 
 ages as well as with those of his own age. In formulating the curves 
 given here, a variation from the accepted method was necessary 
 
34 
 
 The Witmer Cylinder Test 
 
 at the lower end. As the failures are placed here, each line is 
 begun at that point at which the slowest case occurs. Thus, eight 
 ten year old girls of the hundred failed to complete the test, the 
 ninth had a record of 94 seconds. The curve for ten year old 
 girls is therefore begun at 9 per cent, 94 seconds. 
 
 To find the percentile rating of an individual, follow the vertical 
 
 GRAPH I 
 
 QuARTiLE Distribution 
 Boys 
 
 D.N. C 
 
 T 
 
 \ 
 
 
 
 
 
 
 
 
 
 90 
 80 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 70 
 60 
 
 g 50 
 
 
 u 
 u 
 
 M 40 
 30 
 
 1 
 
 \ 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 \, 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 \ 
 
 \ 
 
 
 
 
 
 
 \ 
 
 
 
 ■^ 
 
 \ 
 
 ^ 
 
 
 -— 
 
 
 
 
 \ 
 
 S^ 
 
 > 
 
 V 
 
 "^^ 
 
 
 
 
 
 
 
 
 N 
 
 y 
 
 N 
 
 -— 
 
 ^ 
 
 
 /" 
 
 V 
 
 20 
 
 
 10 
 
 
 
 
 
 
 
 
 
 
 — N 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 10 II 
 
 AGE 
 
 13 14 15 Ad. 
 
 line corresponding to the number of seconds of his shortest trial 
 to its intersection with the curve of his age. At this point the 
 horizontal per cent line indicates where he falls in the distribution 
 of individuals of that age. By way of illustration, to determine 
 the rating of a twelve year old boy who has performed the test 
 in 2,!^ seconds, follow the 'T>'i second line to the intersection with 
 the twelve year old curve, which will be seen to be at 82 per cent, 
 which means that this boy has done better than four-fifths of the 
 boys of that age, or to be more exact, that 8 1 per cent have done 
 more poorly than he and 18 per cent have performed more quickly. 
 
Treatment of Results 
 
 35 
 
 The comparison of a boy with others of his age is more import- 
 ant than comparing him with the standards of other ages, but if 
 it should be desired to do this, it is only necessary to run along the 
 2S second line, to use the same case again, and note the points at 
 which the other curves cross. Thus, 35 seconds is the 89 per cent 
 performance of eleven year old boys, the 67 per cent performance 
 
 GRAPH II 
 
 QuARTiLE Distribution 
 Girls 
 D. N. C. 
 
 90 
 
 80 
 70 
 60 
 
 50 
 40 
 30 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 \\ 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 \, 
 
 
 
 
 
 
 \, 
 
 \ 
 
 
 \ 
 
 \ 
 
 
 
 
 ^ 
 
 \ 
 
 \ 
 
 .^ 
 
 
 
 
 
 , 
 
 
 
 V ^ 
 
 
 
 
 
 
 \ 
 
 . , 
 
 
 
 ~-~_____ 
 
 
 
 ^ 
 
 - 
 
 
 
 
 
 
 
 
 
 "^ 
 
 --^ 
 
 — 
 
 N, 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 10 II 
 Age 
 
 13 
 
 14 15 Ad. 
 
 of thirteen year old boys and is the point below which 42 per cent 
 of adults fall. 
 
 Each age as used here includes all the individuals up to the suc- 
 ceeding birthday. That is, by the nine year group is meant that 
 year group having a median age of nine and five-tenths years. 
 Various divisions have been used in other works, such as includ- 
 ing all as nine years who are between eight and a half and nine 
 and a half years, or including those who are within a month of 
 the birthday. In view of the fact that we are accustomed to 
 
36 
 
 The Witmer Cylinder Test 
 
 Per Cent. 
 
 lOO 
 
 90 
 
 70 
 
 60 
 
 30 
 
 20 
 
 GRAPH III 
 
 Percentile Curves 
 Boys 
 
 50 :q 
 
 40 
 
 30 
 
 40 
 
 50 60 
 
 Seconds 
 
 70 
 
 80 
 
 90 
 
 100 
 
 speak of a child as being nine years of age until he reaches his 
 tenth birthday, such divisions often result in a misinterpretation 
 of results. It has therefore seemed advisable to use this group- 
 ing and to take half of the cases from the lower half-year and half 
 from the upper, except in the ages seven and fourteen which have 
 been previously discussed. 
 
Treatment of Results 
 
 37 
 
 Per Cent. 
 
 90 
 
 70 
 
 60 
 
 50 
 
 40 
 
 30 
 
 20 
 
 GRAPH IV 
 
 Percentile Curves 
 Girls 
 
 30 
 
 40 
 
 50 60 
 
 Seconds 
 
 70 
 
 90 
 
 Sex Differences 
 In performance tests more than in any other kind are sex dif- 
 ferences to be found. Experimental evidence of this was pre- 
 sented as early as 1900 by Bagley (i) who found that boys gave 
 better results on tests in the psycho-motor field, Wallin (14) and 
 Young (19) find a sex difference favoring boys on the form board, 
 
38 The Witmer Cylinder Test 
 
 while Wooley and Fischer (17) declare the puzzle box to be the 
 only test in which they found a great sex difference, boys being 
 much more successful with this. Mrs. Young (18), in an earlier 
 study of the cylinder test in which she has worked out a correla- 
 tion with the formboard, has pointed out a distinct sex difference 
 and has attributed it to the fact that the formboard presents a 
 different problem for men and for women. This is equally true 
 of the cylinder test. 
 
