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There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924030584548 n-o*Wu £ , ;,,.,,. fc LcL^ZtCrvv ?iT THE INTERRELATIONS OF MENTAL ABILITIES BY FREDERICK WILLIAM STEACY SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PHILOSOPHY, COLUMBIA UNIVERSITY PUBLISHED BY Qtatrlpra fflollrgp, (Enlnmbta llninmrttjj NEW YORK CITY 1919 THE INTERRELATIONS OF MENTAL ABILITIES BY FREDERICK WILLIAM STEACY SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PHILOSOPHY, COLUMBIA UNIVERSITY PUBLISHED BY JSmclfns (Collrgr. (Mntnbta IttiurrBttg NEW YORK CITY 1919 n Copyright, 1919, by Frederick William Steacy A ^A\5iq 1.1;! M Si II V CONTENTS SEC. PAGE i The Tests and Their Administration i 2 The Nature of the Abilities Measured: Interre- lations of the Several Tests 38 3 The Composite Abilities and Their Interrela- tions 49 4 The Hierarchy of the Specific Intelligences 52 5 Sex Differences 58 6 Individual and Composite Scores 62 7 Bibliography 78 8 Acknowledgments 79 SECTION I THE TESTS AND THEIR ADMINISTRATION Thirty-two kinds of tests were used in this study, comprising those listed on page 2. In general, two tests of each kind were given, similar in form but varying in content. In some cases only one test was given, it being divided arbitrarily into two halves for scoring. Ai and A2 were such ex post facto halves. So also were A3 and A4, B3 and B4, D3 and D4. In two cases the scores from four (or five) tests were consolidated into two scores, making Ay and A8, and E9 and Eio. In five cases the same test was given the second time and both scores were used, making C3 and C4, C5 and C6, C7 and C8, En and E12, E13 and E14. The subjects were the children of two classes, the 6B1 and the 6B2 of the Bronx Public School No. 51. The two class rooms were adjacent. The two teachers who taught these two classes used the departmental method of instruction, i.e., they divided the subjects to be taught equally between themselves and each taught her allotted subjects to both classes, both classes receiving exactly the same instruction. The two classes contained, at the time the writer began to make his tests, 37 boys and 46 girls. For various reasons, to be explained later, the records of only 31 boys and of only 38 girls were used in the composites and final calculations. The records of the two classes have not been kept separate, though the records of the two sexes have been carefully kept apart. Throughout the whole series of experiments the pupils showed marked interest and a strong desire to do good work. So far as pressure of work would permit, each day the writer read to the classes the results of the previous day's tests, that is, of the six or eight best in each class. As evidence of their interest it may be noted that the pupils showed admirable care of the mechanical tests, very few pieces being damaged or lost. The tests were given during the spring semester of 1916. Those of the Ventilation Commission were given during February, March, and April, while the other tests were given during May and June. The former were given with notable care by expert psychologists. The latter were given either by the writer or in 2 The Interrelations of Mental Abilities THE ABILITIES MEASURED MS- DIS- tinct tinct Manipulative Tests tests scores A1&A2 Stenquist Construction Test Single Series 1 1 2 A3 & A4 Stenquist Recognition of Mechanical Devices .... 1 2 A5&A6 Knot Making Test 2 2 A7&A8 Metal Puzzles 4 2 A9&A10 Diagram Matching 2 2 A11&A12 Diagram Drawing 2 2 A13&A14 Handwriting 2 2 Non-verbal Spatial Relations Tests Bl Rogers' Superposition 1 1 B2 Thurstone Spatial Relations 1 1 B3 & B4 Rogers' Locus or Space Intuition Test 1 2 B5 Briggs' Similar Figures 1 1 B6 Briggs' Congruent Figures 1 1 Non-verbal Computational Tests CI & C2 Bonser's 2A and 2B 2 2 C3&C4 Woody Addition 1 2 CS&C6 Woody Subtraction 1 2 C7&C8 Woody Division 1 2 Arithmetic Tasks Stated in Words Dl & D2 Bonser's 1A and IB 2 2 D3&D4 Starch's Arithmetic Scale 1 2 DS&D6 Teachers College Arithmetic VI and VI (a) 2 2 Very Verbal Tests El Briggs' Transitive Verbs 23 1 1 E2 Briggs' Phrases 24 1 1 E3 & E4 Starch's Grammatical Scales A and C 2 2 ES&E6 Van Wagenen's Mixed Relations 2 2 E7 & E8 Woodworth and Well's Mixed Relations modified by Thorndike 2 2 E9&E10 Thorndike's Reading Tests Alpha and I, J, K, L 5 2 E11&E12 Thorndike's Directions V 1 2 E13&E14 Thorndike's Visual Vocabulary Scale A 1 2 E1S&E16 Thorndike's Visual Vocabulary XII and VIII... 2 2 E17 Thorndike's Visual Vocabulary IX 1 1 E18 Thorndike's Directions VII 1 1 Logical Tests F1&F2 Briggs' Faulty Arguments 37 and 39 2 2 F3&F4 Briggs' Catches 41 and 42 2 2 S2 56 The Tests and Their Administration 3 his presence. All tests were given to the children in any one class under the same conditions, as a group test. It was fre- quently impossible to give to each class the same test on the same day, since, for example, the Knot test required some 8 to 10 minutes for scoring each pupil. Six to eight hours' work on the test was therefore necessary before it was ready to be given the second time. The Construction test and each series of the Puzzle test likewise required several hours for scoring. The paper tests were given as far as possible to both classes on the same day. The administration began usually at 1 :4s p.m. and closed about 2:50 p.m., that is, one-half hour for each class. Moreover, the order in which the classes were taken from day to day was alternately 6B1 and 6B2. The class-room teacher was usually present, but took no part in the administration of the tests. Group A. Construction or Mechanical or Motor Tests Ai & A2 The Stenquist Construction Test Single Series 1 The time for the whole test is 30 minutes. Source. This test has been devised by Mr. John Langdon Sten- quist, a graduate student of Teachers College, who, however, has not published any articles on this particular test, though he has published several articles on other and similar tests. Description. The material for this test is contained in a wooden box, 24 inches long, 5-5 inches wide and 2 inches high, fitted with hinges and containing eleven compartments, in each of which is a mechanical device, which is of full size and standard quality, but has been taken to pieces. The only tool needed is a screwdriver, and one of these is placed in each box. Presentation. To each pupil is given a slip of paper upon which to write his name. He is instructed to place this slip in the box. Then to each pupil a box is given, which is placed before the pupil with the hinges toward him. He is told that when he opens the box he may use the cover for a tray in which to keep the pieces, and he is advised to take the pieces out of one compart- ment and to complete the device and put it back before he disturbs another. This advice is given to prevent the pieces from becom- ing mixed. He is told to begin at his left hand, and to work in order toward his right hand, and that the device is to be put together so that it will work properly. Then the signal is given The Interrelations of Mental Abilities to begin. The usual signal in this and in all other tests in this series is : "Ready ! Hands up ! Go !" Method of Scoring. For each device which is properly put together so that it will work correctly 10 marks are given. For partial success partial credit is allowed according to the sub- joined scheme of marks. For the purpose of correcting for attenuation this test was scored in two parts. Ai represents the score for the alternate odd devices and A2 for the alternate even devices. The highest possible score is no marks for the whole test. Scheme for Scoring the Stenquist Construction Test Single Series 1 A Bicycle Head right — 2, nut right = 8, nut toward handle = 4, Wrench nut toward head = 2, head wrong and nut right = 1, both wrong = 0. Each right link = 1, each half looped link = }£. Lever right = 10, lever reversed = 9, lever under- neath = 3. Lever right = 3, lever reversed = 1, spring right = 4, spring attached to wrong place = 2, cogwheel = 2, ham- mer = 1. Both levers right = 10, one lever right and one reversed = 9, both levers reversed = 8, levers wrong end in spring = 2. Center right = 2, center upside down = 1, the three springs = 1, each cap = 1, cover = 4. Both levers right = 10, spring on tip of levers —2. Tap right = 1, washer right = 2, washer reversed = 1, holding screw = 1, regulating screw properly work- ing = 6. Peg = 1, spring = 1, base correctly fastened = 8. Lug = 1, bolt = 1, spring = 3, cover and screw = 1, key = 0, lug and bolt and spring = 0. Lever = 1, baitholder = 2, coil = 5, rivet = 0, complete trap = 10. A3 & A4 The Stenquist Recognition of Mechanical Devices Tests The time for this whole test is 30 minutes. Source. As the name implies, this test, like Ai & A2, has been devised by Mr. Stenquist. Nothing has hitherto been pub- lished concerning this test. B Ten Link Chain C Rubber Hose Clamp D Bicycle Bell E Paper Clip F Metal Money Safe G Spring Clothespin H Gas Faucet / Electric Push Button / Door Deadlock K Mouse Trap The Tests and Their Administration 5 Description. The test consists of a sheet of foolscap paper con- taining a space for the pupil's name, the date, etc., and a list of the names of fifty-five mechanical devices and also a stout cardboard box 18.25 inches long, 9.25 inches wide and 1.75 inches high. This box contains fifty-five mechanical devices correspond- ing to the names on the list. Each tool, which is of standard size and quality, is numbered and is fastened securely to the bottom of the box. Presentation. To each pupil is given a sheet of paper and a box. When each one has written his name, the purpose of the test is explained. The pupil is to find the mechanical device in the box which corresponds to its name on the list and then to write on the list and opposite the name the number of the device. At the usual signal the pupils begin work. Method of Scoring. For each device properly identified one mark is allowed. For the purpose of correcting for attenuation, this test was scored in two parts. A3 contains the devices num- bered 1 to 28, inclusive, and A4 contains the devices numbered 29 to 55, inclusive. The highest possible score for the whole test is 55 marks. A copy of the sheet used in this test is shown below : Department of Educational Psychology A3&A4 recognition of mechanical devices Test I Series I Name Age years, months. Sex Grade School a. Bushing for packing nut of spark plug. b. Cabinet door hook. c. Carriage bolt. d. Catch for cabinet door hook. e. Central insulation for spark plug. f. Center punch. g. Common ten penny nail. h. Common washer. 1. Coping saw blade. /. Cotter pin. k. Curtain rod fixture. /. Cut nail. m. Dowel screw. n. Drive hook. o. Drill. . p. Eight penny finishing nail. q. Expansion lug nut. r Flat head harness rivet. The Interrelations of Mental Abilities —s. Flat head wood screw. — t. Fuse wire. —*. Gasket or washer for making hose coupling tight. -v. Gimlet. —w. Glazier's point for fastening glass in window. —x. Hack saw blade. -z. Hinge. —a\. Insulating plug for electric light wire in lamp. —bl. Jam nut, or first nut for top of spark plug. —cl. Lock washer. -dl. Machine bolt. -el. Main body of spark plug. -/I. Nail set. —g\. Packing nut for spark plug. -hi. Patent box or mitre frame fastener. -tl. Picture nail. -/I. Pipe reducer bushing. -kl. Plumb bob. -11. Roller skate wrench and key. -ml. Round head rivet. -nl. Saw screw. -ol. Shade fixture for non-revolving end of shade roller. -pi. Shelf stop or support. -gl. Set screw. -rl. Small hasp. -si. Soft solder. -tl. Staple for small hasp. -«1. Stove bolt. -vl. Tar paper nail cap, to prevent nail head from tearing paper. -ail. Thumb nut. -xl. Trunk caster. -yl. Wedge to prevent window from rattling. -el. Wedge for tool handles. - ¥ P^ DIAGRAM MATCHING TEST. UPPER LEFT HAND CORNERS. 14 The Interrelations of Mental Abilities to compare the figures on the two sheets and to select the whole diagram corresponding to the Upper Left Hand Quarter and to write in the whole diagram the corresponding number. These tests, like all the other paper tests, are given face down and at the usual signal are upturned and immediately the time is taken and the task of solution is begun. The two series were given on differ- ent days. Method of Scoring. One mark was allowed for each diagram properly identified. No penalty was imposed for errors. In scor- ing, a shield was used having an opening corresponding to each whole diagram and properly numbered. This sheet, when laid on the sheet marked by the pupil, greatly facilitated the task of scor- ing and much diminished the chance of error. The highest possible score is 20 marks for each series. An & 12 Diagram Drawing Test, Two Series: C and D The time for each of these series is 30 minutes. Source. See above for A9 & Aio. Description. The two series of this test are similar and have been evolved on the same principle. They are of equal or of nearly equal difficulty, since the sixty diagrams which remained when the forty diagrams of A9 & A 10 were removed were equally divided. Two sheets were used for each pupil. The first sheet contains thirty figures. Each of these is the upper left hand quarter of the diagram to be drawn and bears its dis- tinctive number. The second sheet has forty dotted outlines all alike. The purpose of these outlines is to form a background on which the pupils can draw the required diagram, thereby greatly simplifying the task for him and also much facilitating rrTT U4-4 4+. r .4—1 -•-. pTJJ U ...Li 14.: Z|I i i t , j — » — i™. Li +44 L....L-!..--,— : ! 1 i cm: M-i I- 1 1 j ~ ! r ixn _.i~, i_j 1 — I — l._.i — i SECTION OF DIAGRAM DRAWING TEST. The Tests and Their Administration 15 the labour of scoring. The diagrams are 1.5 inches long and the same in width. Each dotted outline has five equidistant lines parallel to the lower margin of the sheet, and five equidistant lines crossing these at right angles. Presentation. The purpose of the test was explained to the pupils at the blackboard, upon which were drawn some diagrams from the previously described test. Some dotted outlines were drawn and then filled in from the patterns. The pupils were told that the extra outlines were for use in case they spoiled an outline and that they were not required to draw the diagrams according to the order of the patterns, but to be careful to write in their drawing the number of the pattern. The use of rulers was allowed but was not encouraged. Method of Scoring. One mark was allowed for each diagram properly drawn. Neatness and beauty were not counted, since these tests are not of artistic ability, but of power to utilize ideas of form. To be correct, each angle must coincide with an intersection of the dotted lines in the background. Therefore subjective criteria for the appraisal of the drawing were wholly unnecessary. Two or three pupils left one diagram each incom- plete. If this were correct partial credit might be given for it by a finer system of scoring, but the cases were so few as to cause but slight difference in the results. The highest possible score is 30 marks for each series. A13 & 14 Handwriting The material for this test was the papers belonging to the other tests. Two of the written tests were used for A13 and two other written tests were used for A14. These samples were graded by two persons. The Thorndike Handwriting Scale was employed as the standard. The highest mark on this scale is eighteen. The papers were graded by quarter marks. In order to avoid fractions these quarter marks were multiplied by four. Since the scores of the two judges were combined the highest mark possible for test A13 or A14 was 18x2x4x2 = 288. The highest mark actually given to any sample was 16. The pupils were advised to write legibly but on the whole very little emphasis was laid upon the handwriting portion of the series. The object 16 The Interrelations of Mental Abilities was to obtain, not the best copy-book style, but the best ordinary samples. Group B. Non-Verbal Spatial Relations Tests B i Superposition Test The time for this test was 2 minutes. Source. This is a modification, for the sake of simplification, by Miss Rogers, 1 of Thurstone's Spatial Relations Test, which will be described in test B2. Description. This test requires the recognition of plane geo- metrical figures, all being equal and symmetrical rhombuses, each side being one-half inch in length. Each rhombus has for one side a heavy line, which may make any angle with the margin of the paper, provided only that one side of the rhombus be parallel to some one margin of the paper. Twenty-four such rhombuses are arranged in two columns. Each contains a small circle in one corner, in any corner so far as the heavy line and the margin of the paper are concerned. Opposite to each of these rhombuses are two rhombuses without circles. These have the heavy line parallel with the base margin and toward it. Moreover, this heavy line is continuous between the two and projects about an eighth of an inch beyond each. The two upper corners of the two rhombuses are one-fourth of an inch apart, while the two lower corners are three-fourths of an inch apart. Presentation. This test was given by Miss Rogers in the writer's presence. Explanations were given at the blackboard, and some practice was allowed before the material for the actual test was distributed. The pupils were required to find the one of the two rhombuses which corresponded to the rhombus with the circle and then to draw the circle in the corresponding corner. Method of Scoring. One mark was allowed if the circle was placed in the proper diagram, and two marks were given if the circle was drawn not only in the proper diagram, but also in the proper corner. Nothing was allowed if the wrong diagram was marked. The highest possible score was 48 marks. a Rogers, A. L., Tests of Mathematical Ability and Their Prognostic Value, Teachers College. The Tests and Their Administration 17 B2 Thurstone Spatial Relations Test The time for this test is 2.5 minutes. Source. This test was devised by Dr. L. L. Thurstone, of the Pittsburgh Institute of Technology. Description. The test is the same in all respects as the Super- position test described above, except that before identifying the rhombus it must be imaginatively turned face downwards and back upwards. Presentation. This test was given by Miss Rogers in the writer's presence. The test was explained at the blackboard and some time (1 or 2 minutes) was permitted for practice before the test sheets were distributed. Method of Scoring. The same as in Bi. Instructions. Prepare three cardboards similar to the three cards shown on the instructions side of the sheet. Make these cards about 10 inches on the side. Paint one edge of each card black on both sides of the card. Cut the holes as indicated. Before giving the test, draw on the blackboard the complete drawing on the instructions side of the blank. This need not be done very accurately. Spatial Relations Test Assume that the lozenge shaped figure with a circle in it represents a small card with one of its edges painted black and with a hole in one corner. Imagine that this card is picked up, turned over, and placed face down with the black edge of the card touching the long heavy black line to the right. Imagine the card moved along this black line until its edges fit the edges of one or the other of the lozenge shaped outlines. With your pencil draw a circle in the corner where the hole will be. Proceed in the same manner and as rapidly as you can with the remaining outlines on the page. Page 1 A7VA i8 The Interrelations of Mental Abilities Page 2 n VA U A7V\ C^ n ya VA A7 VA /VVA VA A7 VA Z7ZZXA. A7 /TVA TA f7 VA fl A7VA /7 /7VA A7 /A7VA VA ^7VA P A7VA ^ rw\ VA /"7VA £3 ^7V~\ Allow two minutes for the group to read the instructions, warning them that the instructions must be read carefully to be understood. At the end of this time limit, repeat orally the marked portion of the instructions ("Imagine" . . . "hole will be") while The Tests and Their Administration 19 moving one of the large cardboards into place on the blackboard drawing. Give this paragraph verbatim for each of the three cards, on the instruction side. Then give the test proper with a time limit of two minutes. I have found three subjects who finished the blank with 24 correct responses in less than the time allowed, but the majority of students make hard work of it and require considerably more than two or three minutes per column. If the test can be given as an individual test, it would be advisable to take the time for each column and thus obtain a reliability measure for the test. This is hardly practicable when giving it as a group test on account of the great range of speed. B3 & B4 Locus Test or Space Intuition Test The time for this test was not limited. Each pupil was per- mitted to work as long as he wished. The maximum time was 15 minutes. Source. This test was prepared by Miss Rogers. Nothing has hitherto been published on this test. Description. The paper, as given to the pupils, has two examples properly answered for the purpose of illustration and nine questions for the test. As the name implies the test is geometrical but unconventional. Presentation. The test was given by Miss Rogers in the writer's presence. Method of Scoring. For a perfect answer two marks are given and for an answer half right one mark is given. The highest possible score is 18 marks. For the purpose of correct- ing for attenuation the test was divided into two parts, though given as a whole. B3 consists of the alternate odd questions and B4 of the alternate even questions. There is much doubt concerning the propriety of including this test in the non-verbal group, considering the age and train- ing of the pupils tested. On the other hand, it is equally or more unsatisfactory to treat it as a verbal test. Its complex nature should be kept in mind when its correlations are dis- cussed. 20 The Interrelations of Mental Abilities Name Space Intuition Test (1) Date. Example a) If a pencil moves on this paper 1 inch from the right-hand edge, draw the path followed by the point of the pencil. b) Show by a drawing the kind of line that passes through all the houses one mile from a certain point. Let — = 1 mile. 2. Show by a drawing in the space opposite, the path of a point that is always half-way between the tip of the hour-hand of a watch and the rim. 3. A number of equal circles are drawn between two parallel straight lines and touching them both. Show by a drawing in the space opposite where their centres must be. A pencil is attached to a string. The string and pencil are held as if a circle were to be drawn, but while the pencil moves round the fixed point at which the string is held, the string is gradually lengthened. Draw in the space opposite, the path marked by the pencil point. b. 1. A motor boat sails up a straight canal midway 1. between the banks. Draw in the space opposite the path of the boat. 4. Draw in the space opposite, the path followed by the tips of a pair of shears, when the bolt or screw remains always fixed in one position. The scissors do not move forward or back. They simply open and shut. 6. 6. A boy starts_ from the southwest corner of a square and walks in a northeasterly direction. Draw in the space opposite, the path he follows. a) If for every foot he walks East, he walks 1 North. b) If for every foot he walks East, he walks 2 North. c) If for every foot he walks East, he walks yi North. 7. Show by a drawing in the space opposite, how a road would have to be constructed so as to be everywhere the same distance from two houses, A and B. 7. B The Tests and Their Administration 21 B$ Similar Figures The time for this test is 3 minutes. Source. This test is No. 17 of Briggs' tests published in 1913. 1 Description. The test consists of four odd figures and eight pairs of figures. The members of a pair are alike in all respects except in size or orientation. The twenty figures are arranged in five columns of four figures each. The members of a pair are never adjacent in a column or in a row. Presentation. At the head of the sheet instructions are given : "Figures are similar when they are exactly alike in shape. Find pairs of similar figures and write in parentheses the numbers representing each pair, e. g., (21, 53)." Before the papers were distributed some oral instructions were given. Method of Scoring. In order to avoid negative scores, 8 marks were added to each score. The highest possible score is 16 marks. For each pair correctly marked = 1 For error in the star figures = — 1 For each other error = — 2 For unattempted or meaningless = — 8 B6 Congruent Figures The time for this test is 3 minutes. Source. This test is No. 18 of Briggs' test. 2 Description. This test consists of four odd figures and eight pairs of figures. The members of a pair are alike in all respects except in orientation. The twenty figures are arranged in five columns of four figures each. The members of a pair are never adjacent either in a column or in a row. Presentation. At the head of the sheet instructions are given : "Figures are congruent when they are exactly alike in shape and size. Find pairs of congruent figures and write in paren- theses the numbers representing each pair, e. g., (21, 53)." Be- fore the papers were distributed some oral instruction was given. Method of Scoring. The same as for B5. ^Teachers College Record, September, 1913, p. 25. 'Ibid., p. 26. 22 The Interrelations of Mental Abilities Group C. Non-Verbal Computational Tests Ci The time for this test was 6 minutes. Source. This test is No. 11A as printed in Bonser (1910, p. 2) 1 and No. 35 in Briggs (1913, p. 34) - 2 Description. Dr. Bonser described this test as composed of one-step problems stated in a manner less conventional than usual, and regards them as a test of reasoning activity and of mathematical judgment. The test consists of five problems. Owing to a typographical error in Dr. Bonser's thesis this test is different from the form in which he gave it though agreeing with the book. The test here agrees with his book which reads "132 plus what number equals 36?" While his test as used by him read "32 plus what number equals 36?" Presentation. This test was conducted in the same way as all other paper tests, except that the pupils were told that this test would be in arithmetic. Method of Scoring. One mark was given for each correct answer. The highest possible score is 5 marks. C2 The time for this test was 3 minutes. Source. This test is No. 11B in Bonser (1910, p. 2) and No. 36 in Briggs (1913, p. 34)- Description. This test parallels Ci above. Presentation. The same as in Ci above. Method of Scoring. The same as in Ci above. The highest possible score is 5 marks. C3 & C4 Addition The time for this test was 25 minutes. Source. This is a preliminary series prepared and used by Woody in the preparation of his Addition Scale (i9i6). s 'Bonser, F. G., Reasoning Ability of Children in Grades 4, 5, 6, Teachers College, 1910. 'Teachers College Record, September, 1913. "Woody, G, Measurements of Achievement in Arithmetic, Teachers College, 1916. The Tests and Their Administration 23 Description. The test has 38 questions. It embraces the addition of one-place, two-place, three-place, and four-place integers, of decimal currency, of proper fractions, of mixed fractions, of decimals, and of compound numbers. Presentation. This test was given twice, once in February and once in April. Method of Scoring. One mark was given for each question which was answered correctly. The highest possible score was 38 marks. C5 & C6 Subtraction The time for this test was 20 minutes. Source. The same as C3 & C4, in subtraction. Description. This test has 35 questions. It embraces the subtraction of simple integers, of proper fractions, of mixed fractions, of decimals, and of compound numbers. Presentation. The same as in C3 & C4 above. Method of Scoring. The same as C3 & C4 above. The highest possible score was 35 marks. Cj & C8 Division The time for this test was 30 minutes. Source. The same as C3 & C4, in division. Description. This test has 36 questions. It embraces the division of simple integers, of decimals, of vulgar fractions, of mixed fractions, and of compound numbers. Presentation. The same as in C3 & C4 above. Method of Scoring. The same as in C3 & C4 above. The high- est possible score was 36 marks. These three tests are similar to but not identical with Series A, Woody (1916). Group D. Arithmetic stated in Words Di & D2 Problems The time for these two series is 3 minutes each. Source. These are iA and iB in Bonser (1910, p. 2) and No. 33 and No. 34 in Briggs (1913, p. 33). Description. Each test consists of five two-step problems. Presentation. The same as in Ci. 24 The Interrelations of Mental Abilities Method of Scoring. The same as in Ci. The highest possible score is five marks for each series. D3 & D4 Arithmetic Scale The time for this whole test is 20 minutes. Source. This test is by Dr. Daniel Starch (1916, p. 213). x Description. This test consists of a graded series of problems of the sort ordinarily found in text-books. Presentation. The same as in Ci. Method of Scoring. One mark was allowed for each correct answer. The twelve questions were given on one sheet and afterwards divided for the purpose of correcting for attenuation. D3 consists of the alternate odd questions and D4 of the alter- nate even questions. The highest possible score for the whole paper is 12 marks. D5 & D6 Problems. Two Series: Tests VI and VI (a). The time for these series was 30 minutes each. Source. The Laboratory of Educational Psychology, Teach- ers College. Description. Each series consists of six problems, which become progressively more difficult. Presentation. The same as in Ci. Method of Scoring. One mark was allowed for each problem correctly answered. The highest possible score is 6 marks for each series. Test VI Write your name here Write the date here Find the answers to these problems. Do all your work on the sheets of white paper. Write your answers here. The answer to 1 is The answer to 2 is The answer to 3 is The answer to 4 is The answer to S is The answer to 6 is iStarch, D., Educational Measurements, 1916. The Tests and Their Administration 25 Write your name on every sheet of white paper that you use and hand in all the sheets of white paper. 1. There are 550 pupils on the roll. If fy& of them are here to-day, how many are absent? 