 This factor can best be observed in our present results by super- 
 imposing Graphs i and 2. It will be seen here that the minimum 
 line of the boys is below that of the girls except at ten years, 
 where they are equal, and at fifteen, where that of the 
 girls tails below. The lower quartile line for girls falls 
 midway between the lower quartile and median lines of the boys 
 and the median line for girls falls midway between the median 
 and the upper quartile lines for boys up to the age of fifteen. The 
 upper quartile runs far behind for girls up to adult. 
 
 While the points for adults coincide at the median, lower quartile 
 and minimum, it is to be noted that the men's group consists of 
 fifty per cent good and fifty per cent poor cases while the records 
 of women are taken from the good group alone, university stu- 
 dents. The figures for the women are given in Table 7, page 48, 
 accompanying those of the three groups of men and show that up 
 to and including the median, the women rank above the college 
 men and prisoners and behind the aviation cadets. They are 
 much behind the college men at the upper quartile and maximum 
 which has the effect of making the median and average deviation 
 higher. 
 
 Probably the most important factor in producing this difference 
 is the attitude with which the test is approached. Boys and men 
 quite generally show a spirit of competitiveness, attempting to 
 make the best time record that they can. Girls of the upper ages 
 and women attempt to determine how to do the test rather than 
 how to do it the most quickly. They seem satisfied if they do it 
 at all, refuse to hurry, or when they do try to rush, become con- 
 fused. As a whole, the sexes show a difference of poise when 
 facing a performance test. 
 
IV 
 QUALITATIVE ASPECTS 
 
 If by intelligence we mean "the ability to solve that which for 
 the individual is a new problem," the cylinder test as here pre- 
 sented is not a test of intelligence primarily. In practically all 
 cases, the best trial occurs after the nature of the problem has 
 been learned. If on the first trial, it is because the end to be at- 
 tained has been seen before the test is actually performed. It 
 does, however, offer a problem to children from six to nine years 
 of age. For children at this stage, the test presents the question, 
 "How can this be done?" Above this age, the question becomes, 
 "How can this be done the most quickly?" To be sure, they 
 may not appreciate the order of the blocks before the third trial, 
 or possibly not at all, but the correct solution they do foresee. 
 
 The first trial, then, is a learning trial for one doing the test for 
 the first time, or a relearning trial for one who has done it before. 
 For those ages within which a problem is set, the amount of in- 
 struction necessary to enable the child to learn how to perform 
 the task is a measure of the intelligence and it was for this reason 
 that the method of smallest didactic steps was adopted. Can the 
 child grasp the problem when the board is presented to him? If 
 not, can he determine what should be done when told that his 
 solution is not the correct one? Can he find a way of making all 
 the cylinders fit when told that they must be level with the top? 
 
 Will one successful placement suggest to him the manner of 
 correcting other errors? The qualitative differences between the 
 normal and the feeble-minded appear most strongly here. Not 
 infrequently, especially in the upper ages, the shortest time trial 
 is fairly satisfactory in low grade cases, but the mental status is 
 suggested in any of these by the performance upon the initial trial. 
 
 In an article on "The Relation of Intelligence to Efficiency" 
 (i6). Professor Witmer presents the proposition that twelve per- 
 formance scales are necessary to grade and level an individual, 
 
 39 
 
40 The Witmer Cylinder Test 
 
 the intelligence level being measured by the invention scale and the 
 resource scale, the proficiency level by the efficiency scale and the 
 operation scale. The general proficiency of an individual is a 
 complex of the efficiency (a term confined to single operations) 
 and the number of operations over which efficiency may be shown. 
 The measurement of efficiency by the cylinder test would re- 
 quire a large number of trials; in confining ourselves to three trials 
 and using the shortest time trial as an index, we are rather making 
 a determination of the competency in this one field of operations, 
 the psycho-motor. Competency is here used in a more limited 
 sense but with the same general meaning as in the above article. 
 By competency in this sense is meant the sum total of all the fac- 
 tors, mental and physical, operative in a particular performance. 
 As Professor Witmer has shown, the effect of competency upon 
 efficiency lies not so much in the ultimate degree as in the rate 
 of its attainment. Using this more limited meaning of competency, 
 it would perhaps be better to say that proficiency is determined 
 by the number of fields of operations in which competency may 
 be shown. 
 
 It is in the qualitative aspects that the superiority of the cyl- 
 inder test lies. Any performance test which is going to with- 
 stand the culling that is sure to follow the standardization of a 
 large number, must have features which differentiate it from other 
 tests. The principal advantages possessed by the cylinder test 
 seem to us to be: 
 
 (i) Distributive attention may be brought out better in this 
 test than in any other so far standardized. Unlike other factors 
 which may or may not appear, this may always be observed. 
 The one-hand worker, who cannot distribute attention sufficiently 
 to work well with both hands, the individual who uses both hands 
 until a situation arises, when he forgets all about the blocks he 
 is holding in one of them, the one who places a block with one 
 hand while engaged in picking up another to fit a recess in another 
 part of the board, these are types which are brought out clearly 
 by this test. 
 
 (2) There are certain steps in performance which seem to 
 appear with increasing age. The distinguishing between Series 
 A and Series B, that is, to tell on which side of the board a given 
 block belongs, or distinguishing the direction of decrease in size 
 in Series C, and again, the estimation of distance on Series C, 
 
Qualitative Aspects 41 
 
 these appear in succession with an interval of several years. Chil- 
 dren up to the age of ten quite generally try any small block in 
 some C recess and then pass in either direction by adjacent steps 
 until the correct recess is found. At ten, the direction is generally 
 correct, or is quickly corrected. Later there appears a knowledge 
 of the nature of this series, and from thirteen years on, it is quite 
 usual to find an estimation being made of the approximate posi- 
 tion both in the placement and in correction. The use of two 
 hands also appears at about the age of nine, being unusual before 
 and usual after that age. 
 