2. A boy had 210 marbles. He lost 1/3 of them. How many were left? 3. The children of a school made small boxes to be filled with candy and given as presents at a school party. 600 were needed. In 4 days grades 3 to 7 made 20, 25, 83, 150 and 150 boxes. The eighth grade agreed to make the rest. How many did the eighth grade make? 4. A boy lost one-fourth of his kite string in a tree, one-third in some wire, and one-fifth in a hedge. What part of his string was left? 5. How much will 8J4 dozen pencils cost at the rate of %%. for a half dozen? 6. John had $1.20 Monday. He earned 30 cents each day on Tuesday, Wednesday, Thursday and Friday. Saturday morning he spent one-third of what he had earned in four days. Saturday afternoon his father gave John half as much as John then had. How much did his father give John? Test VI (a) Write your name here Write the date here Find the answers to these problems. Do all your work on the sheets of white paper. Write your answers here. The answer to 1 is The answer to 2 is The answer to 3 is The answer to 4 is The answer to 5 is The answer to 6 is Write your name on every sheet of white paper that you use and hand in all the sheets of white paper. 1. If $1991 a day is paid to 724 men who each earn the same wages, how much does each man receive? 2. A baseball team played 160 games during the season and won 100 of them. What part of the whole number of games did the team win? 3. A store-keeper sold 12 yards of cloth, which was 4/15 of the whole piece. How many yards were there in the whole piece ? 4. A grocer had a tank holding 44 3/16 gallons of oil. One day he drew out 15j4 gallons and the next day 9Y% gallons. How many gallons were left in the tank? 5. One summer a farmer hired 43 boys to work in an apple orchard. There were 35 trees loaded with fruit, and in 57 minutes each boy had picked 49 apples. If in the beginning the total number of apples on the trees was 19,677, how many were there still to be picked? 6. A boy had 3 dollars. He paid it all for four articles, which we will call A, B, C. and D. B cost as much as C. C cost as much as D. A cost as much as B, C and D together. The boy sold A and B for \y 2 times what he paid for them. He sold C and D for lj£ times what he paid for them. How much did he get for the four articles? 26 The Interrelations of Mental Abilities Group E. Very Verbal Tests Ei. Understanding and Applying a Definition: Transitive Verbs The time for this test was i minute, 30 seconds. Source. This test is No. 23 in Briggs (1913, p. 28). Description. This test consists of twelve simple sentences. Nine of them have a transitive verb in the active voice. One each of the other verbs is intransitive or copulative or passive. Presentation. Since the pupils had not received any school training in transitive verbs, the writer fearing that they would be confused by the printed instructions modified them to read "Mark the sentences with objects," i. e., 1, 2, 3, 7, 8, 9, 10, 11, 12. The papers were thus scored and the results used herein. Since this modification may have increased the confusion the papers were scored also by the original method, i.e., 1, 2, 7, n, and the correlations with E2 were computed. These are: boys +25 and girls — 01. The original method gives a slightly higher correlation than the modified method, though the average marks received by the pupils are much lower: boys 6.28 and girls 6.90. Method of Scoring. One mark was allowed for each sentence containing a transitive verb in the active voice which was checked and one mark for any other sentence which was not checked. The highest possible score is 12 marks. E2 Understanding and Applying a Definition: Phrases The time for this test was 2 minutes. Source. This test is No. 24 in Briggs (1913, p. 29). Description. The test consists of twelve sentences. Four of these sentences contain a phrase according to the instructions given as stated below. Presentation. At the top of each sheet two paragraphs are printed: "A phrase is a group of words not containing a subject and predicate and used like an adjective or an adverb. "Make a ^ by each sentence which, according to this definition, contains between the parentheses a phrase and nothing beside the phrase and its modifiers." The Tests and Their Administration 27 Method of Scoring. One mark was allowed for each sentence which was checked correctly and one mark for each other which was left unchecked. The highest possible score is 12 marks. £3 & E4 Grammatical Scales: A and C The time for A was 12 minutes and for C 6 minutes. Source. These tests are by Starch (1915, p. 615 and p. 620). 1 Description. Scale A contains 37 sentences and Scale C 20 sentences of various degrees of difficulty. Each sentence con- tains two or more words in parentheses between which choice is to be made. One of these alternatives is right and the other is wrong. Presentation. At the top of the paper for each scale direc- tions are printed as follows : "Each of the following sentences gives in parentheses two ways in which it may be stated. Cross out the one which you think is incorrect or bad. If you think both are incorrect cross both out. If you think both are correct underline both." These instructions were explained before the papers were distributed. Method of Scoring. One mark was allowed for each sentence which was properly lined. The highest possible score for scale A is 37 marks and for scale C is 20 marks. The key supplied by Dr. Starch was invariably followed, though, in the writer's opinion, some of the usages thus scored wrong are allowable. E$ & E6 Mixed Relations. Two Series The times was about 1 minute, 15 seconds for each half of each series. Source. The two series are developments of the Woodworth- Wells test, made by Mr. M. J. Van Wagenen, of the University of Minnesota. Nothing has hitherto been published upon these two series. Description. Three words are read and the pupils are re- quired to write the fourth word which must bear the same relation to the third word which the second bears to the first word. Each series consists of fifty such groups. ^■Journal of Educational Psychology, December, 1915. 28 The Interrelations of Mental Abilities Van Wagenen Mixed Relations Test — C Directions — Give at the rate of 5 seconds each — J4 second between each word and 4 seconds for the written response. 1 Light day Dark 2 Birds fly Fish 3 Chalk white Carbon 4 Sun shines Wind 5 Summer hot Winter 6 Cats scratch Bees 7 Emerald green Ruby S Water drink Air 9 Father son Mother 10 Hat head Shoe 11 Chair wood Stove 12 Fast fastest Great 13 Cup saucer Knife 14 Man husband Woman IS Write stories Draw 16 Lamp oil Stove 17 Daily newspaper Monthly 18 Hair black Eyes 19 Food eat Books 20 Clothes tear Dishes 21 Air birds Water 22 Barn hay Library 23 Month week Day 24 Far near There 25 July month Friday 26 Opaque wood Transparent 27 Thermometer temperature Clock 28 Potato vegetable Veal 29 Light dark Dry 30 Sight blind Hearing 31 City mayor State 32 Slipper shoe Cap 33 Present known Future 34 Work problems Play 35 Water glass Coffee 36 Factory workman Store 37 Fat heavy Thin 38 Bread flour Candy 39 Live die Life 40 After before Earlier 41 Sparrow bird Mosquito 42 Picture frame Field 43 Happy laugh Sad 44 Ounce pound Inch 45 Mail write Telephone 46 Complex difficult Simple 47 Linen cool Wool 48 Victory defeat Success 49 Cheap many Costly 50 Pencil write Broom Presentation. These tests were given by Mr. Van Wagenen in the writer's presence. In addition to the directions printed at the top of the sheet, some oral explanations were given ; these The Tests and Their Administration 29 however, were few since the pupils had had some experience with similar tests. A few minutes rest was allowed between each half. At the end of each half, another triad (25a and 50a) was given, being any one of the preceding except the next preceding, 1 Work day 2 Vinegar sour 3 Rain summer 4 Year month 5 Iron heavy 6 Rose bush 7 Country road 8 Eat food 9 Horn blow 10 High low 11 Water liquid 12 Stove heat 13 Snow sledge 14 Rugs floor 15 Boston city 16 Silver tarnishes 17 Hard soft 18 Triangle three 19 Delicious taste 20 Number figures 21 See colors 22 Box wood 23 Fruit basket 24 Front back 25 Foot ankle 26 Raise lower 27 Much more 28 Foot leg 29 Sugar bowl 30 Navy sailors 31 River Hudson 32 Coal black 33 Hair goat 34 Grain wheat 35 Leg knee 36 Park play 37 Baker bread 38 Wall paper 39 People house 40 Sit sat 41 Bright colors 42 Park gate 43 Man legs 44 Lilac shrub 45 Violet odor 46 Under over 47 Kettle utensil 48 Fire warms 49 Fork tine 50 April March Van Wagenen Mixed Relations Test — D Sleep Sugar Snow Week Aluminum Oak City Wear Bell Near Ice Lamp Ice Pictures Kentucky Iron Rough Square Fragrant Word Hear Bottle Water Top Hand Open Good Hand Milk Army Mountain Gold Wool Fruit Arm School Bees Floor Birds Fly Loud House Carriage Fern Red Down Chair Ice Knife Tuesday 30 The Interrelations of Mental Abilities in order to make the time limits as abrupt for triads 25 and 50 as for any other. Method of Scoring. One mark was allowed for each correct response. The highest possible score for each series is 50 marks. £7 & E8 Mixed Relations. Two Series The time for these tests was 9 minutes each. Source. An extension of the Woodworth- Wells test by Dr. E. L. Thorndike. Woodworth and Wells (1911, p. 64). 1 Description. These are in general similar to tests E5 & E6. Each series contains 40 groups of words. Presentation. To each pupil was given a sheet of paper con- taining the forty groups of words. Opposite each group was a blank space large enough to hold the fourth word. At the top of each paper of each series instructions were printed thus: "Write in each line a fourth word that fits the third word in that line in the way that the second word fits the first, as shown in the first three lines." color — red name — John page — book handle — knife fire — burns soldiers — fight The presentation of these two series differs from the presenta- tion of tests E5 & E6 in that in these two it was wholly visual while in tests E5 & E6 it was oral and auditory. Test E7 was given in February and test E8 was given in April. Method of Scoring. One mark was given for each correct response. The highest possible score for each series is 40 marks. Eg & 10 Reading Tests. Two Series: Alpha and I, J, K, L The time allowed was as follows: — Alpha, 30 minutes; I, 5; J, 10; K, 10; L, 15. Source. Test E9 is Thorndike's original Scale Alpha (not the well-known Alpha 2), for Measuring the Understanding of Sentences. Test Eio consists of similar material but much harder to read, and is designated I, J, K, L. (Sept. 1914, pp. 44, 60-64). 2 ^Psychological Review Monographs, vol. 13, 1911. 'Teachers College Record, September, 1914. The Tests and Their Administration 31 Description. Scale Alpha (Test E9) has four paragraphs (the third and the fourth being the same), after each of which some questions are asked. Scales I, J, K, L have each one paragraph and are followed by five, seven, eight, and eight questions respectively. Presentation. Test E9 was given in February. Test Eio was given at one time in April. Above each paragraph instructions are given thus : "Read this and then write the answers. Read it again as often as you need to." Method of Scoring. Each correct answer received two marks ; each answer nearly but not quite correct received one mark; other answers received no mark. The highest possible scores are Alpha 32 and I, J, K, L 56. En & E12 Directions V The time for this test was 5 minutes. Source. This test is by Dr. Thorndike (Sept. 1914, p. 38). * Description. Ten commands are given to the pupils to be executed by them with a pencil on the given sheet of paper. Presentation. The pupils were told that this was a Directions test and were asked to follow the printed instructions. Extensive explanations were unnecessary since the pupils had had experience with this sort of test. The same test was given twice but on different days. Method of Scoring. One mark each was given for a correct response to Directions 1, 2, 3, 4, 8. Two marks each were given for a correct response to Directions 5, 6, 7, 9, 10. If one of these five was not wholly right but more than half right, one mark was given for it. The highest possible score is 15 marks. E13 & E14 Visual Vocabulary The time for this test was 30 minutes each. Source. This test is Thorndike's original Reading Scale A, Visual Vocabulary (not the well-known Reading Scale A2, Visual Vocabulary) (Sept. 1914, p. 3). 1 Loc. cit. 32 The Interrelations of Mental Abilities Presentation. This test was given twice. The instructions are printed at the top of each paper: "Look at each word and write the letter F under every word that means a flower," etc. Method of Scoring. This was in terms of penalties. Score = Errors-|-Omissions. For the purpose of comparison with the other tests the deviations from these marks had their positive and negative signs transposed. The plus signs were made minus and the minus signs were made plus. The highest possible merit score is 43 marks. E15 & E16 Visual Vocabulary. Two Series: XII and VIII The time for each series is 25 minutes. Source. These two tests are by Thorndike (Sept. 1914, pp. 27 and 29) . Description. These are similar to tests E13 and E14 except that only four rubrics are used. Test E15 (XII) has 104 words. Test E16 (VIII) has 100 words. These words are not arranged in groups and only roughly in the order of difficulty. Presentation. Instructions are printed at the top of each sheet similar to tests E13, E14 and E17. Method of Scoring. Same as in tests E13 and E14. The highest possible merit score is 104 marks for test E15 and 100 marks for test E16. EiJ Visual Vocabulary IX The time for this test is 15 minutes. Source. This test is by Thorndike (Sept. 1914, p. 27). Description. This test is similar to E13, E14, E15 and E16. One hundred and thirty words are given. These differ widely in degree of commonness; only four rubrics are used. Presentation. This is the same as for tests E13, E14, E15, and E16. Method of Scoring. One mark was allowed for each word correctly denoted. The highest possible score is 130 marks. E18 Directions VII The time for this test is 10 minutes. The Tests and Their Administration 33 Source. This test is by Thorndike. Nothing has hitherto been published upon it. Description. Twelve commands are given to the pupils to be executed by them with pencils on the given paper. The fulfillment of the commands depends on the knowledge of certain words. Presentation. The pupils were told that this was a Directions test and were asked to follow the instructions which were printed at the top of the sheet. Method of Scoring. c ame as in tests E13 & E14. The highest possible merit score is 54 marks. Two samples (21 the easiest and 32 the hardest) of the ques- tions are given below: Do what it says to do. 21. Show by a cross which costs most : an orange a suit of clothes a pair of skates a pound of sugar 32. Show by a cross each word that means "to make clear" or some- thing like "to make clear" : execrate expound clarify traduce elevate extort satisfy explain elucidate antipathy Group F. Logical Tests Fi & F2 Faulty Arguments. Two Series The time for each of these is 5 minutes. Source. These are tests No. 37 and No. 39 Briggs (1913, PP- 34-35 )•* Description. Each series consists of four arguments. Three of these are invalid and one is valid. Presentation. At the top of each sheet are given instructions thus: — "Some of these arguments are faulty. Find each one that is unsound and in the blank space below it briefly tell why." These instructions were supplemented by some oral explanations. Method of Scoring. One mark was given for each fallacy explained. If the valid argument was left untouched and the others were attempted one mark was given for it. The highest possible score for each series is 4 marks. 