 Method also becomes increasingly complex with increasing age. 
 The younger children take the blocks as they happen to pick 
 them up, or even begin to work with the smaller ones. The best 
 children of five or six years work at one recess at a time, taking a 
 block they think will fit, discarding it for one slightly larger until 
 they find the correct one, then go to the next recess and repeat the 
 performance. After age seven, blocks are seldom discarded, but 
 an attempt is made to find where they belong by trial and error. 
 This age finds children placing the upper two series systematically 
 and then filling C at random. Next, the use of logical procedure 
 is continued through C with a tendency to drop away from it be- 
 fore the test has been completed, or with the first bit of trouble 
 in placing a cylinder. Not until the age of eleven or twelve do 
 we find adherence to a system throughout the entire trial. Yet, 
 even with adults, it is quite usual to see these theoretically best 
 methods of solution dropped where there is increased ability due 
 to speed or distribution of attention. Failures to use methods 
 appropriate to the age, therefore, must be interpreted in the light 
 of the entire performance. The fact that they are not used will 
 be less significant often than the positive fact of their use. 
 
 This is not meant to be a definite statement of just what occurs 
 at different ages, for the data is insufficient. It is merely meant 
 to point out distinctive qualitative difi^erences that do appear 
 and which suggest that a qualitative standardization, comparable 
 to the standardiit:ation of errors in certain other performance tests, 
 can greatly increase the value of this test for diagnostic purposes. 
 An attempt to carry this out along with this investigation resulted 
 only in a determination of the nature of the problem, and the set- 
 ting forth of the preliminary classifications. 
 
42 The Witmer Cylinder Test 
 
 (3) Another advantage of this test is the large number of move- 
 ments required. Our conclusions regarding the mental processes 
 of a child are drawn from the observation of his behavior, there- 
 fore, the more points at which behavior may be observed, that is, 
 the more adequately behavior represents the mental steps, the 
 better are we enabled to form judgments regarding the mental 
 operations. 
 
 Young (20) has called attention to the necessity of distinguish- 
 ing between the real extent of any capacity and the amount that 
 may be brought out by a single test. He has used the words 
 epideixis and hyparxis, meaning by the former the power dis- 
 played on a particular occasion and by the latter the power that 
 the individual is capable of displaying. It is the hyparxis re- 
 garding which we desire information and this can only be reached 
 through the epideixis. The nearer the epideixis approaches the 
 hyparxis, the more valuable our test results. The more chances 
 we have of observing any process, the greater the probability of 
 a correct estimation of the hyparxis. The number of possibil- 
 ities of the repetition of similar situations gives more chance of 
 a satisfactory observation than could be obtained from a test in 
 which but a few moves are made. The number of moves in re- 
 placing the cylinders is usually much greater than the minimum, 
 for false placements appear in all but the most careful perform- 
 ances. 
 
V 
 
 THE RELATION OF CYLINDER TEST PERFORMANCE 
 TO PROFICIENCY 
 
 If our hypothesis is warranted, that the cylinder test is a test 
 of competency in the psycho-motor field and to that extent is a 
 measure of proficiency, we should expect to find a relationship 
 existing between the performance of this test and the proficiency 
 that the individual has displayed. For the investigation of this, 
 three fields have been chosen, school standing as a basis of the 
 study of children, adults of three levels of daily performance, and 
 mechanical or manual ability as shown in shop ratings. 
 
 Age-Grade Distribution 
 
 The school grade of a child is the only general measure we have 
 of his proficiency. That we speak of a child as being "at age" or 
 "over age" for his grade is evidence that a normal child is expect- 
 ed to be in a certain grade at a certain age. There are many 
 factors tending to nullify this as a measure, not the least of which 
 is the custom of school authorities of retaining a child in a grade 
 higher or lower than that to which his ability entitles him. But 
 taken as a whole, the grade is usually considered as a measure of 
 a child's daily performance. 
 
 Tables 5 and 6 give separately for boys and girls the distribu- 
 tion of shortest time trials by age and grade. The first column 
 gives the grade, the second, the number of cases credited with a 
 shortest trial, omitting those included under D. N. C. (Did Not 
 Complete) and Failure of the preceding tables, both of which are 
 included under F. (Failures) in the third column. The mean, 
 average deviation and median of the successful cases is given, 
 with the minimum, maximum and the upper and lower quar- 
 tiles where the number of cases is sufficiently large to make this 
 at all indicative. 
 
 These values differ from those in Chapter 3, where the F. cases 
 were considered as in the poorer quartiles, but for purposes of 
 
 43 
 
44 
 
 The Witmer Cylinder Test 
 
 comparison of parts of an age group, this is much more concrete. 
 However, this changes the distribution previously given to a 
 negligible amount above the eighth year, except in the cases in 
 the third grade. 
 
 It will be observed that for Age 7, the number of failures, the 
 mean, median, A. D., and maximum decrease with increasing 
 
 
 
 
 
 TABLE V 
 
 
 
 
 
 
 
 
 Age-Grade Distributio 
 
 N^BOYS 
 
 
 
 Gr. 
 
 No. 
 
 F. 
 
 Mean 
 
 A. D. 
 
 Age 7 
 
 Min. 
 
 L.Q. 
 
 Med. 
 
 U.Q. 
 