1 Loc. cit. 34 The Interrelations of Mental Abilities F3 & F4 Catches. Two Series The time for F3 is 5 minutes and for F4 is 6 minutes. Source. These are tests No. 41 and No. 42 Briggs (1913, P- 36). Description. Each series consists of five statements, each of which contains some impossibility. Presentation. At the top of each sheet are given instructions thus: "In each of the following sentences there is a 'catch.' Tell where the nonsense in each case is." These instructions were supplemented by some oral explanations. Method of Scoring. In F3 for each nonsensical sentence ex- posed, one mark was given. In F4 one mark each was allowed for 1, 2, and 5, and two marks each for 3 and 4. The highest possible score for F3 is 5 marks and for F4 is 7 marks. The Statistical Treatment of the Scores 1. The tests were in general treated as six groups according to the similarities of the tests. Group A. Mechanical or Motor or Constructive. Group B. Non-Verbal Spatial Relations. Group C. Non-Verbal Computational. Group D. Arithmetic stated in words. Group E. Very Verbal. Group F. Logical. These names are not adequately descriptive, nor, in the case of F, exactly appropriate, but are used for convenience. All that is implied by any one of them is the reference to the group of tests themselves. Words, for example, are involved to some extent in the so-called Test of Non-Verbal Spatial Relations; the tests of Diagram Matching and Diagram Drawing are not so strictly mechanical or constructive as the Assembling tests. The grouping, however, is probably the most significant single grouping to make. From data to be given later in this monograph, a critic may regroup in any desired way. 2. The records of the two sexes have been kept apart and treated separately. The Tests and Their Administration 35 3. Every test in a given group has been correlated by the Bravais- Pearson "product-moments" method (formula d) with every other test in that group. The record of every pupil who was present in both the tests to be correlated, was retained. The record of a pupil who was absent from one or both the tests, was omitted. For these correlations see Tables 49 to 56. 4. These correlations have been modified for attenuation by the formula (e), that is, using geometrical averages or when negative correlations made the use of geometrical averages impossible by the formula (/), that is, using the arithmetical averages. Though the geometrical average is always smaller than or equal to the arithmetical average, yet a modification for attenuation by the geometrical average is not necessarily smaller than a modification made by the arithmetical average, since the difference between the two denominators may be equal to, or greater than, the differ- ence between the two numerators. For these modified correla- tions see Tables 57 to 62. 5. The Average Deviations for each test were calculated and the sum of the average deviations for both parts of each pair for both sexes was found, and this sum was employed as a basis of calculation for the weights to be allowed for each test in the composites. One exception was made. The sums of the average deviations of tests E17 and E18 were computed sep- arately. For these average deviations and their sums and the weights allowed see Table 13. 6. Six Composite Scores for each individual have been com- puted, weight being given as above described. 7. The correlations of these composites one with another have been computed. See Tables 5 and 6. 8. These correlations have been modified for attenuation. See Table 65. 9. Each group of correlations has been tabulated in rows and in columns. 10. Each column of the raw correlations of the composites for the boys has been correlated with every other column. The same procedure has been followed for the girls. The correla- tions (Rab) are given in Tables 20 and 21. 11. Each of these correlations (Rab) has been corrected by Spearman's formula (;') and these corrected correlations (R'ab) are given in Table 28. Concerning these formulae (rab, Rab, and 36 The Interrelations of Mental Abilities R'ab) Dr. Spearman writes (1914, p. 109): "The significance of Rab is by no means confined to the present problem. In par- ticular, its relations to rab are most interesting: the one may easily be positive when the other is negative, or vice versa. For many purposes, Rab seems to be the more important value of the two. . . . The question arises, whether or not the coefficients should be corrected for 'attenuation' before calculating Rab. The matter is simplified by the easily demonstrable fact that if Rab is = 1 for the corrected coefficients, it must be so for the uncorrected ones also, and vice versa. And even if Rab has any other value, it will not in general be appreciably modified by correcting for 'attenuation' (the statement sometimes made that the hierarchy tends to be much better for uncorrected than for corrected coefficients is erroneous). The correcting process has the disadvantage of greatly complicating equation R'ab." Formulae m = a measure of an individual in a test. n = the number of individual m's in a group. S or 5 = Summation. A = Arithmetic average. x or y = the deviation of any m from A. A. D. = Average Deviation from A. S.D. or n = Standard Deviation. r — Correlation according to the "Product-moment" method. P. E. = Probable Error, or Sampling Error : used only when an inference is drawn from the particular to the general. Rab = The Correlation of the respective correlations in two columns. R'ab = Rab corrected for the Sampling Errors of pax and pbx by the Spearman formula (;) . pax — Deviation of each value of rax from the mean of rax. pbx — Deviation of each value of rbx from the mean of rbx. "Sax = P.E. of rax. %bx = P.E. of rbx. t^ax = mean value of % 2 ax -4- .674s 2 . n^bx = mean value of ~2?bx -^- .674s 2 . aax obx = mean value of %ax %bx -i- .674s 2 . The Tests and Their Administration 37 Formulae Arithmetic Average = 2«m (a) A.D. = Arithmetic 5 x\n or Arithmetic %y\n (b) « or S.D. = M** or V*z! or Ml* - A 2 (,) n n n *-*» = = or ± ^ ( d ) "V2(x 2 ) — 2(y) 2 °x°v Modifying formula for f r r r ■ r ■> . b . „4 ' Xl VI ' XI »a ' xz VI ' XI 112 f „\ attenuation using geo-y *v ^ K e ) metrical averages [ C«i* 2 • ^vw) Modifying formula for] r \ r \ r \ r attenuation using arith- y *v — zr, 7^ ^ \T) metical averages J iC^fmsJ V«" /-6745 —P. E.r (fc) .6745 \V«~ TJ — S(p<„; p l r ) ... \2(p 2 a ,)2( P 2 te ) _ SCp.wPfta,) — (»— 1) r ab a ax a ix R * = /( — )( J 0) "V \ %iP 2 ax) — in— D' 2 „ 5 \ 2(p 2 6j ,) - (»- l)o« to \ •6745 P.E.a =± -— : — (*) (0 .6745(7 distribution P.E. =P.E. — P.E. average true average obtained average \n SECTION II THE NATURE OF THE ABILITIES MEASURED: THE INTERRELATIONS OF THE SEVERAL TESTS The Manipulative or Mechanical Tests The abilities measured by the Manipulative tests are not by any means identical. The notes which follow are based upon Tables i and 2. All correlation numbers are hundredths. Tests A1&A2 (Stenquist Construction or Assembling Test) ^require synthetic ability. The subject must be able to pick up two or more pieces and to combine them, without any pattern, into a workable whole. Symbols of all kinds are omitted. The subject may succeed with some of these devices by the method of trial and error, but he is much more likely to succeed if he recognizes the device and knows its use and the way it looks when it is properly united. The average correlations of this pair with the other Manipulative tests, excluding handwriting, are only +25 (raw) and only -j-47 (modified), while the average reliability coefficient is -(-49- Assembling correlates with one of the other half as well as it does with itself. Tests A3&A4 (Recognition of Mechanical Devices) require some knowledge of names, some knowledge of mechanical de- vices, and some slight ability to reach a conclusion by the method of exhaustion. This pair does not require any motor or manipu- lative skill. The average correlations of this pair with the other members of the group, excluding handwriting, are only +19 (raw) and only +33 (modified), while, the average reliability coefficient is +59. It correlates with one of the others only one third as well as it does with itself. Tests A5 & A6 (Knot Making) require synthetic ability. The subject does not need any knowledge of words, but he must be able to understand a pattern and to apply the pattern to concrete substances. He needs also some power of visual imagery and some manual dexterity. The average correlations of this pair with the other members of the group, excluding handwriting, are only +31 (raw) and only +50 (modified), while the average reliability coefficient is +65. It thus correlates with one of the others about half as well as it does with itself. Interrelations of the Several Tests 39 TABLE 1— INTERRELATIONS OF THE MANIPULATIVE TESTS Averages of Boys' and Girls' Average Raw Correlations Stenquist Construe- Recogni- tion or tion of Diagram Diagram Iland- Assem- Mech- Knot Metal Match- Draw- writ- bling anisms Making Puzzles ing ing ing A1&A2 A3&A4 A5&A6 A7&A8 A9&A10 A11&A12 A13&A14 Al & A2 30 30 27 27 12 —22 A3 & A4 30 .. 15 22 14 16 —16 A5 & A6 30 15 .. 22 39 48 —20 A7 & A8 27 22 22 .. 22 14 —02 A9 & A10 27 14 39 22 .. 32 03 All & A12 12 16 48 14 32 .. —05 126 97 154 107 134 122 — «2 Averages 25 19 31 21 27 24 —10 A1&A2 A3&A4 A5&A6 A7&A8 A9&A10 A11&A12 A13&A14 Reliability Coefficients... 49 59 65 32 52 80 64 TABLE 2— INTERRELATIONS OF THE MANIPULATIVE TESTS Averages of Boys' and Girls' Correlations Modified for Attenuation A1&A2 A3&A4 A5&A6 A7&A8 A9&A10 A11&A12 A13&A14 Al & A2 57 50 63 50 16 —36 A3 & A4 57 .. 22 44 24 18 —24 A5 & A6 50 22 .. 4G 70 64 —30 A7 & A8 63 44 46 .. 46 25 —04 A9 & A10 50 24 70 46 .. 49 12 All & A12 16 18 64 25 49 —07 236 165 252 224 239 172 —89 Averages 25 19 31 21 27 24 —10 Tests A"j & A8 (Puzzles) require analytic ability. The subject does not need any knowledge of words more than that required to understand instructions. He does not need to know the purpose of the devices, in fact they have none except to perplex him. The simpler puzzles may be solved by merely fumbling with them, but the more complex puzzles require some insight into their construction. The subject does not need any knowledge of patterns or of mechanical instruments. He can clearly see the whole of each component part. He needs to know only the method by which the parts can be separated. The puzzles of the three graduated series measure, to some extent, the subject's learning ability, since if he recognizes the principle underlying the first puzzle in a graduated series and can use to advantage ' this knowledge, he will find the succeeding puzzles much simpler than they otherwise would be. If he fails to recognize the principle then he must proceed under increasing difficulties as the puzzles become more complicated. The average correlations of this pair with the other members of the group, excluding 40 The Interrelations of Mental Abilities handwriting, are only +21 (raw) and only +45 (modified), while the average reliability coefficient is +32. This is much the lowest reliability coefficient of the group. Its smallness is due probably to the element of chance which enters so largely into all kinds of puzzle tests. This reliability coefficient agrees closely with the findings of Burt and Moore (1912, p. 375), 1 who report a reliability coefficient of +3° f° r w i re puzzles. The test thus correlates two thirds as well with one of the others as it does with itself. Tests A9&A10 (Diagram Matching) require analytic ability. The easiest method of procedure is to isolate the essential part of the whole diagram and to match it with the given quarter. The tests require ability to recognize identities and to carry a spatial scheme in mind. The subject does not need any knowl- edge of words beyond that required to understand instructions. Of the arabic numerals he needs merely enough knowledge to enable him to write the identification numbers. The average correlations of this pair with the other members of the group, excluding handwriting, are only -f-27 (raw) and only -(-48 (modified), while the average reliability coefficient is +52. This test thus correlates half as well with one of the others as with itself. Tests An & A12 (Diagram Drawing) require synthetic ability. The subject must be able to understand and to follow a pattern and to carry a spatial scheme in mind. A knowledge of words beyond the instructions is unnecessary. The average correla- tions of this pair with the other members of the group, excluding handwriting, are only +24 (raw) and only +34 (modified), while the average reliability coefficient is -)-8o. This very large re- liability coefficient is due probably to the very large average deviations, which are larger than any others in the whole investi- gation except tests E7 & E8, and also to the fact that both chance and practice have but little effect on the subjects' scores. This test thus correlates less than one third as closely with one of the other tests as it does with itself. Tests A13&A14 (Handwriting) require a highly complex form of motor activity and coordination of the arm, of the wrist, 1 "The Mental Differences Between the Sexes," Journal of Experi- mental Pedagogy, 1912. Interrelations of the Several Tests 41 of the fingers, of the eyes, and of the cerebro-spinal system. The exceeding complexity of handwriting can be perceived by right-handed persons if they will endeavor to write with the left hand. These tests require some, but not an accurate knowl- edge of spelling, since the subjects were not penalized for mis- spelled words. They require ability to transmute sounds into legible symbols, and to make these symbols clear, even, and beautiful. The average correlations of this pair with the other members of the group are — 10 (raw) and — 15 (modified), while the reliability coefficient is -(-64. This is the highest reliability coefficient in the croup except An and A 12 which is +80 and A5 and A6 which is +65. Handwriting as tested is thus nowise a symptom of the sort of ability required to assemble mechanisms tie knots or dismember puzzles. The low average correlations, apart from handwriting, the highest raw being — |— 31 and the highest modified being +50, indicate that the functions involved in any one test are not identical with the functions involved in the other tests. This is especially true of the handwriting, the correlations of which indicate not only that the functions are different, but that they are somewhat incompatible. The Spatial Relations Tests The notes which follow are based upon Tables 3 and 4. Much more extended tests are needed before anything certain can be inferred about the community of these tests. So far as these results go it is slight. Because of the low correlations of the two halves of the Locus test one with another, and of the test for Similar Figures with the test for Congruent Figures, the modifications for attenuation are subject to very large probable errors. Tests Bi & B2 (Rhombuses). The average correlations of this pair with the other members of the group is only +10 (raw) and only -(-28 (modified), while the average reliability coefficient is +58. Tests B3 & B4 (Locus) seem to demand selective thinking with spatial relations and a knowledge of words and of some well-known objects: canal, boat, watch, circles, parallel straight 42 The Interrelations of Mental Abilities TABLE 3— SPATIAL RELATIONS TABLE 4^SPATIAL RELATIONS TESTS TESTS Averages of Boys' and of Girls' Averages of Boys' and of Girls' Average Haw Correlations Correlations Modified lor Attenuation Matching Matching Similar and Similar and Rhombus Locus Congruent Rhombus Locus Congruent Tests Tests Figures Tests Tests Figures B1&B2 B3&B4 B5&B6 B1&B2 B3&B4 B6&B6 B1&B2 14 05 34 21 B3&B4 14 08 34 47 BS&B6 05 08 21 47 19 22 13 55 81 68 Averages : 10 11 06 28 40 34 B1&B2 B3&B4 B5&B6 Reliability Coefficients 58 22 04 lines, pencil, string, helix, scissors, curves, points of the com- pass, houses, roads. The average correlations of this pair with the other members of the group are only + n (raw) and only +40 (modified), while the average reliability coefficient is only -{-22. This low reliability coefficient is probably due to the in- trinsic difficulty of the test. With some 150 high school girls Miss Rogers obtained a reliability coefficient of only +05. Tests B§ & B6 (Applying Definitions of Similar and of Con- gruent). Understanding of the definitions given for "Similar" and for "Congruent" and recognition of similarities and of dif- ferences in form are the essential requirements. The average correlations of this pair with the other members of the group are only -)-o6 (raw) and only +34 (modified), while the average reliability coefficient is only +04. Arithmetical Tests — Computation Each of these eight tests requires some addition, some subtrac- tion, some multiplication and some division, although tests C3 & C4 are primarily concerned with addition, tests C5 & C6 with subtraction, and tests Cj & C8 with division. Tests C3 to C8 are alike in that they require no ability in reading words and do measure stock arithmetical knowledge. Tests Ci & C2 should have been put in a group by themselves or in the D group, but this was realized too late. That these tests do not belong to this C group is clearly shown by their Interrelations of the Several Tests 43 TABLE 5— ARITHMETICAL TESTS: TABLE 6— ARITHMETICAL TESTS: COMPUTATION COMPUTATION Averages of Boys' and of Girls' Average Raw Correlations. Averages of Boys' and of Girls' Correla- tions Modified for Attenuation. "Catch Prob- lems" Addi- tion Sub- trac- tion Divi- sion "Catcli Prob- Addi- lems" tion Sub- trac- tion Divi- sion C1&C2 C3&C4 C5&C6 C7&C8 C1&C2 C3&C4 C5&C6 C7&C8 CI & C2. C3 & C4. C5 & C6. C7 & C8. '.'. if! .. 24 .. 26 16 34 34 24 34 42 26 34 42 CI & C2 C3 & C4... 36 C5 & C6... 51 C7 & C8... 56 36 84 86 51 84 94 56 86 94 Averages 66 .. 22 84 28 100 33 102 34 143 Averages.. 48 206 60 229 76 236 79 Averages, ing CI exclud- & C2 34 38 38 Averages, exclud ing CI & C2. . . . 85 89 90 Reliabilit r Coefficients . . C1&C2 44 C3&C4 C5&C6 34 49 C7&C8 40 average correlations with the other members of the group, which are only +22 (raw) and only -(-48 (modified), while the aver- age reliability coefficient is +44. Tests C3 & C4 have average correlations of only -j-28 (raw) and only +69 (modified) with the other members of the group, while the reliability coefficient is only +34. If tests Ci & C2 are omitted from the group then the average correla- tions become +34 (raw) and +85 (modified). Tests C5 & C6 have average correlations of only — |— 33 (raw) and +76 (modified) with the other members of the group, while the reliability coefficient is only +49, though this is the highest reliability coefficient in the group. If tests Ci & C2 are omitted from the group then the average correlations become -(-38 (raw) and +89 (modified). Tests Cj & C8 have average correlations of only — |— 34 (raw) and +79 (modified) with the other members of the group, while the reliability coefficient is only +40. If tests Ci & C2 are omitted from the group then the average correlations become -(-38 (raw) and +90 (modified). A test in Addition, Subtraction or Division thus correlates almost as closely with one of the others as it does with itself. Arithmetical Problems: Verbally Stated Even a cursory reading of these tests shows that their contents are very similar. This conclusion is supported by their correla- tions, which show that the difference between any two pairs is 44 The Interrelations of Mental Abilities about the same as the difference between any other two pairs, and this statement is true whether the raw or the modified coeffi- cients are considered. All the average raw correlations are low, the largest is only +35 ; likewise all the average reliability coeffi- cients are low, the largest is only +38. On the other hand, all the average modified correlations are very large, the smallest being -(-83 and their average being +98. The largest of these exceeds even unity, which condition is due to the small size of the reliability coefficients compared with the size of the cross correlations (e. g., Di & D3, Di & D4, D2 & D3 and D2 & D4). TABLE 7— ARITHMETICAL PROB- TABLE 8— ARITHMETICAL PROB- LEMS: VERBALLY STATED LEMS: VERBALLY STATED Averages of Boys' and Girls' Average Averages of Boys' and Girls' Correla- Raw Correlations tions Modified for Attenuation Dl & D2... D3 & D4 , . , D5 & D6. . . D1&D2 38 30 D3&D4 D5&D6 38 30 32 32 70 62 Dl & D2..., D3 & D4 D5 & D6 D1&D2 '.'.'.'. 104 .... 83 187 D3&D 104 106 210 4 D5&D6 83 106 68 189 Averages . 34 35 31 .... 94 105 94 Reliability Coefficients D1&D2 38 D3&D4 30 D5&D6 34 Dr. Bonser's description of his tests (1910, p. 14) 1 may be applied to all these : "The problems in arithmetic test the mathe- matical judgment, in general that form of deductive reasoning most closely resembling the syllogistic movement of formal logic. The steps here involved are three: First, the analysis of the situation by which the essential features of the problem are con- ceived and abstracted; second, the recall of an appropriate prin- ciple to be applied to the abstracted problem, a search among various principles which may suggest themselves for the right one; and third, involved in the second, the inference, the recog- nition of identity between the known principle and the new situa- tion. While this process goes on as implicit, explicitly there are made the concrete applications in the resolution of the prob- lems. Clearly these are examples of deductive reasoning of the usual scientific type, involving data, principles, and inferences. The only element omitted is that of verification, which, by the nature of the tests, cannot here be brought out." x Loc. cit. Interrelations of the Several Tests 45 Very- Verbal Tests All these tests are based essentially upon a knowledge of words and thus differ from many of the preceding tests. The notes which follow are based upon Tables 9 and 10. Tests Ei & E2 (Use of Grammatical Definitions) require a knowledge of grammar, the former especially of verbs and the latter especially of subject, predicate, adjective, adverb and modi- fiers. Ability to reason would be desirable, though the subjects in these tests probably preferred to respond under the influence of first impressions. The tests are far too short to measure the abilities concerned. The average correlations of this pair with the other members of the group are only — |— 19 (raw) and -(-78 TABLE 9— VERT VERBAL TESTS Averages of Boys' and of Girls' Average Raw Correlations Gram- mar Para- Use of Gram- Mixed Mixed graph Direc- Word Knowledge Deflni- mar Rela- Rela- Read- tions . ' . tions Usage tions tions ing E11& E13& E15& E17& E1&E2 E3&E4 E5&E6 E7&E8 E9&E10 E12 E14 E16 E18 El & E2 —04 26 20 25 22 19 30 12 E3 & E4 —04 .. 16 09 —04 —03 02 12 08 E5 & E6 26 16 57 48 41 52 66 33 E7 & E8 20 09 57 .. 36 24 41 46 26 E9 & E10 25 —04 48 36 .. 26 32 46 24 Ell & E12.... 22 —03 41 24 26 .. 26 30 14 E13 & E14.... 19 02 52 41 32 26 .. 53 33 E15 & E16.... 30 12 66 46 46 30 53 34 E17 & E18.... 12 08 33 26 24 14 33 34 150 36 339 259 233 180 258 317 184 Average 19 04 42 32 29 22 32 40 23 E11& E13& E15& E17& E1&E2 E3&E4 E5&E6 E7&E8 E9&E10 E12 E13 E16 E18 Reliability Co- efficients ... 08 31 76 74 37 52 64 72 16 TABLE 10— VERT VERBAL TESTS Averages of Boys' and of Girls' Correlations Modified for Attenuation E11& E13& E15& E17& E1&E2 E3&E4 E5&E6 E7&E8 E9&E10 E12 E13 B16 E18 El & E2 —10 60 48 120 73 62 80 192 E3 & E4 —10 28 15 —08 —07 04 22 80 E5 & E6 60 28 .. 76 90 64 75 90 75 E7 & E8 48 15 76 66 40 58 62 58 E9 & E10 120 —08 90 66 .. 57 61 86 84 Ell & E12.... 73 —07 64 40 57 .. 46 48 44 E13 & E14.... 62 04 75 58 61 46 76 85 E15 & E16.... 80 22 90 62 86 48 76 .. 80 E17 & E18.... 192 80 75 58 84 44 85 80 625 124 558 423 556 365 467 544 698 Averages .... 78 16 70 53 70 46 58 68 87 A VA?*B POH OHlit - tingE3&E4 91 .. 76 58 81 53 66 75 88 46 The Interrelations of Mental Abilities (modified), while the average reliability coefficient is only -(-08. The difference between the raw and the modified coefficients is due, of course, to the small size of the reliability coefficient. This is especially true when Ei & E2 and E17 & E18 are compounded by the formula (e), the denominator of the fraction being nec- essarily very small, and thereby making the value of the whole fraction very large. The low raw correlation may be due to the element of chance which enters largely into these tests and to the short space of time given for the replies. Tests E3 & E4 (Grammatical Usage) require a knowledge of grammar, both etymological and syntactical, both of abstract rules and of concrete examples. Reasoning ability might, therefore, determine very largely the response, yet many of the pupils seem to have marked as correct those forms which they were in the habit of using or which they had often heard approved. The average correlations of this pair with the other members of the group are only +04 (raw) and only -f-16 (modified), while the reliability coefficient is only +31. The average raw and the aver- age modified correlations are the lowest in this whole group, while the average reliability coefficient is much lower than all the others except two: Ei & E2 and E17 & E18. The very low raw correlation may be due to the element of chance, which enters largely into it. The lowness of both the raw and the modified correlations may be due also to the ambiguity of cer- tain of the replies as signs of intellect. Expert teachers of Eng- lish composition are not unanimous in their opinions concern- ing some of the forms, therefore answers which some teachers would mark correct, others would mark incorrect. Tests £5 & E6 (Mixed Relations) have comparatively a high average correlations with the other members of the group: -(-42 (raw) and +70 (modified), while the reliability coefficient +76 is the highest in this group. Tests £7 & E8 (Mixed Relations) have only moderately high average correlations with the other members of the group: +32 (raw) and +53 (modified), while the reliability coefficient +74 is next to the highest in the group. The difference between the correlations of the two pairs may be due to the fact that tests E5 & E6 were given orally and the time allowed for each quartette was the same. The tests thus given are more difficult than when given visually, as were tests Interrelations of the Several Tests 47 E7 & E8, and when the time for the whole, but not for each quartette, is limited. The element of chance has but little influ- ence on this kind of tests. Tests Ep & Eio (Paragraph Reading). The average correla- tions of this pair with the other members of the group are mod- erately high: +29 (raw) and +70 (modified), while the relia- bility coefficient is only -(-37. The element of chance enters but slightly into these tests. Tests En & E12 are a test of sentence reading plus care in performing simple clerical operations. The test is very short and has a reliability coefficient of only -f-52 between the two trials, three months apart. It correlates with the two tests of paragraph reading about two thirds as clearly as they do one with the other. The averages of its correlations with the other tests in the group are -|-22 (raw) and -f-46 (modified). Tests E13 & E14, £15 & E16 and E17 & E18 are all tests of word knowledge. Tests E13 & E14 have eight rubrics, tests E15 & E16 and E17 have four rubrics, and test E18 uses the method of checking synonyms, together with that of choosing words of stated properties. The interrelations of these tests with each other and with all the others save the tests in Grammatical Usage E3 & E4 are, as shown in the tables, fairly close. In general, Tables 9 and 10 give evidence that Word Knowl- edge and Paragraph Reading are clearly correlated, but that a knowledge of correct usage (if the Starch Scale tests such) is much less clearly related to them than they are to each other. A difference in the difficulty of the paragraphs to be read or in the varieties of words to be classified seems to reduce correla- tion measurably from unity, but the probable errors of all the coefficients are too large to make this indubitable. Tests Fi & F2 (Faulty Arguments) and Fj & F4 (Catches) require ability to perceive and to explain fallacies. They require a knowledge of facts, a practical though not a theoretical knowl- edge of the syllogism, and some subtlety of thought. These four tests are probably somewhat too difficult for pupils of the sixth grade. Moreover, they would be better if more questions were added, thus having four times as many tests, or if each paper were four times as long. The average correlations between the two 48 The Interrelations of Mental Abilities Logical Tests TABLE 11— LOGICAL TESTS TABLE 12— LOGICAL TESTS Averages of age Boys' and of Girls' Aver- Raw Correlations Averages lations of Boys' and modified for of Girls' Corre- Attenuation Faulty Arguments F1&F2 Fl & F2 F3 & F4 26 Catches F3&F4 26 Faulty Arguments F1&F2 90 Catches F3&F4 90 26 26 90 90 Averages 26 26 90 90 F1&F2 Reliability Coefficients 31 F3&F4 16 pairs are -|-26 (raw) and +90 (modified), while the average reliability coefficient of tests Fi & F2 is +31 and of tests F3 & F4 -{-16. The low reliability coefficients accounts for the large difference between the raw and the modified coefficients. SECTION III THE COMPOSITE ABILITIES AND THEIR INTERRE- LATIONS All the #A Tests (Manipulative), except A13 & A14, were combined into two composite scores for each individual by multi- . plying his deviation from the average for his sex in Ai & A2 by 2, his deviation from the average of his sex in A3 & A4 by 6, and so on as shown in the table of weights below (Table 13)- The Ai, A3, A5, Ay, A9, An products were added to form #Ai. The A2, A4, A6, A8, Aio, A12 products were added to form #A2, #Bi and #B2, two composite scores for each individual in all the B Tests (Spatial Relations) were formed similarly. Similarly for #Ci and #C2, #Di and #D2, #Ei and #E and #Fi and #F2. It will be seen in the table that all the tests