 Max. 
 
 I 
 
 12 
 
 7 
 
 86.2 
 
 20.7 
 
 53 
 
 65 
 
 78.0 
 
 39 
 
 137 
 
 2 
 
 37 
 
 14 
 
 72-3 
 
 18.5 
 
 43 
 
 58 
 
 63.0 
 
 74 
 
 195 
 
 3 
 
 5 
 
 
 
 56.8 
 
 15-4 
 Age 8 
 
 41 
 
 
 48.0 
 
 
 78 
 
 I 
 
 6 
 
 2 
 
 84.7 
 
 26.3 
 
 43 
 
 - 
 
 84.0 
 
 - 
 
 121 
 
 2 
 
 34 
 
 3 
 
 70.6 
 
 16.3 
 
 37 
 
 55 
 
 68.0 
 
 72 
 
 152 
 
 3 
 
 45 
 
 3 
 
 62.9 
 
 13-4 
 
 :!,?, 
 
 51 
 
 59.0 
 
 69 
 
 144 
 
 4 
 
 6 
 
 
 
 55-3 
 
 14. 1 
 
 40 
 
 - 
 
 48.5 
 
 - 
 
 91 
 
 5 
 
 I 
 
 
 
 49.0 
 
 Age 9 
 
 
 
 49 -o 
 
 
 
 I 
 
 I 
 
 I 
 
 52.0 
 
 
 
 
 52.0 
 
 
 
 2 
 
 20 
 
 I 
 
 53-9 
 
 II. 8 
 
 31 
 
 43 
 
 54-5 
 
 67 
 
 79 
 
 3 
 
 30 
 
 8 
 
 54-7 
 
 9.6 
 
 37 
 
 48 
 
 51.0 
 
 61 
 
 90 
 
 4 
 
 28 
 
 3 
 
 50.5 
 
 8.3 
 
 2,^ 
 
 43 
 
 50.5 
 
 60 
 
 71 
 
 5 
 
 4 
 
 
 
 46.8 
 
 91 
 
 39 
 
 - 
 
 41-5 
 
 - 
 
 65 
 
 6 
 
 4 
 
 
 
 40.7 
 
 7.6 
 Age ic 
 
 26 
 
 
 44.0 
 
 
 49 
 
 I 
 
 I 
 
 
 
 53 -o 
 
 
 
 
 53 -o 
 
 
 
 2 
 
 4 
 
 
 
 55-0 
 
 4.0 
 
 49 
 
 - 
 
 56.5 
 
 - 
 
 60 
 
 3 
 
 10 
 
 3 
 
 54-5 
 
 II. 5 
 
 34 
 
 - 
 
 52.8 
 
 - 
 
 78 
 
 4 
 
 46 
 
 
 
 49.8 
 
 (>-s 
 
 32 
 
 43 
 
 50.5 
 
 54 
 
 72 
 
 5 
 6 
 
 30 
 
 I 
 
 47-1 
 
 8-3 
 
 32 
 
 38 
 
 47-5 
 
 SZ 
 
 72 
 
 5 
 
 
 
 46.0 
 
 8.0 
 
 37 
 
 - 
 
 43 -o 
 
 
 62 
 
 
 
 
 
 Age II 
 
 
 
 
 
 
 I 
 
 I 
 
 I 
 
 92-° 
 
 
 
 
 93 -o 
 
 
 
 2 
 
 
 
 I 
 
 
 
 
 
 
 
 
 3 
 
 
 
 I 
 
 
 
 
 
 
 
 
 4 
 
 23 
 
 2 
 
 48.2 
 
 II. 
 
 32 
 
 37 
 
 43-2 
 
 58 
 
 108 
 
 1 
 
 35 
 
 I 
 
 42.7 
 
 6.0 
 
 25 
 
 38 
 
 42.8 
 
 47 
 
 67 
 
 :i?, 
 
 
 
 43-6 
 
 ^■2 
 
 30 
 
 39 
 
 43 -o 
 
 51 
 
 (>2 
 
 7 
 
 2 
 
 
 
 42.0 
 
 2.0 
 Age 12 
 
 40 
 
 
 42.0 
 
 
 44 
 
 4 
 
 7 
 
 
 
 43-7 
 
 5-0 
 
 35 
 
 - 
 
 42.8 
 
 _ 
 
 61 
 
 5 
 6 
 
 22 
 
 
 
 43.8 
 
 7.2 
 
 28 
 
 37 
 
 44-5 
 
 51 
 
 66 
 
 41 
 
 
 
 43-7 
 
 9.2 
 
 26 
 
 37 
 
 41.2 
 
 48 
 
 105 
 
 7 
 8 
 
 21 
 
 I 
 
 40.0 
 
 7-4 
 
 26 
 
 34 
 
 38.2 
 
 44 
 
 63 
 
 7 
 
 
 
 47 -o 
 
 9-4 
 
 38 
 
 - 
 
 41.8 
 
 
 65 
 
The Relation of Cylinder Test Performance to Proficiency 45 
 
 
 
 
 
 TABLE V 
 
 — Continued 
 
 
 
 
 Gr- 
 
 No. 
 
 F. 
 
 Mean 
 
 A. D. 
 
 Age 
 
 Min. 
 13 
 
 L.Q. 
 
 Med. 
 
 U.Q. 
 
 Max. 
 