within any one group are given about equal weight, with the following excep- TABLE 13— AVERAGE DEVIATION OF THE SEPARATE TESTS Multiplier used in obtaining Approximate Weight Boys Girls Total Composite Scores Attached AI &A2 8.06 7.72 6.31 5.84 27.93 2 56 A3 &A4 2.62 1.97 1.89 1.16 7.64 6 46 A5 &A6 3.22 4.20 3.66 5.41 16.49 3 50 A7 &A8 6.53 5.08 5.02 5.12 21.75 2 44 A9 &A10 2.72 3.88 2.88 3.88 13.36 4 53 A11&A12 8.77 7.06 6.51 8.51 30.88 2 62 A13&A14 12.14 12.70 10.47 10.40 45.71 Bl &B2 5.95 5.02 3.45 5.75 21.07 1 21 B3 &B t 1.62 1.27 .75 1.23 4.87 4 19 B5 &B6 3.00 1.91 3.53 2.10 10.54 2 21 CI &C2 1.09 1.00 .88 .76 3.73 2 8 C3 &C4 2.25 2.22 2.31 2.16 8.94 1 9 C5 &C6 2.34 2.59 1.98 2.67 9.58 1 10 C7 &C8 2.65 2.39 2.39 2.22 9.65 1 10 D1&D2 .97 .80 1.20 1.05 4.02 1 4 D3&D4 .97 .88 1.05 .95 3.85 1 4 D5&D6 1.19 .89 1.13 .80 4.01 1 4 El &E2 1.36 1.43 1.19 1.51 5.49 3 16 E3 &E4 3.52 2.23 3.51 3.21 12.47 3 37 ES &E6 5.97 5.32 5.71 5.14 22.14 1 22 E7 &E8 7.19 9.73 7.62 8.69 33.23 1 33 55 E9 &E10 3.14 4.08 3.07 5.02 15.31 3 45 E11&E12 2.57 2.12 2.22 1.66 8.57 1 9 54 E13&E14 3.38 3.22 3.43 3.28 13.31 1 13 1 E15&E16 8.00 5.31 8.04 4.98 26.33 1 26 64 E17 6.26 9.71 15.97 1 16 &E18 2.26 2.09 4.35 2 9 J Fl &F2 .59 .63 1.00 .86 3.08 1 3 F3 &F4 1.36 .81 1.35 .75 4.27 1 4 50 The Interrelations of Mental Abilities tions: Handwriting is given no weight at all. Ei & E2 (Under- standing and Use of Grammatical Definitions) are given about one quarter as much weight as E5 & E6 and E7 & E8 (Mixed Relations), E9 & Eio (Paragraph Reading) or E13 & E14, E15 & E16 and E17 & E18 (Word Knowledge), and half as much weight as the tests E3 & E4 (Usage). On the basis of present knowledge these weightings could be improved, as by the separation of Ci & C2 or by their transfer to the D group, and by attaching much less weight to E3 & E4. The correlations of the two composites of the same group were as follows: TABLE 14— RELIABILITY COEFFICIENTS OF THE COMPOSITE SCORES 31 Boys 38 Girls Average #A1 & #A2 90 77 84 #B1 & #B2 55 17 30 #C1 & #C2 70 69 70 #DI & #D2 56 70 63 #E1 & #E2 82 80 81 #F1 & #F2 39 25 32 TABLE 15— AVERAGE RAW CORRELATIONS OF THE COMPOSITES Boys #A #B w #D #E #F Girls #A #B #C #D #E #F #A 60 00 30 —07 15 29 14 31 08 #B 60 12 03 18 08 15 07 18 21 29 #C 24 12 51 31 —25 29 07 60 47 10 #D 00 03 51 22 —13 14 18 60 59 26 #E 30 18 31 22 32 31 21 47 59 42 #F —07 08 —25 - -13 32 08 29 10 26 42 TABLE 16— CORRELATION OF THE COMPOSITES MODIFIED FOR ATTENUATION Boys #A #B #C #D #E #F Girls #A #B #C #D #E #F #A 86 29 01 34 —11 30 29 19 39 10 #B 86 18 05 25 16 30 14 50 46 128 #C 29 18 80 41 —41 29 14 86 61 21 #D 01 05 80 31 —24 19 50 86 79 57 #E 34 25 41 31 49 39 46 61 79 92 #F —11 16 —41 - -24 49 10 128 21 57 92 TABLE 17— AVERAGES OF THE BOYS' AND OF THE GIRLS' CORRBLA- TIONS MODIFIED FOR ATTENUATION #A #B #c #D #E #F #A 58 29 10 37 00 #B 58 16 28 36 72 #C 29 16 83 51 —10 #D 10 28 83 55 17 #E 37 36 51 55 71 #F 00 72 —10 17 71 When the Composite Scores are correlated, it appears that #C Arithmetical Computation and #D Arithmetical Problems, stated in words, are most akin; The Very- Verbal #E and the Log- ical #F tests are closely allied; the so-called Manipulative #A group and the Spatial Relations #B group are next most closely The Composite Abilities and Their Interrelations 5 1 allied. Between the Manipulative #A group and the Logical #F group the correlation appears to be very low. The facts are given in Tables 15 and 16. The differences between the results for boys and those for girls show regrettably great unre- liability which attaches to even these results from the Composites. If we assume that the Boy-Girl division of the material is a random division, we have as a result of all the errors that have accumulated in correlating and modifying for attenuation, unre- liabilities attached to the final section of Table 17 as follows: TABLE 18 #A #B ftC #D #B r P.B. r P.B. r P.B. r P.B. r P.B. #B #C #D #E #F 58 29 10 37 00 14 00* 045 01 05 16 28 36 72 01 11 05 28 83 51 —10 015 05 155 55 17 12 20 71 11 •This technical zero is not, of course, to be taken at its face value. TABLE 19 #A #c r P.B. r P.B. 29 small 10 015 83 015 37 01 51 05 If we leave out the Spatial Relations #B and Logic #F Com- posites, which have low coefficients of self-correlation, we have: #d P.B. #C #D #B 37 01 51 05 55 12 These results are sound enough, perhaps, to justify the asser- tions (1) that the Mechanical and Diagram test ability is much less closely related to ability with numbers or ability with words than these are one with another; (2) that Arithmetical Problems of the sort used for the pupils in grade six are only slightly con- taminated by differences in ability to read words (55 vs. 51), (3) that such problems are a very unsafe test of general ability to reason, and (4) that the Verbal Composite is the best single representative of the whole set of Composites. SECTION IV THE HIERARCHY OF THE SPECIFIC INTELLIGENCES The writer had not the slightest intention of employing the data of this study as a criterion of Spearman's theory of intelli- gence until all the coefficients of correlation had been obtained. Then, perceiving that the material was well suited for such a study, he calculated the correlations of the correlational columns for the six Composites. He was wholly unbiased ; he cared noth- ing whether the unifocal theory was supported or discredited. Either result would have been equally satisfactory to him. Dr. Spearman writes (1904, p. 225) : "We must insist upon a precise quantitative expression derived impartially from the entire available data ; we must renounce adroit manipulation of tables and graphs, still further rounded into the required shape by ingenious argument; the whole of our experimentally gained figures must without any selective treatment simply of them- selves issue into one plain numerical value." The correlations used here correspond in every way to these requirements. The correlations of the correlations for the Composites go dead against the theory of a single factor as the explanation of the amounts of resemblance found amongst the six Composites abili- ties, whether the raw or the modified coefficients, the coefficients for one sex separately or the averages of the corresponding coeffi- cients for the two sexes, the most reliable or the less reliable col- umns are taken, the average correlation of the correlations is far below unity, being in general much nearer zero than unity. The data, underlying a study of the theory of the hierarchy, may be manipulated in various ways and the results obtained depend upon the method of manipulation which has been em- ployed. First Method: All the correlational columns of the raw com- posites have been correlated and the results have been tabulated and are given in Tables 20 and 21. In this method no manipula- tion of any kind whatsoever has been practised. Every correla- tion, without any regard to the size of the coefficient, has been allowed full weight. The boys show 66 correlations, the total of the positive correlations being 1,458, the total of the negative The Hierarchy of the Specific Intelligences 53 #D1 #D2 #E1 #E2 #F1 #F2 —11 —23 —01 04 —01 01 —10 —18 —07 —02 —07 —16 —26 —56 —07 —09 09 —08 —40 —il —08 —15 03 —19 91 83 —03 —02 —66 —69 77 82 —03 06 —58 —70 91 21 —02 —56 -^9 HI 01 05 —56 —52 21 01 58 45 33 —02 05 58 31 60 —56 —56 45 31 76 —49 —52 33 60 76 TABLE 20— BOYS KAW CORRELATIONS OF THE COMPOSITE CORRELATIONAL COLUMNS „ , Non-Verbal Verbal Very- Manipulative Spatial Arithmetic Arithmetic Verbal Logical #A1 #A2 #B1 #B2 #C1 #C2 #A1 97 95 90 —03 14 #A2 97 .. 89 87 10 14 #B1 95 89 .. 94 —11 —04 #B2 90 87 94 .. —15 —03 #C1 —03 10 —11 —15 .. 91 #C2 14 14 —04 —03 91 #D1 —11 —10 —26 —40 91 77 #D2 —23 —18 —56 -A~ 83 82 #E1 —01 —07 —07 —08 —03 —03 #E2 04 —02 —09 —15 —02 06 #F1 —01 —07 09 03 —66 —58 #P2 01 —16 —08 —19 —69 —70 301 297 287 274 275 284 280 262 158 1^64 ~164 ^70 —39 —60 —121 —147 —169 — 13S —194 —252 —29 —30 —244 —283 TABLE 21— GIRLS #A1 23 —15 03 #A2 23 .. —74 06 #B1 —15 —74 .. —39 —3 #B2 03 06 39 #C1 10 39 —37 —21 #C2 02 30 —14 —43 #D1 —12 14 —20 03 #D2 —24 02 —09 —16 #E1 —02 15 30 43 #E2 —12 04 —11 05 #F1 —22 —16 38 43 #F2 —17 —50 50 56 38 133 157 198 478 —104 140 210 80 —66 —7 —53 118 394 313 462 414 486 439 342 102 10 02 —12 —24 —02 —12 —22 —17 39 30 14 02 15 04 —16 —50 -3'i —44 —20 —09 30 —11 38 50 -21 —43 03 —16 43 05 43 56 98 84 81 60 72 34 —26 98 80 79 52 69 10 —20 84 80 95 66 85 65 02 81 79 95 68 84 44 10 60 52 66 68 77 51 :>« 72 69 K5 84 77 45 21 34 10 05 44 51 45 50 -26 —20 02 10 26 21 50 t78 420 494 463 488 462 380 215 81 107 32 49 o 23 38 113 correlations being 853, and the average being +09. The girls show 66 correlations, the total of the positive correlations being 1,963, the total of the negative correlations being 491, and the average being -f-22. The average for both sexes, +16, gives no evidence for the theory of the common factor. Second Method: The manipulation employed in this method is the combining of the correlations from #Ai and #A2, those from #Bi and #B2, etc., and the using of their averages. The results are given in Table 22. The boys show 15 correlations, the total of the positive correlations being 299, the total of the nega- tive correlations being 286 and the average being -4-oi. The girls show 15 correlations, the total of the positive correlations being 509, the total of the negative correlations being 169 and the aver- age being +23. The average for both sexes, +12, is as before against the theory of the Common Factor. 54 The Interrelations of Mental Abilities TABLE 22— CORRELATIONS OF THE CORRELATIONS. FORMULA (O BOYS GIRLS Boys #A #B #C #D #E #F Girls #A #B #C #D #E #F #A #B 86 12 20 —59 41 —64 46 91 09 04 86 06 —27 29 03 —64 —60 —38 —04 78 #C 12 06 85 —53 —33 46 —60 73 81 21 #D 20 - -27 85 17 —14 91 —38 73 76 30 #E —59 29 —53 17 —73 09 —04 81 76 —03 #F 41 03 —33 —41 —73 04 78 21 30 —03 TABLE 23— CORRECTED BY DR. SPEARMAN'S FORMULA (■) #A #B #C #D #E #F #A #B #C #D #E #F #A 09 30 m 04 09 04 #E 30 #F 68 TABLE 24— ARITHMETIC COMBINED RAW. FORMULA <£ #A #B #CD #E #F #A #B #CD #B #F #A 86 62 —99 37 —56 91 49 65 #B 86 39 16 —11 —56 —18 —19 82 #CD 62 39 —50 82 91 —18 55 77 #E —99 16 —50 —73 49 —19 55 —34 #F 37 —11 82 —73 65 82 77 —34 Third Method: The manipulation employed in this method is the same as that of the second method, only it proceeds farther and averages the correlations for the two Arithmetical Com- posites : C and D. The boys show io correlations with an aver- age of +09. The girls show 10 correlations with an average of +29, giving an average of -(-19 for the two sexes together. It will be observed that the elimination of the correlations between two identical or closely similar abilities does not raise the correla- tions of the columns toward the high values required by the theory of a common factor. Table 24. Fourth Method: Dr. Spearman lays down the standard ( 1912, p. 56) : "In order to attempt to estimate the correct correlation between the columns, it is required that in each of these columns the mean square deviation should be at least double the correc- tion to be applied to that deviation." And again he writes (1914, p. 112) : "Reject all pairs of columns, in either of which the sum of the squares of the probable errors exceeds one-fourth of the sum of the deviations from the average." This fourth method is in harmony with the above standard, otherwise it is the same as the first method. The columns and their correlations which remain are : The Hierarchy of the Specific Intelligences 55 TABLE 25 Boys Girls r ' r r #A1 & #A2 97 #B2 & #C1 —15 #A1 & #C1 10 #C1 & #D1 81 #A1 & #C1 -03 #B2 & fC2 -03 #A1 & JC2 02 #C1 & #C2 81 #A1 & #C2 14 #B2 & #D1 -A0 #A1 & #D1 —12 #C1 & #B1 60 &£4 £ %£\ -3S #B2 & t D2 -* 7 # A1 * # D2 - 24 #C1 & #E2 72 #A1 & #D2 —23 #B2 & #F1 03 #A1 & #E1 -02 #C2 & #D1 80 £41 $ 4E 1 - 01 # C1 & # c2 91 #A1 & #B2 —12 #C2 & #D2 79 #A2 & #C1 10 #C1 & #D1 91 #A2 & #C1 39 #C2 & #B1 52 #A2 & #C2 14 #C1 & SBl -66 #A2 & #C2 30 |c2 & #B2 69 S4 2 £ f 5! - : 2 #C2 & « D1 77 #A2 & #D1 14 #D1 & #D2 95 #A2 & #D2 —18 #C2 & #D2 82 #A2 & #D2 02 #D1 & #E1 66 S^ 2 t # S 1 — ^ #D1 & # F1 — S 6 #^2 & # E1 !5 #D1 & #E2 85 £1J 4 SSI "iS #D2 & # F1 - 56 #^2 & # E2 °* # D2 & #E1 68 #B1 & #C2 —04 #C1 & #C2 98 #D2 & #B2 81 The Probable Errors for the single correlations of the Com- posites are as follows : TABLE 26 Formula (g) Formula (A) 31 Boys 38 Girls 31 Boys 38 Girls r P.E. P.E. r P.B. r p.b. 10 12 11 Oto 22 12 Oto 20 11 20 12 11 23 to 36 11 21 to 36 10 30 11 10 37 to 46 10 37 to 47 9 40 10 9 47 to 54 9 48 to 56 8 50 9 8 55 to 61 8 57 to 63 7 55 8 8 62 to 68 7 64 to 70 6 60 8 7 69 to 73 6 71 to 76 5 65 7 6 74 to 79 5 77 to 82 4 70 6 6 80 to 84 4 83 to 86 3 75 5 5 85 to 89 3 87 to 92 2 80 4 4 90 to 93 2 93 to 97 1 85 3 3 94 to 97 1 98 to 100 90 2 2 98 to 100 95 11 100 The boys show 25 correlations, the total of the positive correla- tions being 479, the total of the negative correlations being 371, and the average being -)~ 4- The girls show 26 correlations, the total of the positive correlations being 1,189, th e total of the negative correlations being 50, and the average being +44. The combined result is +24. Fifth Method: This is the same as the second method, except that the standard mentioned in the fourth method is employed. For the boys three columns and their correlations remain, the other twelve being excluded by the standard. These three are: #A & #C+i2, #A & #D+20, #B & #C+ 06. The aver- age is -(-13. For the girls all the columns are excluded by the standard. Sixth Method: This is the same as the third method, except that the standard mentioned in the fourth method is employed. By this method all the columns for both boys and girls are excluded by the standard. Seventh Method: This is the same as the first method, except 56 The Interrelations of Mental Abilities that both the standard and the formula (;') are applied. The columns and their correlations, which remain, are : TABLE 27 Boys Girls #A1 & #A2 102 #B2 & #C1 —19 #A1 & #C1 13 #C1 & #D1 96 #A1 & #C1 00 #B2 & #C2 00 #A1 & #C2 00 #C1 & #D2 93 #A1 & #C2 14 #B2 & #D1 —59 #A1 & #D1 —19 #C1 & #E1 78 #A1 & #D1 -13 #B2 & #D2 -78 #A1 & #D2 —11 #C1 & #E2 84 #A1 & #D2 —32 #B2 & #F1 11 #A1 & #B1 00 #C2 & #D1 85 #A1 & #F1 —01 #C1 & #C2 104 #A1 & #B2 —05 #C2 & #D2 86 102 #B2 & #C1 —19 00 #B2 & #C2 00 14 #B2 & #D1 —59 —13 #B2 & #D2 —78 —32 #B2 & #F1 11 —01 #C1 & #C2 104 07 #C1 & #D1 106 07 #C1 & #F1 —85 —10 #C2 & #D1 89 —24 #C2 & #D2 113 —10 #D1 & #F1 —77 —12 #D2 & #F1 —88 #A2 & #C1 07 #C1 & #D1 106 #A2 & #C1 41 #C2 & #E1 57 #A2 & #C2 07 #C1 & #F1 -85 #A2 & #C2 21 #C2 & #E2 74 #A2 & #D1 —10 #C2 & #D1 89 #A2 & #D1 08 #D1 & #D2 109 #A2 & #D2 —24 #C2 & #D2 113 #A2 & #D2 00 #D1 & #E1 75 #A2 & #F1 —10 #D1 & #F1 —77 #A2 & #E2 00 #D1 & #E2 97 #B1 & #C1 —12 #D2 & #F1 —88 #A2 & #E1 03 f D2 & #E1 81 #B1 & #C2 00 #C1 & #C2 112 #D2 & #E2 95 Twenty-five correlations remain for the boys. The total of the positive correlations is 553, the total of the negative correla- tions is 508, and the average is +02. Twenty-six correlations remain for the girls. The total of the positive correlations is 1,308, the total of the negative correlations being 65 and the average being +48. The combined result, +25, is far from the approach to 100 required by the theory of the hierarchy, due to one common factor as the main cause of correlation. Eighth Method: This is the same as the second method, except that both the standard and the formula (/) have been applied. For the boys three columns and their correlations remain: #A & #C+09, #A & #D+30, #B & #C+04. The total is -{—43, and the average is +11. For the girls all the columns are excluded. The evidence for the boys is against the hierarchy, and for the girls it is non-existent (Table 23). Ninth Method: This is the same as the third method, except that both the standard and the formula (/) are employed. All the columns for both the boys and the girls are excluded. Tenth Method: The manipulation employed in this method was the arranging in columns of the average raw correlations of boys and of girls for each Composite (Table 28), and then correlating these columns. The results are given in Table 29. TABLE 28 TABLE 29 Average Raw Correlations of the Boys' Correlations of the columns of the and of the Girls' Composites Average Raw Correlations of the Boys' and of the Girls' Composites #A #B #c #D #B #F #A #B #C #D #B #F #A 38 26 07 30 00 07 08 32 —73 36 #B 38 10 10 20 18 07 —26 —70 —99 04 #C 26 10 56 39 —08 08 —26 73 35 —02 #D 07 10 46 40 07 30 —70 73 54 —08 #E 30 20 39 40 37 —73 —99 35 54 —71 #F 00 18 —08 07 37 36 04 —02 —08 —71 The Hierarchy of the Specific Intelligences 57 These correlations extend quite evenly from -(-73 to — 99. Table 30 shows 15 correlations, the total of the positive correla- tions being 249, the total of the negative correlations being 349, and the average being — 07. Eleventh Method: The manipulation used in this method was the arranging in columns of the average modified correlations of the boys and of the girls for each Composite (Table 30), and then correlating these columns; the results are given in Table 31. The correlations extend quite evenly from -j-68 to — 97. Table 31 shows 15 correlations, the total of the positive correlations being +196, the total of the negative correlations being — 467, and the average being — 18. Twelfth Method: The writer applied to Table 28 the standard and the formula (/), but these excluded all the columns and their correlations. TABLE 30 TABLE 31 Average Modified Correlations of the Correlations of the columns of the Boys' and of the > Girls ' Composites Average Modified Correlations of the Boys' and of the Girls' Composites #A #B #C #D #E #P #A #B #C #D #E #F #A 58 29 10 36 00 —66 —01 19 —93 68 #B 58 16 28 36 72 —66 —97 —95 24 10 #C 29 16 83 51 —10 —01 —97 68 —17 —31 #D 10 28 83 55 16 19 —93 68 07—18 #E 36 36 51 55 70 —93 24 —17 07 —VJ #E 00 72 - -10 16 70 68 10 —31 —18 —47 It should be noted that the combination of the results reducing the sampling errors does not cause a closer approach to the -j-ioo required by the unifocal theory ; nor does the use of correlations modified to offset the effect of the chance inaccuracies in the original measures. The correlations of the correlations for this group show no evidence of the unifocal theory, but on the contrary reveal a notable specificness in the abilities measured by the #A, #B, #C, #D, #E and #F groups. The question needs retesting with larger groups to reduce the sampling errors and with more extended tests to reduce the complexities of inference due to the low self-correlation coefficients. Spearman's use of the correla- tions of the correlations as a criterion of the nature of the organization of human faculty is most ingenious and important, but the actual working of his "standard" seems to cut out the columns with the low correlations and so the cases where specific- ness would be especially shown. SECTION V SEX DIFFERENCES These tests give results supporting the conclusion of recent years that the abilities of boys and of girls of like age are on the whole approximately equal, that the boys are better in dealing with mechanical contrivances and a little better in mathematics, while the girls are better in dealing with words and verbal rela- tions. The results may be stated most briefly in terms of per- centages of overlapping or in terms of the multiple of the varia- bility for the score in question by which the boys' average sur- passes that of the girls. In this study the latter method has been chosen. With the results from the present investigation are recorded also the results from similar tests by Mrs. Woolley (H. B. Thompson), Thorndike, Rusk, Bonser, and Burt and Moore. These are shown in Tables 32 to 37. TABLE 32 Number Boys' of Separate Boys Boys' Average — Tests, in Which Exceed Average — Formulae Girls' One Sex Exceeds Girls Girls' (e) (b) Average the Other- by Average P.E. A.D. A.D. Boys Girls Total #A (Odds) 2.90 #A (Evens) 2.39 2.65 .18 4.92 .50 9 3 12 fi «::::: i:l ™* •" 3.0* .45 4 2 « IS ( (Evenl)-.:::: -m - 26 ° 5 199 - 13 3 5 8 $5 ( ( Evensj::::: :! 8 - 35 - 05 " •» 6 ° 6 IS Ksj::::: i:SI lu ° 3 4 - 37 ■* 12 6 18 If ( ( Evens)::::: =:» - 18 ° 6 - 92 - 20 ° 4 4 Handwriting ... -j^J . —10.54 .94 11.43 —.92 J) J J 34 22 56 Puzzles A7&A8.. 5.16 —3.14 1.01 2.93 5.44 .19 Analogies .54 E5 to E8 1.40 .97 .30 6.92 .14 TABLE 33 Computed from Mrs. Woolley's data (1903, 109, 125) 50 students. Boys' Median — . Ingenuity Tests , Girls' Median #1 #2 #3 #4 #5 Physics Average A.D. —.13 +.32 +.62 +.60 +.73 +.89 +.50 TABLE 34 Computed from Thorndike's data (Ed. Psych., Vol. Ill, 1914, page 183). Boys' Median — Associative and High School College Girls' Median Conceptual Processes Mathematics Mathematics A.D. —.06 .22 —.17 Sex Differences 59 TABLE 35 Computed from Miss Rusk's data (Thomdike, Ed. Psych., Vol. Ill, p. 181). Boys' Median — High School English High School Physics Girls' Median A.D. —.55 .35 TABLE 36 Computed from Dr. Bonser's data (1910). (Grades 4A to 6A) Boys' Median — Boys' Median — Girls' Median Girls' Median Average P.E. A.D. A.D. Mathematical 3.14 Judgment 5.73 Table VI 3.83 3.27 ± .44 8.21 .53 Page 25 1.55 2.08 Controlled — .15 Association .39 Table XIII .18 .29 ± .08 3.43 .08 Page 35 .71 .30 Controlled —12.16 Association — 3.50 Table XX —5.25 —5.35 ±1.08 15.10 —.35 Page 42 — 4.58 — 1.25 Selective .51 Judgment 1.90 Table XXVI —4.25 .20 ± .83 9.90 .02 Page 52 4.00 —1.16 TABLE 37 Computed from Burt and Moore's data (1912, pp. 372-375). Boys' Median — Boys' Median — 65 Liverpool Children : Girls' Median Girls' Median Addition 15 .49 Multiplication 13 .41 130 Wallsey School Children: Wire Puzzles 22 .74 Reconstructing Picture Blocks 28 .92 Reconstructing Picture Postcards — 02 — .07 Analogies — 15 — .48 Completion of Arguments 07 .21 The average ages of the boys and of the girls are almost identical. TABLE 38 Subjects in the Composites All the Subjects 31 Boys 38 Girls 37 Boys 46 Girls Totals : 364. years 450. years 434. years 542. years Averages: 11.741 years 11.842 years 11.73 years 11.782 years The average marks of the two sexes obtained in the class- room examinations during February, March, April, May, and June in arithmetic, geography, history, grammar, composition, and spelling are almost identical: Boys' average marks, 79.874 marks; and girls' average marks, 79.528 marks. Therefore no appreciable difference exists between these two groups so far as ages and scholastic attainments, as measured by class-room examinations, are concerned. 60 The Interrelations of Mental Abilities If the average (see Sex Difference, Tables 33 to 38) be taken of excesses in the Manipulative Tests (#A), in Mrs. Woolley's Ingenuity Tests and Physics, in Miss Rusk's Physics and in Burt and Moore's Puzzles (wire, block, and postcard), it is +.50; that is, the boys exceed the girls by 50 per cent of one A.D. If the average be taken of excesses in the Mathematical Tests (#B and #C and #D), in Thorndike's high school subjects, in Bonser's Table VI, and in Burt and Moore's Addition and Multi- plication, it is +.27; that is, the boys exceed the girls by 27 per cent of one A.D. If the average be taken of excesses in the Reasoning Tests (#D and #F) in Bonser's Tables VI and XXVI, and in Burt and Moore's Completion of Arguments, it is -(-.18; that is, the boys exceed the girls by 18 per cent of one A.D. If the average be taken of excesses in the English Tests (#E) and Miss Rusk's High School English, it is — .15 ; that is, the girls exceed the boys by 15 per cent of one A.D. If the average be taken of excesses in the Analogies E5 to E8, Thorndike's Associative and Conceptual Processes, Bonser's Con- trolled Association (Tables XIII and XX), and Burt and Moore's Analogies, it is — .13; that is, the girls exceed the boys by 13 per cent of one A.D. If the average be taken of excesses in the simple Arithmetic (#C) and in Burt and Moore's Addition and Multiplication, it is +.26 ; that is, the boys exceed the girls by 26 per cent of one A.D. If the average be taken of excesses in the Puzzle Tests A7 & A8 and in Burt and Moore's Puzzles (wire, blocks, and post- cards), and in Mrs. Woolley's Ingenuity Tests I, III, and IV, it is +.41 ; that is, the boys exceed the girls by 41 per cent of one A.D. In the handwriting the girls exceed the boys by 92 per cent of one A.D. In the Separate tests of this study (Table 32) the boys are superior in 34 tests and the girls in 22 tests out of 56. In the Composites the boys are superior in (#Ai), (#A2), (#Bi), (#B2), (#Di), (#D2), (#Ei) and (#E 2 ), while the girls are superior in (#Ci), (#C2), (#Fi) and (#F2). Sex Differences 61 Sex Variability The variability of the boys is, on the whole, a trifle greater than that of the girls. The respective average deviations in the Composites are as follows: TABLE 39 AVERAGE DEVIATIONS (WEIGHTED) OP THE COMPOSITES #A1 #B1 #C1 #D1 #E1 #F1 #A2 #B2 #C2 #D2 #E2 #F2 Boys 56.5 12.0 7.41 2.32 33.3 1.67 53.2 10.4 6.93 1.87 31.8 1.85 Girls 39.1 8.8 5.73 2.47 41.6 1.92 47.1 9.7 6.42 2.07 33.6 1.26 SECTION VI INDIVIDUAL AND COMPOSITE SCORES Appended in Tables 40 and 41 are the original gross scores for each individual in each test and in Tables 42 and 43 are the Composite Scores devised by adding the weighted deviations as described on page 49. Appended in Table 44 are the averages for each sex in each test, and in Tables 45 to 48 the Reliability Coefficients or Correlations between the two trials of the same test, or two similar tests, and in Tables 49 to 56 the raw Correlations of each with every other test in its group, and in Tables 57 to 62 the correlations, modi- fied by Spearman's formulae (e and /) for Ai & A2 with A3 & A4, Ai & A2 with A5 & A6, and so on, and in Tables 63 and 64 the raw correlations of the Composite Scores, and in Table 65 the modified Correlations of the Composites. Individual and Composite Scores 63 31 OnOt-OMUNNNNNNW^ONTjieNONO^NNrlNOOtOTKNO^NNlM | t- pCJ rH CO rH rH rH rH rH rH rH rH rH CMCM tH tH CMrHrH rHrH OS CO PQ rH rH CM rH rH rH rH rH rH tH CM rH cS r-i rH r-i rHCOi-t WrHrH t5 1M I OO I I CSr-trHCOt-OOCM I O^OS© I I rH t-t-©-*OS«^ W CM© 00 ttIOQO© tH I t- . ^ I* m tf — 1 |OaO|iHO«>»OCBTH'*THrHO»OlftOO| INOOi'cgo I i COC-Ot-CMlOCM t-CO I O Q Jh I CM CO I CO CMrH CO C4NH I I CMiHrHrHiH I rH HC4 CM rH ■* o < r* Of m O IOO I ^OOOOQOONHOO^OOO | |lO©Ot-CM©0 I HNOOOJOOOO© IN JT iHJ 1 CMCM I rH CM rH CM rH CM rHrH CMCM r-l CM CM I I HNW rH rHCMCM IrHrHCMCM CMrHrH MM g q |» J 5 INH I rHrH rHrH rHrH rH rHCMrHrHrH (rH I NHihHt-ii-i-i | ,H CM rH rH rH ,-" rH OS J °Q OCO®ttt-lOCOCqWOOO^»OS«iQO«t-(»t-«eOt-C30COOOQOClO®0»l£3M5Dt-0^ I CO 2 ■ j © rHCMOCOCS t- 1-00 I M JCOCOlO'*e^Mf-(f-(COTt-* rH Q P QOriiMOOOnOOi-liHOSMO^t- I M^tJHHNIOM t»t-MOioot-ooaHH©T( " I OS a £ 50WMOSrHCOC^t-«OCOiHNtH«COt-*T*CO^TOIOTON'#TO''#MTOM«Nir5rHCOCONN**tiH^ 100 lO w 1 'S3 ,h I iowD^wcoTt S I rHrHrHrHrHTHrHrHi-H HrH li-ir-C rHrH rH tH t-J rH rH rH | I l-t rH rH rH rH H rH I rH I N w ©©COCO©10M©«ONMN^^^^eOiraeO«5DCOCO^NMeOCOiH*i*«lO«rHCO©^<© I o* « rHrHrHrHrHrH i-tr-tr-liHrHrHrHrHrHrHiHTHrHrH r-frHrHi-HrHrHrHrHrHrHrH rH I TO qtHNTO-* IO CO t- CO OS © rH N CO •«* lO CO t- 00 OS© HW CO ^ Iffl CO t- 00 OOHN TO -#IQ CO fr- ig HHHHHHHHHHN«C4CSIC4NiNCilNC4mmne9mc5«m Individual and Composite Scores 65 g* I dCOCOCOCOCOlNCJCOCHNIOCOCOrHCI I CO I OMNCONMW I OCQlNHnCO I WCO I IN CO j M«^COO-*THW^M-*rHociCooooio©ai ih (VJ rH rHrH rH rHrH iH r4 W rHrH r-1 rHrH rH rH CO I CO H Is SQ H "3 S32S® ww S t rt W' - i?2 T * , c , ?!3wcooot--^!iHrHeoco i »wiraoiC'icowi-io>tt>(NOSiHM r co JT3 rH CaWoOt-t-t-CBOC-C3 00t-OiC005(»lr-CseDt-l>*t-OOC-OOCOinQOt-aOOOt-l>OOQOC100 w © I cm m ^J WOOTlOCOOOt>OQO&rHr*lOC I 10 «* w eococococ^cjeoc^c^coc^c^coeococjcoMC^cococ^coc^coeocjc-JDjcoc^cJcJc-ic-iccc^ © - H a OS >H CO ^LO lOCO COO rH ^ t>lOCO^^ Mb- COCO rH CO ©iHe0d©0QdlT3© OS CO W©eM©t-t-lO I© m H IS '. CI I CO t* CO© ■*!-!© W OS rH COOS "-UTt* rHrH -«a« I I rH©©T}«Ttl CI© t-WHWOH -*"*C0O IN .-s rj I H rH rH rH rH rH rH rH rH rHrHrHrHrH I i rH rHrHrHrH iH rH rH rH rH H r-1 rH CO Tj H W 4) I £ rH I MIO^OOM»0^001GOO>CllOlOOCOOOO«CO , *OOt-0)0'*Cft'*«CONOOCO I HO I CI ^ rH I rHrHrH iH rH rHrHrHrH i-t rH rHrHrH rH rHrH CO aH « o ' 3, O C*©^©^CO©CO>#©©©^tot-©eOCOt-©Cp^©T*©00©eMCl^CliraClrHCM©CO I IO rH ^cocococidcocjco^coeocjcococMeococicoddcoc^^codcocococococoeocococo as s lrt Ol OQ000C0Tt<^OO®01^ r HM*00CSIrHOOO I OS H H CQWCJCsiC^C^MMC^C^C^C^C^CJfN^C^C^rHC^C^CgC^C^COC^CJWWCJC^CJOJCSieacOCg CI J I* ffi j 00 rHWCOMCOrH©a000OS©rH^^rH©COCftt-'*Tr'©lOinWlOOcoeOOSt-lOCOrHrHaJC>lOCNIU3NOOeD I 5; Q rHrHCOrH CMCO rH CO rH rH CI rH rH d rH CO iHddrHdrHCOd rH d d d rH d d i-i d CO © rHOaOa5COCOCOCOGO©-*CSh-©OS©T*«OS©t-dd©OSOOC3St-©rHlOdaOCOO©©© I Ol g eOrHCOdddCOrHrHCOdddCOddddrHddddrHdd CO CI CO CO d CI CO CO CC CO g IO ©Cft ^ ^ rH Q0©00 rH © t- ©© b-dCQd'*** CO t-lOrH OS lflM CO i-n^dlO©-*©©!-!!-! 31 I CI g ^H^^WHNHWMNWWNMNNMH«NNWMMMMNMM^NWMCOH*CI g I r^ -j- I ©1Q I I ^WCOCO^rH-^t- I OdlOOO I I OOOSOJOOC) CO lOOOCOd COO CI CI rH IO I g> ra I H I IrHrHrH rHrHrHiHlrHrHrH I I i^r-i i-\i-ir^ rli-irHi-ti-li-lrli-i \ie0^*lO©t , -00©©rHCieO^*lO©^00©©rHCIC0-^lC3«Dt- PQ 66 The Interrelations of Mental Abilities TABLE 41— GIRLS' SCORES Girl Al A2 A3 A4 A5 A6 A7 A8 A9 A10 All A12 A13 A14 1 11 9 7 5 2 7 25 20 11 8 188 211 2 27 28 4 3 13 24 20 18 20 15 216 208 3 9 2 5 3 '9 4 214 210 4 1 1 4 9 12 9 19 2 223 236 5 19 1 3 '2 9 17 17 19 18 9 206 226 8 2 2 2 1 6 12 26 18 15 20 19 27 231 239 7 6 6 3 6 1 22 18 14 15 15 22 217 209 8 6 20 5 4 4 10 23 31 20 20 13 6 224 235 9 14 8 7 2 13 9 31 18 16 20 25 29 213 235 10 2 2 27 18 12 19 1 2 235 244 11 6 10 2 2 6 5 20 14 16 217 219 12 9 4 4 1 12 13 19 16 5 2 5 19 27 18 17 17 8 20 214 207 14 27 25 3 3 2 4 21 45 15 12 1 1 221 233 15 9 2 7 6 2 37 22 12 17 4 6 230 219 16 5 1 3 15 32 30 18 20 4 1 205 201 17 i9 16 5 6 1 1 38 23 14 13 7 6 235 229 18 9 10 2 5 9 28 9 18 14 220 234 19 16 3 1 9 6 29 18 19 8 2 12 213 230 20 4 17 1 2 1 4 27 27 20 20 11 11 210 214 21 6 3 1 2 4 18 17 12 10 205 197 22 9 25 2 15 22 37 23 IS 20 27 29 204 216 23 11 19 4 2 14 20 37 20 5 2 231 233 24 16 7 3 3 8 12 22 34 is 18 22 30 231 231 25 9 3 1 6 13 23 17 18 8 9 13 241 231 26 23 5 6 6 15 24 28 23 20 20 26 18 198 219 27 16 1 3 6 4 22 13 18 17 2 7 214 207 28 8 4 2 2 10 18 25 23 15 14 15 25 230 216 29 18 6 6 3 4 4 22 18 12 9 8 4 207 206 30 16 6 4 4 6 10 25 22 20 20 9 12 223 236 31 10 12 2 3 1 6 26 23 20 17 6 232 226 32 2 1 2 21 14 17 5 228 238 33 2 4 3 6 24 11 14 '8 15 247 227 34 3 8 '2 4 3 12 23 20 19 9 6 230 244 35 9 10 4 3 6 6 19 9 9 11 1 9 195 219 36 17 4 2 3 14 28 35 19 18 19 11 10 203 212 37 10 21 13 18 29 215 216 38 27 5 1 4 7 10 24 23 20 is> '5 21 209 227 39 6 2 1 3 7 10 18 15 11 19 8 11 236 237 40 8 1 1 2 3 25 18 10 9 14 19 211 218 41 16 1 2 2 2 5 5 16 210 215 42 8 4 2 2 9 15 20 2 202 226 43 17 4 4 2 6 15 17 24 13 20 ii 20 217 226 44 26 24 10 6 11 18 16 8 20 218 210 45 11 4 2 3 5 18 22 18 16 19 20 29 226 226 46 8 7 2 2 16 20 20 21 27 208 214 498 353 137 117 250 416 970 839 658 647 340 510 9803 10010 Individual and Composite Scores 67 TABLE 41— GIRLS' SCORES Girl Bl B2 B3 B4 B5 B6 CI C2 C3 C4 C5 C6 C7 C8 1 10 24 2 2 14 10 3 3 32 31 32 31 31 31 2 5 11 2 4 16 13 3 5 33 33 33 32 31 33 3 3 4 2 2 10 14 4 4 33 33 31 30 34 29 4 8 9 2 4 14 14 1 5 32 31 34 28 34 SO 6 4 2 11 15 3 2 34 31 32 32 31 27 6 3 6 2 1 13 16 2 2 33 33 32 29 28 7 2 4 4 14 14 1 2 32 36 22 25 27 29 8 4 4 2 2 14 12 5 4 30 34 33 31 26 31 9 4 19 4 4 14 14 3 2 33 31 — 30 27 29 10 4 11 2 14 2 3 2 36 34 33 27 30 31 11 4 2 2 11 2 2 33 28 30 29 33 28 12 2 4 1 4 — — — — , 36 29 31 — 28 30 13 4 2 4 15 15 3 3 34 35 31 31 33 33 14 2 10 2 2 10 13 3 3 25 28 34 32 31 30 15 4 4 4 4 16 11 2 2 30 33 29 — 28 27 18 8 16 2 4 14 4 31 33 32 34 29 26 17 4 7 2 4 10 11 3 3 30 31 29 29 28 25 18 1 4 2 2 14 15 1 2 30 29 32 28 25 31 19 18 28 2 6 16 12 2 2 25 31 29 29 29 29 20 3 2 2 15 14 2 3 37 37 34 35 28 33 21 8 4 2 2 8 14 2 3 35 29 32 28 32 28 22 16 10 3 10 16 4 3 32 32 31 33 34 32 23 9 13 4 16 12 4 3 37 — 30 34 33 33 24 18 36 3 12 12 3 2 34 32 35 34 34 34 25 2 2 2 2 14 14 5 3 34 34 29 30 29 27 28 . 