 4 
 
 I 
 
 
 
 38.0 
 
 
 
 
 38.0 
 
 
 
 5 
 
 8 
 
 
 
 40.9 
 
 4-4 
 
 32 
 
 - 
 
 40.5 
 
 - 
 
 50 
 
 6 
 
 27 
 
 I 
 
 39-9 
 
 7-1 
 
 27 
 
 34 
 
 40.4 
 
 46 
 
 67 
 
 7 
 
 32 
 
 
 
 36.3 
 
 5.6 
 
 23 
 
 30 
 
 34-5 
 
 42 
 
 52 
 
 8 
 
 31 
 
 
 
 38.3 
 
 6.6 
 
 Age 
 
 26 
 14 
 
 32 
 
 37-6 
 
 42 
 
 64 
 
 4 
 
 3 
 
 
 
 37-0 
 
 6.0 
 
 31 
 
 - 
 
 340 
 
 - 
 
 46 
 
 5 
 
 7 
 
 
 
 41.9 
 
 5-0 
 
 2,(^ 
 
 - 
 
 39-0 
 
 - 
 
 S3 
 
 6 
 
 24 
 
 
 
 38.2 
 
 5-3 
 
 23 
 
 35 
 
 39-0 
 
 44 
 
 51 
 
 7 
 
 22 
 
 
 
 40.1 
 
 7.2 
 
 27 
 
 34 
 
 38.8 
 
 46 
 
 61 
 
 8 
 
 31 
 
 
 
 40.9 
 
 5-2 
 
 Age 
 
 26 
 15 
 
 37 
 
 42.2 
 
 45 
 
 54 
 
 4 
 
 2 
 
 
 
 32.5 
 
 ZS 
 
 29 
 
 - 
 
 32.5 
 
 - 
 
 36 
 
 5 
 
 I 
 
 
 
 33 -o 
 
 
 
 
 33 
 
 
 
 6 
 
 8 
 
 
 
 37-6 
 
 5-4 
 
 32 
 
 - 
 
 35-0 
 
 - 
 
 S3 
 
 7 
 
 5 
 
 
 
 37-8 
 
 2.2 
 
 34 
 
 - 
 
 37-2 
 
 - 
 
 43 
 
 8 
 
 14 
 
 
 
 37-6 
 
 4-9 
 
 30 
 
 32 
 
 36.5 
 
 40 
 
 52 
 
 
 
 
 
 TABLE VI 
 
 
 
 
 
 
 
 
 Age-Grade Distribution — Girls 
 
 
 
 Gr. 
 
 No. 
 
 F. 
 
 Mean 
 
 A. D. 
 
 Age 
 
 Min. 
 7 
 
 L.Q. 
 
 Med. 
 
 U.Q. 
 
 Max 
 
 I 
 
 12 
 
 15 
 
 84.0 
 
 26.2 
 
 49 
 
 59 
 
 69.0 
 
 90 
 
 188 
 
 2 
 
 36 
 
 16 
 
 80.3 
 
 18.2 
 
 44 
 
 62 
 
 75-2 
 
 82 
 
 205 
 
 3 
 
 4 
 
 
 
 75-5 
 
 9-5 
 
 Age 
 
 65 
 8 
 
 
 72.5 
 
 
 92 
 
 I 
 
 I 
 
 4 
 
 62.0 
 
 
 
 
 62.0 
 
 
 
 2 
 
 45 
 
 6 
 
 69.7 
 
 'i^:!>-2, 
 
 41 
 
 58 
 
 68.8 
 
 81 
 
 105 
 
 3 
 
 24 
 
 5 
 
 63.1 
 
 10. 1 
 
 46 
 
 S3 
 
 59-5 
 
 70 
 
 95 
 
 4 
 
 12 
 
 2 
 
 56.5 
 
 9.6 
 
 42 
 
 46 
 
 55-0 
 
 62 
 
 91 
 
 5 
 
 
 
 I 
 
 
 Age 
 
 9 
 
 
 
 
 
 2 
 
 5 
 
 3 
 
 77.2 
 
 II. 8 
 
 55 
 
 — 
 
 75.0 
 
 — 
 
 99 
 
 3 
 
 25 
 
 6 
 
 54-4 
 
 8.4 
 
 z(> 
 
 46 
 
 54.0 
 
 64 
 
 69 
 
 4 
 
 49 
 
 2 
 
 61 .4 
 
 II. 7 
 
 zs 
 
 48 
 
 54.8 
 
 70 
 
 98 
 
 5 
 
 7 
 
 
 
 54.0 
 
 12.0 
 
 2Z 
 
 - 
 
 54-0 
 
 - 
 
 78 
 
 6 
 
 I 
 
 
 
 74.0 
 
 Age 
 
 10 
 
 
 74.0 
 
 
 
 2 
 
 I 
 
 
 
 72.0 
 
 
 
 
 72.0 
 
 
 
 3 
 
 5 
 
 3 
 
 52.2 
 
 9-4 
 
 39 
 
 - 
 
 56.0 
 
 - 
 
 66 
 
 4 
 
 43 
 
 2 
 
 51.0 
 
 8.7 
 
 34 
 
 45 
 
 48.0 
 
 58 
 
 75 
 
 5 
 
 30 
 
 2 
 
 51-9 
 
 II. 7 
 
 32 
 
 43 
 
 46.5 
 
 60 
 
 94 
 
 6 
 
 13 
 
 I 
 
 54.2 
 
 10.3 
 Age 
 
 39 
 II 
 
 48 
 
 50.0 
 
 ss 
 
 85 
 
 3 
 
 5 
 
 
 
 52.4 
 
 7-9 
 
 23 
 
 - 
 
 55-0 
 
 - 
 
 ^J 
 
 4 
 
 9 
 
 3 
 
 51-0 
 
 5.8 
 
 3(^ 
 
 47 
 
 51.0 
 
 57 
 
 60 
 
 5 
 
 34 
 
 
 
 50.9 
 
 II. 6 
 
 32 
 
 40 
 
 47.0 
 
 S9 
 
 98 
 
 6 
 
 47 
 
 
 
 46.7 
 
 6.6 
 
 30 
 
 41 
 
 48.2 
 
 S3 
 
 66 
 
 Z, 
 
 2 
 
 
 
 53-5 
 
 6.5 
 
 
 
 S3-S 
 
 
 
46 
 
 The Witmer Cylinder Test 
 
 TABLE VI— Continued 
 
 Gr. No. 
 