14 1 2 31 30 31 31 27 27 27 4 3 3 2 11 13 1 2 32 36 30 29 26 30 28 13 4 4 12 15 4 3 — 35 — 26 — 29 29 7 2 2 13 1 31 32 29 24 27 20 30 8 5 3 4 13 1 3 34 35 33 33 34 31 31 5 12 1 3 16 13 4 3 29 32 31 31 31 30 32 2 3 1 15 13 — — 30 33 29 31 31 27 33 7 12 2 4 1 1 33 — 28 21 29 24 34 8 4 4 2 14 11 4 3 35 34 32 34 30 33 35 6 22 2 2 12 11 2 2 27 35 — 21 29 30 38 1 6 2 2 12 30 25 26 37 — — — — 16 15 3 3 30 33 33 31 29 33 38 10 8 2 16 14 3 3 26 23 31 23 28 29 39 14 3 2 12 13 3 29 32 30 24 23 24 40 10 4 1 2 16 11 2 2 33 30 28 32 31 33 41 2 7 4 12 29 33 27 26 31 30 42 2 5 4 13 12 3 3 32 33 29 28 33 30 43 4 4 1 2 9 13 4 3 34 36 35 29 30 32 44 1 6 3 4 15 14 3 5 35 37 27 30 33 34 45 8 12 1 4 12 3 5 36 36 33 32 34 32 46 6 5 4 4 14 13 — — 35 29 33 34 34 32 280 349 87 120 544 502 107 114 1442 1392 1324 1271 1321 1334 68 The Interrelations of Mental Abilities TABLE 41— GIRLS' SCORES 3irl Dl D2 D3 D4 D5 D6 El E2 E3 E4 B5 E6 E7 E8 1 2 4 5 4 4 4 10 11 21 12 23 26 16 16 2 5 4 6 3 5 5 12 3 23 18 35 39 34 36 3 5 5 3 3 12 7 — — 32 27 34 35 4 5 3 3 4 4 4 12 6 20 9 15 21 15 16 5 2 1 1 3 4 10 8 9 11 16 17 20 20 6 4 3 5 4 3 4 11 8 20 14 23 20 20 16 7 2 1 3 2 3 8 9 25 14 24 19 16 13 8 5 5 6 5 4 5 10 8 18 — 40 40 36 37 9 4 3 4 4 2 2 10 10 25 13 32 28 36 36 10 3 4 4 2 4 4 12 7 15 9 21 24 14 28 11 3 1 3 4 4 3 10 9 6 22 22 19 30 12 4 3 — — — — 28 25 28 — 13 3 3 4 3 2 4 10 6 11 7 25 25 22 25 14 3 3 4 3 2 4 9 9 26 10 21 19 12 19 15 2 2 3 4 3 2 6 6 19 10 — — 17 21 16 5 4 4 3 4 5 11 9 18 13 25 25 29 26 17 2 2 3 1 3 5 — 6 20 20 — 26 19 13 18 2 2 2 3 4 10 9 21 15 16 19 12 24 19 4 3 2 4 2 4 11 8 18 11 33 28 25 28 20 3 4 4 5 3 5 7 8 11 5 21 21 13 18 21 2 4 5 5 4 4 10 9 20 17 31 27 20 19 22 3 5 5 3 2 3 11 10 19 9 28 25 29 32 23 4 3 5 6 4 5 8 11 12 — 28 33 35 36 24 2 2 4 4 4 3 10 8 19 15 18 12 8 18 25 1 2 3 3 2 3 11 11 18 2 33 27 26 18 26 3 5 3 3 10 6 21 8 25 20 17 24 27 4 2 5 4 2 2 10 8 22 6 24 20 16 11 28 4 4 4 4 3 3 12 10 22 6 38 36 31 29 1 2 2 2 4 10 4 13 6 13 15 13 17 30 4 1 4 5 1 3 12 9 22 13 26 31 20 27 31 2 3 4 5 1 3 10 10 18 9 35 31 13 32 — — 6 4 2 4 7 10 13 — 18 12 15 1 33 1 1 2 9 8 — 6 — — 14 13 34 5 3 6 4 4 5 11 9 IS 12 32 29 28 34 35 4 2 3 2 3 5 9 10 18 8 26 28 31 33 36 _ 4 3 5 3 . 10 14 9 20 11 14 10 37 4 3 5 4 5 5 5 8 16 10 31 28 33 34 38 1 3 3 2 2 12 5 20 12 — — 6 9 39 1 1 2 3 2 3 11 6 13 10 23 22 12 12 40 2 4 4 4 4 4 11 8 23 7 20 22 16 13 41 3 3 8 28 25 10 19 42 4 3 2 5 5 4 11 10 18 13 — — 21 19 43 5 3 5 3 5 2 12 4 28 13 28 27 31 34 44 4 3 6 6 4 5 12 10 22 — 44 38 38 37 45 3 4 5 3 4 4 10 8 24 14 38 32 35 33 46 — — 5 3 5 5 11 11 10 6 25 26 32 39 124 110 167 153 138 169 426 368 763 408 1084 1048 970 1030 Individual and Composite Scores 69 TABLE 41— GIRLS' SCORES Girl E9 E10 Ell E12 E13 E14 E15 E16 B17 E18 El E2 P3 F4 1 28 25 10 12 26 31 83 77 101 48 2 1 2 2 27 32 13 14 31 33 S6 78 92 51 1 1 4 3 3 26 32 13 14 27 29 93 65 70 48 2 1 3 4 27 34 9 13 25 26 78 71 88 47 2 2 3 3 5 22 30 6 10 29 29 78 75 88 46 1 2 6 27 28 9 12 20 27 72 66 64 49 2 2 7 30 22 9 12 25 31 74 71 87 46 3 5 2 8 32 40 12 13 37 36 94 78 112 46 2 2 4 3 9 26 32 14 12 24 28 82 68 99 48 4 3 3 10 29 29 10 10 20 28 80 67 89 46 1 2 3 3 11 20 30 11 11 27 29 75 63 96 46 2 2 12 23 36 — — 22 27 79 70 44 13 26 28 15 12 25 26 74 61 80 51 1 1 3 1 14 20 22 11 10 27 30 57 67 89 44 1 2 1 15 26 28 9 9 26 30 74 64 89 42 2 2 4 3 16 30 28 11 12 28 26 78 67 99 49 1 3 5 17 28 33 7 9 20 24 69 65 71 42 1 2 2 3 18 24 25 6 9 24 20 70 62 73 45 4 1 3 2 19 26 26 15 14 28 32 78 70 97 49 1 2 3 5 20 28 37 12 13 24 26 71 65 92 49 2 2 3 3 21 29 39 14 9 28 29 78 69 96 47 3 2 2 3 22 27 44 10 12 31 34 92 74 105 47 2 1 4 2 23 27 40 12 14 27 30 84 69 79 4 3 3 2 24 26 32 8 14 23 27 60 63 71 47 4 3 25 23 28 11 11 35 39 98 79 99 48 2 5 3 26 28 21 12 13 28 23 64 62 86 45 1 3 27 22 24 9 11 21 25 73 68 85 47 2 1 2 28 28 34 9 11 27 33 98 77 113 48 2 4 4 5 29 28 20 6 5 22 18 53 56 93 48 3 30 28 29 8 7 29 29 79 67 99 46 2 1 2 5 31 30 40 15 13 24 29 88 78 95 44 3 1 3 32 22 29 — — 24 27 61 60 75 2 2 1 3 33 19 23 14 10 20 18 72 67 72 44 34 32 32 13 14 25 34 75 68 80 47 2 1 3 35 28 26 9 9 29 35 81 72 95 51 2 2 3 36 24 28 __ 10 19 25 74 64 76 44 3 37 32 27 8 13 19 27 — 70 90 45 2 1 2 2 38 24 20 9 12 26 22 76 67 82 44 2 1 2 3 39 18 30 8 12 23 25 65 62 77 37 2 2 2 40 14 24 9 11 19 26 78 63 87 43 2 1 3 1 41 22 36 25 28 78 73 78 48 _ _ 42 26 36 13 11 18 29 95 82 112 — 3 2 4 3 43 21 30 8 — 25 27 87 69 101 48 1 2 2 44 32 46 14 — 35 36 98 92 116 50 4 2 6 3 45 32 32 11 13 24 26 94 71 106 48 3 46 26 38 — 13 33 30 76 73 93 51 2 2 3 5 1193 1405 432 469 1174 1299 3522 3185 4037 2003 64 60 98 119 70 The Interrelations of Mental Abilities TABLE 42— BOYS' DEVIATIONS OP THE COMPOSITES Boy 1 #A1 #A2 : #b: i #b: ! #C1 #C2 #D1 #D2 #E1 #E2 #P1 #F2 2 69 101 —2 3 —6 10 4 —1 —12 —35 —1 — 1 3 4 5 53 55 10 17 3 8 3 73 58 3 2 —113 —126 —1 —12 —2 —1 1 2 —10 —21 1 2 6 126 94 23 30 4 6 —1 —3 —13 —20 —2 1 7 —23 26 —9 —I —7 —2 —2 62 36 3 2 8 —14 —32 —36 7 6 —6 2 —80 —65 —2 9 —37 —25 2 —11 10 5 2 —2 —2 —23 —1 10 36 —2 —14 —3 17 14 4 2 61 63 3 11 —91 —16 —1 —11 13 8 3 4 —3 25 1 — 1 12 —144 —138 —14 —6 —25 —16 —1 —1 —18 —18 3 2 13 —37 —45 —2 —3 2 —1 2 2 37 —20 6 14 86 101 10 18 — 5 —1 —3 —3 —18 9 1 1 15 —82 —70 —18 —15 —3 —14 2 21 —2 2 2 16 53 39 —19 8 3 —9 1 1 15 5 2 — 1 17 34 50 14 4 7 —3 —1 —1 5 2 1 18 19 —100 —86 1 1 —2 o —1 —128 —89 —1 2 20 21 —10 —38 2 5 —12 —17 —2 —1 —71 —34 22 32 37 16 —10 —3 —2 — 5 —1 —34 —59 —2 23 90 31 —11 9 7 —5 —3 —22 2 24 9 6 13 19 7 11 —1 1 11 —45 —1 1 25 33 9 7 12 1 —1 2 2 4 44 —1 26 —12 —11 9 —14 7 10 1 —1 44 46 —2 1 27 16 22 12 12 — 5 —3 3 2 —51 —28 2 2 28 29 —30 —75 —24 —14 5 3 —47 —59 —3 —2 30 121 72 20 20 —12 —6 —1 -A 42 47 3 2 31 —31 —19 14 24 14 6 4 4 27 14 —2 32 53 55 6 5 5 7 2 2 11 10 —1 —1 33 —76 —108 —24 —6 —19 —11 —8 — 5 3 —35 1 1 34 18 60 8 1 8 12 2 —1 29 9 2 1 35 36 4 28 8 12 6 6 1 1 52 45 3 5 37 —120 —43 786 —20 194 —5 207 4 129 10 116 5 40 —1 23 1 493 17 435 —2 30 1 833 35 —920 —864 ■ -179 • -114 -101 —99 —32 V —35 —540 —553 —22 —7 Individual and Composite Scores ys TABLE 43— GIRLS' DEVIATIONS OF THE COMPOSITES Girl #A1 #A2 #B1 #B2 #C1 #C2 #D1 #D2 #E1 #E2 #F1 #F2 1 —24 —51 2 14 2 1 1 1 17 2 —2 3 61 71 3 13 4 10 6 1 58 61 2 4 —124 —78 8 7 3 1 2 —12 —12 2 1 5 —28 —23 —6 —12 4 — * —7 —3 —59 —10 —4 6 —4 24 7 —10 —2 — t 2 —37 —11 —3 7 —4 —19 —6 2 —16 — 4 —5 —5 5 —27 2 1 8 18 56 —6 6 5 4 92 70 3 1 9 97 37 12 17 —2 -^ —2 51 33 3 10 —84 —66 —20 —7 6 —2 1 —1 —17 —16 1 1 11 12 13 —42 —53 —24 —16 1 —9 —3 —37 —18 —1 —2 33 53 6 5 7 —1 —1 —37 —26 1 —2 14 —6 28 —8 —3 —2 —1 —1 —37 —44 —3 15 2 —22 6 6 —8 —6 — _' —3 —25 —35 3 1 10 17 17 6 18 1 3 3 1 28 4 2 17 29 —11 —2 —3 —6 —7 —2 —3 —38 —2 1 18 — 27 —59 3 —6 —10 —6 —3 —5 —53 —29 4 —1 19 9 —70 12 38 —12 —5 2 22 5 1 3 20 —15 22 3 —14 4 13 3 —48 —9 2 1 21 —86 —88 8 —18 4 —7 1 2 25 42 2 1 22 75 120 12 —4 6 5 47 60 3 —1 23 58 76 —3 15 9 12 3 3 —13 41 4 1 24 34 76 18 14 10 6 —2 —66 —7 1 —1 25 2 —55 2 —8 3 —1 -4 —3 39 —7 4 —1 26 127 88 —22 2 —8 —6 _^ —3 —10 —63 —2 — 1 27 —12 —54 6 —13 —9 1 1 —3 —29 —57 —1 — 1 28 10 34 23 —6 —2 1 81 34 3 5 29 4 —70 —21 —12 —10 —22 —5 —5 —66 —103 —3 —1 30 34 22 —16 1 4 7 —1 —2 28 6 1 2 31 32 33 —17 —8 —1 10 1 —3 25 16 34 —51 —9 10 —6 6 n 5 1 17 32 —1 35 —52 —56 8 —17 —8 —2 17 11 —1 l 36 37 38 31 36 10 —8 —8 —17 —6 — 1 —26 —66 1 39 —53 —12 16 —14 —11 —14 —5 -^ —85 —55 —1 40 —58 —51 —2 —3 1 1 —46 —62 2 —2 41 42 —61 —11 —10 1 1 —1 1 1 31 37 4 1 43 2 41 —2 —16 8 5 5 —3 44 2 —2 44 87 66 5 6 2 13 4 3 124 127 7 1 45 -9 58 —24 6 10 12 2 87 33 —3 —1 46 739 925 178 178 93 113 43 21 838 616 53 27 -748 —866 - -157 - -189 - -125 - -131 —51 - -58 - -741 - -659 -20 —21 72 The Interrelations of Mental Abilities TABLE 44— ARITHMETIC AVERAGES Highest Boys Girls i possible 1 Score Al & A2 17.17 15.61 11.32 8.02 55 55 A3 & A4 5.14 4.14 3.11 2.66 28 27 A5 & A6 6.06 8.69 5.95 9.45 35 35 A7 & A8 28.82 16.84 23.66 19.98 56 70 A9 & A10 15.47 16.31 16.05 16.18 20 20 All & A12 14.19 21.52 9.35 12.44 30 30 A13 & A14 208.64 210.57 217.84 222.44 288 288 Bl & B2 9.57 10.76 5.91 7.93 48 48 B3 & B4 3.05 2.35 1.98 2.73 10 8 B5 & B6 11.86 13.28 12.95 11.16 16 16 CI & C2 3.34 3.43 2.68 2.78 5 5 C3 & C4 33.31 31.95 32.04 32.37 38 38 C5 & C6 29.71 29.05 30.79 29.56 35 35 C7 & C8 28.41 28.58 30.02 29.64 36 36 Dl & D2 3.66 3.00 3.02 2.68 5 5 D3 & D4 4.36 3.67 3.88 3.56 6 6 D5 & D6 3.11 4.08 3.00 3.67 6 6 El & E2 9.86 8.14 10.14 8.18 12 12 E3 & E4 19.18 11.90 18.61 10.46 37 20 E5 & E6 28.70 25.92 26.44 24.95 50 50 E7 & E8 18.84 23.32 21.56 22.89 40 40 E9 & ElO 25.11 32.30 25.93 30.54 Ell & E12 9.49 11.24 10.54 11.44 15 15 E13 & E14 27.19 29.86 25.52 28.24 43 43 E15 & E16 79.81 72.58 78.27 69.24 104 100 E17 & E18 97.78 47.03 89.71 46.58 130 54 Fl & F2 1.00 1.38 1.42 1.43 4 i F3 & F4 2.19 2.56 2.28 2.70 5 7 Individual and Composite Scores 73 TABLE 45 RELIABILITY COEFFICIENTS : Paired Tests arranged according to the Groups Boys Girls TABLE 46 RELIABILITY COEFFICIENTS : Paired Tests arranged according to Magnitude of the Coefficient Al & A2 A3 & A4 A5 & A6 A7 & A8 A9 & A10 All & A12 A13 & A14 Bl & B2 B3 & B4 B5 & B6 n 36 37 35 34 31 29 r 61 62 58 41 69 76 n 44 44 40 41 38 37 45 r 37 56 72 24 34 84 59 37 67 37 51 32 —18 44 48 44 —07 42 27 CI C3 C5 C7 Dl D3 D5 & C2 & C4 & C6 & C8 & D2 & D4 & D6 El E3 E5 E7 & E2 & E4 & E6 & E8 & E10 Ell & E12 E13 & E14 E15 & E16 E17 & E18 35 36 35 33 35 33 37 36 30 37 37 37 33 37 36 34 41 29 50 34 20 16 27 31 21 65 65 40 61 62 66 05 40 42 40 43 41 43 46 42 37 41 44 46 39 46 45 42 46 38 48 45 55 44 42 -15 41 86 82 34 43 65 77 26 Boys r All & A12 76 A9 & A10 69 A13 & A14 68 Bl & B2 67 E15 & E16 66 E7 & E8 65 E5 & E6 65 A3 & A4 62 E13 & E14 62 Al & A2 61 Ell & E12 61 A5 & A6 58 B3 & B4 51 C5 & C6 50 CI & C2 41 A7 & A8 41 E9 & E10 40 C7 & C8 34 El & E2 31 Fl & F2 30 C3 & C4 29 D5 & D6 27 E3 & E4 21 Dl & D2 20 F3 & F4 19 Girls r E5 & E6 87 All & A12 84 E7 & E8 82 E15 & E16 77 A5 & A6 72 E13 & E14 65 A13 & A14 59 A3 & A4 56 Dl & D2 55 Bl & B2 48 C5 & C6 48 CI & C2 46 C7 & C8 49 D3 & D4 44 Ell & E12 43 D5 & D6 42 E3 & E4 41 C3 & C4 38 Al & A2 37 A9 & A 10 34 E9 & E10 34 Fl & F2 32 B5 & B6 27 E17 & E18 26 A7 & A8 24 D3 & D4 16 F3 & F4 14 Fl & F2 32 30 42 32 E17 & E18 05 B3 & B4 —07 F3 & F4 30 19 43 14 B5 & B6 —18 El & E2 —15 TABLE 47 TABLE 48 Reliability Coefficients of the Com- Reliability Coefficients of the Com- posites arranged according to posites arranged according to the the Groups Magnitude of the Coefficients 3 Boys Girls Boys Girls #A1 & #A2 31 90 38 77 #A1 & #A2 90 #E1 & #E2 #A2 80 #B1 & #B5 ; 31 55 38 17 #E1 & #E2 82 #A1 & #D1 & 77 #C1 & #C2 31 70 38 69 #C1 & #C2 70 #D2 70 #D1 & #D2 31 56 38 70 #D1 & #D2 56 #C1 & #C2 69 #E1 & #E2 31 82 38 80 #B1 & #B2 55 #F1 & #F2 25 #F1 & #F2 31 39 38 24 #F1 & #F2 39 #B1 & #B2 17 TABLE 49 RAW CORRELATIONS OF THE MANIPULATIVE TESTS Boys Al A2 A3 A4 A5 A6 A7 A8 A9 A10 All A12 A13 A14 Al 61 27 25 42 26 41 16 52 36 31 19 —35 —39 A2 61 37 13 36 25 4", ■2-.i 28 10 17 09 —10 —22 A3 27 37 62 09 15 30 33 33 16 26 05 —08 —08 A4 25 13 62 17 38 44 18 34 15 48 26 —22 —29 A5 42 36 09 17 58 24 30 39 35 44 20 —25 —33 A6 26 25 15 38 58 31 27 49 38 68 54 —24 —17 A7 41 45 30 44 24 31 41 46 15 22 23 —13 —18 A8 16 23 33 18 30 27 41 40 05 15 —01 07 —05 A9 52 28 33 34 39 49 46 40 69 53 22 —02 —11 A10 36 10 16 15 35 38 15 05 69 51 21 37 21 All 31 17 26 48 44 68 22 15 53 51 76 —17 —22 A12 19 09 05 26 20 54 23 —01 22 21 76 —13 03 A13 —35 - -10 —08 —22 —25 —24 ■ -13 07 —02 37 - -17 —13 68 A14 —39 - -22 —08 —29 —33 —17 ■ -18 —05 —11 21 - -22 03 68 74 The Interrelations of Mental Abilities TABLE 50 RAW CORRELATIONS OF THE MANIPULATIVE ' rESTS Girh I Al A2 A3 A4 A5 A6 A7 A8 A9 A10 All A12 A13 A14 A1 37 34 51 29 39 09 22 36 11 —01 08 —29 —24 A2 37 27 28 16 23 22 41 26 18 11 —03 —08 —14 A3 34 27 56 14 12 12 08 —03 —02 17 02 —12 —28 A4 51 28 56 04 10 18 09 19 07 05 —04 —11 —15 A5 29 16 14 04 72 22 05 37 36 58 53 —16 —10 A6 39 23 12 10 72 25 15 37 42 50 40 —16 —15 A7 09 22 12 18 22 25 24 16 08 26 34 —03 —10 A8 22 41 08 09 05 15 24 17 27 18 —05 08 14 A9 36 26 —03 19 37 37 16 17 34 26 20 01 02 A10 11 18 —02 07 36 42 08 27 34 41 26 03 14 All —01 11 17 05 58 50 26 18 26 41 84 02 04 A12 08 —03 02 —04 53 40 14 —05 20 26 84 05 —02 A13 —29 —08 —12 —11 —16 —16 ■ -03 08 01 03 02 05 56 All —24 —14 —28 —15 —10 —15 ■ -10 14 02 14 04 —02 56 TABLE 51 RAW CORRELATIONS OF THE SPATIAL RELATIONS TESTS Boys Bl B2 B3 B4 B5 B6 Girls Bl B2 B3 B4 B5 B6 48 15 04 —07 —03 48 00 09 —02 02 15 00 —07 —03 08 04 09 —07 —04 02 —07 —02 —03 —04 27 —03 02 08 02 07 TABLE 52 RAW CORRELATIONS OF THE COMPUTATIONAL ARITHMETIC Boys CI C2 C3 C4 C5 C6 C7 C8 CI 41 13 21 —03 31 14 24 Bl 67 16 33 13 13 B2 67 12 22 30 —09 B3 16 12 51 30 —10 B4 33 22 51 28 08 B5 13 30 30 28 —18 B6 13 —09 —10 08 —18 C2 41 23 08 13 27 11 11 C3 13 23 29 64 55 54 43 C4 21 08 29 38 50 23 44 C5 ■ -03 13 64 38 50 47 37 C6 31 27 55 50 50 43 47 C7 14 11 54 23 47 43 34 C8 24 11 43 44 37 47 34 Girls CI 46 10 06 23 29 19 31 C2 46 18 24 30 38 45 52 C3 10 18 38 20 42 38 38 C4 06 24 38 -10 10 05 22 C5 23 30 20- -10 48 28 35 C6 29 38 42 10 48 41 54 C7 19 45 38 05 28 41 45 C8 31 52 38 22 35 54 45 TABLE 53 RAW CORRELATIONS OF THE ARITHMETIC PROBLEMS Boys Dl D2 D3 D4 D5 D6 Girls Dl D2 D3 D4 D5 D6 Dl 20 25 38 31 —04 55 57 33 51 34 D2 20 40 05 32 16 55 69 37 45 34 D3 25 40 16 45 22 57 69 44 49 34 D4 38 05 16 35 19 33 37 44 29 23 D5 31 32 45 35 27 51 45 49 29 42 D6 —04 16 22 19 27 TABLE 56 34 34 34 23 42 RAW CORRELATIONS OF THE LOGICAL TESTS Boys Fl F2 F3 F4 Girls Fl F2 F3 F4 Fl 30 21 36 32 30 02 F2 30 24 38 32 35 18 F3 21 24 19 30 35 14 F4 36 38 19 02 18 14 Individual and Composite Scores 75 I I g «nHHiocoio*iora»m«* Sco© ^cociSStSgScoiomMSlto KSco I 00 E -1 2 m8S2S§mS;S2£iS8?3 2S2SJ cog & I I H g H I H o S£JSSSS3r!525 NMooot-Mo iocooo-*mnioio-* w©co-*intnep© w rt o»Q«ooh«« romrf^xinrorirH .-icor-irfoin-jicoco rannlunnn Eh H I I I O M nM 9 H «^ , «'* ^HHMIOIOI-NO ©i-f©CO-*-t"*CO CO H W Ot CO CO CO CO CO H I T O 00 ONNHOH- _- — — ^.^.^ — HH g »WOOl-*C <* •* i-j * IO ri CO CO O ■"■}< ■* C4 CO "* Ol tM © w I II « iHNeO-^lOCDt-OOOSrHiHi-lr-lrHiHrHiHTH pj tH .', 3yMr ;i ' ■*•