 Mean 
 
 I 
 6 
 
 21 
 
 38 
 27 
 
 6 
 
 I 
 
 5 
 8 
 
 23 
 41 
 21 
 
 2 
 
 5 
 
 13 
 
 16 
 
 42 
 
 50. 
 51. 
 44 
 46 
 46, 
 41 
 
 A. D. Min. 
 Age 12 
 
 L. Q. Med. U. Q Max. 
 
 17.9 
 10.7 
 
 6.9 
 II .0 
 
 8.2 
 
 40 
 
 29 
 29 
 29 
 
 Age 13 
 
 II. 2 
 
 7.0 
 9.2 
 
 lO.I 
 
 7-4 
 
 37 
 36 
 
 28 
 
 27 
 25 
 
 Age 14 
 
 42 
 36 
 
 30 
 
 27 
 
 44.2 
 42.6 
 50.5 
 
 45 
 
 Age 15 
 
 6.7 34 
 12.4 28 
 
 ID. I 38 
 10.9 26 
 
 39 
 38 
 39 
 
 36 
 39 
 36 
 
 37 
 38 
 36 
 
 36 
 
 69.0 
 
 47 -o 
 44.0 
 
 45-5 
 43-2 
 43-5 
 
 50.0 
 46.0 
 41. o 
 48.6 
 42.8 
 39-9 
 
 49.0 
 37-2 
 
 47.0 
 12.0 
 
 54 
 49 
 
 52 
 
 53 
 49 
 46 
 
 57 
 47 
 
 50 
 
 96 
 85 
 79 
 99 
 
 54 
 
 65 
 65 
 
 63 
 
 72 
 63 
 55 
 98 
 65 
 
 50 
 93 
 
 77 
 78 
 
 grade. The decreasing proportion of failures is particularly sig- 
 nificant. The Age 8 distribution shows a decrease in the percent- 
 age of failures with increasing grade and a decreasing mean, median, 
 A. D. and quartiles for both sexes. In Age 9, the third grade 
 boys, whom we may consider "at age," show to disadvantage as 
 compared with the second grade boys, there being a marked in- 
 crease in the number of failures. Those in the fourth are better 
 throughout and the fifth and sixth grade boys are still better. 
 In the girls' group, with the exception of the single case in the sixth 
 grade, there is an increase in ability with increasing grade, though 
 the fourth grade girls do slightly worse, other than in failures, 
 than the third grade girls. The Age 10 boys show a steadily 
 decreasing time and failure distribution, particularly favoring the 
 sixth grade. The girls of this age show a similar distribution, 
 with the exception of the sixth grade, where their performances 
 are poorer than in either of the two preceding grades. The next 
 age shows the same general tendency, but with the exception of a 
 slight advantage favoring the fifth grade over the sixth grade 
 boys. In this group, the two year advanced boys give the best 
 
The Relation of Cylinder Test Performance to Proficiency 47 
 
 results but the girls do poorly, though there are only two cases 
 of each. The same tendency appears in Age 12 as in the previous 
 ages, but here, for once, the girls who are two years in advance do 
 better while the boys of that grade do poorer work than the "at 
 age" boys. From this point on, the evidence is not so conclusive, 
 though there is a general tendency favoring the "at age" as com- 
 pared with the one year "over age." But the "above age" do 
 not do so well and those several grades behind show up to better 
 advantage than in the younger years. This is probably to be 
 attributed to the higher specialization in the upper grades, where 
 intellectual abilities are demanded and where the capacities 
 brought out in this test are not so important. 
 
 The tendency of these distributions shows, then, that there is 
 an increase in cylinder test performance with increasing pedagog- 
 ical age, which is the best measure we have of the general pro- 
 ficiency of children. A similar correspondence between pedagog- 
 ical age and mental test results was found by Stern (11) with the 
 Binet Scale and by Humpstone (4), who found that the number 
 of pupils successful in repeating a given series of digits increased 
 with each successively higher grade. 
 
 Adult Performances 
 The three groups of adults used in Chapter 3 represent three 
 grades of proficiency. That the inmates of our penal institutions 
 represent a low grade of proficiency need but be said. Some of 
 them have been engaged in branches of crime in which they have 
 shown themselves to have ability which, rightly directed, would 
 have made them successful in the business world and the acci- 
 dental criminal is often a man of good mental ability, but these 
 cases are few. Basing an estimate upon a previous investigation 
 of the writer (5), one-fifth of the prisoners would be comparable 
 in intelligence to a college group and would fall almost entirely 
 within the lowest quartile of the latter. It is generally con- 
 ceded that a college group ranks higher in general proficiency than 
 a non-college group picked at random from normal individuals 
 of the same age. A more proficient group than that of the men 
 from the Aviation Section of the Signal Enlisted Reserve Corps, 
 in training at an army aviation field, is not readily available. 
 The mental and moral examination for entrance is most rigid, 
 past performances in school and business being given considera- 
 
48 
 
 The Witmer Cylinder Test 
 
 tion in connection with the decision as to mental ability. There 
 are some, it is true, whom we would not class as among the high- 
 est in proficiency, but by far the greater number would fall within 
 the highest quartile of the college group used in this study. 
 
 The distribution of the shortest trial performances of these three 
 groups is given in Table 7, and in it is included that of university 
 women, which was used in the discussion of sex differences in a 
 previous chapter. The lower quartile, median and upper quartile, 
 as well as the less reliable mean and the mode, place the aviation 
 cadets first, the college men two seconds behind (and two seconds 
 is not an inconsequential interval where fifty per cent fall within 
 seven seconds), while the prisoners trail far in the rear. The 
 better half of the women rank above the better half of the college 
 
 TABLE VII 
 
 Distribution of Performances of Adult Groups 
 
 
 College Men 
 
 Aviation Cadets 
 
 Prisoners 
 
 College Women 
 
 No. of Cases 
 
 123 
 
 54 
 
 791 
 
 154 
 
 Mean 
 
 33-2, 
 
 32.0 
 
 38.1 
 
 35-4 
 
 A. D. 
 
 4.6 
 
 4.8 
 
 7-5 
 
 7-2 
 
 Mode 
 
 34(31) 
 
 32(29) 
 
 37 
 
 32 
 
 Minimum 
 
 20 
 
 22 
 
 18 
 
 18 
 
 L. Quartile 
 
 30 
 
 28 
 
 31 
 
 29 
 
 Median 
 
 34 
 
 32 
 
 37 
 
 33 
 
 U. Quartile 
 
 31 
 
 35 
 
 44 
 
 41 
 
 Maximum 
 
 51 
 
 46 
 
 115 
 
 66 
 
 men, but as in the case of the prisoners, the frequency of poor 
 performances in the slower half causes the mean and upper quar- 
 tile to be much poorer than those of the other two groups. The 
 figures for the prisoners might have been improved slightly had 
 the test been given to every man who entered during the period 
 of gathering this material, but it was many times omitted in those 
 cases in which the performance ability was shown to be good by 
 other tests, when time could not be taken to give tests not essential 
 to that particular examination. 
 
 A comparison of these figures leads us to the conclusion that 
 there is, in general, a direct relation between proficiency, as 
 judged by the level of daily performance, and cylinder test per- 
 formance among adults. 
 
The Relation of Cylinder Test Performance to Proficiency 49 
 
 Correlation with Shop Rating 
 
 This investigation was the outgrowth of the observation at 
 the Indiana Reformatory that many men, particularly of the 
 colored race, whose mental age according to the Binet Scale was 
 so low as to indicate that they were seriously deficient mentally, 
 were nevertheless successful in the performance of quite compli- 
 cated shop tasks. A tendency of the results of the cylinder test 
 to give a higher rating in these cases than did the Binet Scale, 
 suggested a comparison of such results with shop ability. 
 
 Eight shops of that institution were chosen for this study, in 
 each of which the men are received in most cases without pre- 
 vious training, to be taught the trade. The instructor in charge 
 of each of these shops was asked to name his most skillful work- 
 man, the poorest workman, the next in skill, the next poorest, 
 and then the shop roll was examined to find men who could be 
 placed between these two extremes in a rank order.* All men 
 were eliminated from consideration who were not giving consistent 
 effort, thus confining the ranking to a basis of skill and effi- 
 ciency. Ten men were so rated in each of the shops, except 
 the tin shop, where eight men were reported. 
 
 Table 8 presents the correlation between this rank order and 
 the rank order of cylinder test performance, according to the 
 method of Rank-Differences, as presented by Whipple (15). 
 
 Assuming that the cylinder test measures that ability which is 
 demanded in manual or mechanical work, a correlation with shop 
 ability is the best experimental means of determining which meth- 
 od of scoring is the most valid. For this reason, there have been 
 included in this table the correlations of this shop rank with the 
 first trial, the second trial, the shortest of three trials, the average 
 of three trials and the average of the last two trials. 
 
 Before the correlations had been computed, the shops were 
 arranged in the order in which mental ability seemed to be de- 
 manded. That is, it has been the belief of the officials of the in- 
 stitution that the demands made upon intelligence were greater 
 in the foundry moulding room than in any other shop, with the 
 tin shop a close second and the tailor and shoe shops following 
 with practically the same rating. Men may be placed in the 
 
 *The writer is indebted to Mr. C. P. Stone of the Department of Research of 
 the Indiana Reformatory for this rating and the tabulation of the cylinder test 
 records of these men. 
 
50 The Witmer Cylinder Test 
 
 TABLE VIII 
 
 Correlation of Cylinder Test Performance with Shop Ability 
 Indiana Reformatory 
 
 
 Trial 
 
 Shop 
 
 First 
 
 Second 
 
 Short 
 
 Av. of 3 
 
 Av. of 2 
 
 Foundry 
 (Moulding) 
 
 —.18 
 
 -^.3(^ 
 
 + •57 
 
 + .05 
 
 + •36 
 
 Tinning 
 
 + .08 
 
 + .29 
 
 + •44 
 
 — .31 
 
 + •23 
 
 Tailor 
 
 + .55 
 
 + .58 
 
 + •69 
 
 + .81 
 
 + .51 
 
 Shoe 
 
 + .32 
 
 + .64 
 
 + .72 
 
 -^•33 
 
 + .68 
 
 Cabinet 
 
 — .07 
 
 + .07 
 
 — .11 
 
 + .16 
 
 + •23 
 
 Barber 
 
 — .06 
 
 + .22 
 
 ^■33 
 
 — .14 
 
 + .46 
 
 Foundry 
 (Grinding) 
 
 — ■33 
 
 + .04 
 
 — •13 
 
 — •44 
 
 — .01 
 
 Broom 
 
 -.48 
 
 + .03 
 
 + .15 
 
 — .02 
 
 + .05 
 
 Average 
 
 — .02 
 
 + .28 
 
 -^■33 
 
 + .06 
 
 + •31 
 
 grinding room without any requirements as to intelligence, while 
 the broom shop is made up of the physically and mentally in- 
 competent. 
 
 A perusal of this table shows that the first trial gives negative 
 correlations, except for fairly high positive correlations in the 
 tailor and shoe shops. This trial is the only one to give a nega- 
 tive average correlation, it being — .02. The second trial gives 
 positive results throughout, with the upper four shops giving much 
 higher correlations. The average of this trial is +.28. The short- 
 est trial, except for the cabinet and grinding departments, gives 
 a positive correlation higher in each shop than that of any of the 
 other bases of scoring. The shoe and tailor shops have a correla- 
 tion of about .70, while the foundry moulding and tin shop follow 
 with .57 and .44, with the barber shop giving .22)' The average 
 of three trials gives both high positive and high negative correla- 
 
The Relation of Cylinder Test Performance to Proficiency 51 
 
 tions. It furnishes the highest positive, +.81, and the highest 
 negative result, — .44, the eight shops having an average correla- 
 tion of but + .06. The average of the last two trials gives results 
 following closely upon those of the shortest trial. In the upper 
 four shops, it falls distinctly below the shortest trial and slightly 
 below the second trial, but in the lower four shops it gives twelve 
 points higher correlation, except in the broom shop. Its average 
 of +.31 is but two points behind that of the shortest trial. 
 
 The probable errors for the shortest trial correlations are, — 
 Foundry Moulding, .15; Tinning, .20; Tailor, .12; Shoe, .11; 
 Cabinet, .22; Barber, .20; Grinding, .23; and Broom, .22. 
 
 There are several factors which have their effect upon the cor- 
 relation. The length of time in a shop will work to the advantage 
 of the older men in determining their shop rating. The man who 
 has been in a shop for four years will, of course, be more skillful 
 than one who has been in the shop but a year, and the extent to 
 which the rate of progress has been taken into account in form- 
 ing the rank order, there is no means of determining. This is 
 but one of the ways in which the personal equation of the in- 
 structor affects the correlation. The fact that the men are not 
 all engaged in the same operations within a shop is of importance. 
 Some men who are highly successful as moulders when working 
 upon one pattern, find another almost impossible, yet the tasks 
 are sufficiently similar to warrant a rank order. The miscella- 
 neous character of the broom shop and grinding room men makes 
 any figures based upon their rating of doubtful value. Regardless 
 of these things, the controlled environment and the close observa- 
 tion of the workmanship through a prolonged period, makes this 
 an especially valuable source of material for such an investiga- 
 tion. 
 
 This study supports our previous argument that the shortest 
 trial is the best measure of performance or psycho-motor ability. 
 It further indicates that there is a positive correlation of rather 
 high proportion between the cylinder test performance and manual 
 or mechanical capacity. 
 
VI 
 SUMMARY 
 
 The conclusions that have been reached in the consideration of 
 performance tests in general and the cylinder test in particular 
 and in the experimental investigation reported herein, may be 
 summarized as follows: 
 
 I. An understanding of the capacities and the disabilities of an 
 individual, a complete clinical picture, requires an investigation 
 into those powers which have been variously termed manual 
 ability, motor ability, performance ability and psycho-motor 
 capacity. Intelligence tests tend to place too great emphasis 
 upon the ability to use language, hence they give a false impres- 
 sion of the mentality of the less favored, the deaf, the illiterate or 
 those with language defect. 
 
 1. The Witmer Cylinder Test is a performance test which pos 
 sesses those qualities necessary in a piece of apparatus foi measur- 
 ing this ability: (i) a qualitative difference in performance, (2) 
 a series of graded stimuli, when used in connection with the in- 
 dividual blocks of cylinders of Dr. Montessori's didactic material, 
 (3) applicability to a wide age range, (4) a uniform method of 
 procedure for all ages and (5) an absence of factors favoring lan- 
 guage ability. 
 
 3. This test has both qualitative and quantitative aspects, — 
 it tests at the same time two different things. Qualitatively, the 
 first trial tests the ability to make an adaptation to a new problem 
 and is sufficiently complicated as to permit the differentiation of 
 subjects, especially in the years of childhood. Quantitatively, 
 the series of trials gives a measure of psycho-motor capacity. 
 
 4. The shortest of three trials gives the best time index of this 
 particular mental factor. 
 
 5. There is a decrease in time of performance with increasing 
 age. 
 
 6. There is a distinct sex difference in the time required to per- 
 form the test, favoring the boys. This is largely due to the dif- 
 
 52 
 
Summary 53 
 
 ference in attitude and poise and to the fact that it sets a different 
 problem for men and for women. 
 
 7. The cylinder test is peculiarly adapted to the determination 
 of the degree of distributive attention of an individual. 
 
 ». There is, in general, a direct relation between the cylinder 
 test performance and pedagogical age, which is the only measure 
 we have of the proficiency of children, 
 
 9. Differences of proficiency of adults, based upon the level of 
 daily performance, are accompanied by differences in psycho- 
 motor capacity as measured by the cylinder test. 
 
 10. A positive correlation is found between manual skill and 
 efficiency as measured by shop rating and the performance of the 
 cylinder test. 
 
54 The Witmer Cylinder Test 
 
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