LB 1131 .Si THE INTERRELATIONS OF MENTAL ABILITIES BY FREDERICK WILLIAM STEAGY SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PHILOSOPHY. COLUMBIA UNIVERSITY PUBLISHED BY WmtlitrB (EalUgr. QIalnmbia Imttrrflitg NEW YORK CITY 1919 THE INTERRELATIONS OF MENTAL ABILITIES BY FREDERICK WILLIAM STEAGY SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PHILOSOPHY. COLUMBIA UNIVERSITY PUBLISHED BY Wmt^ne QlnUpgp, ©nittmbta ImtiprattH NEW YORK CITY 1919 Copyright, 1919, by Frederick William Steacy CONTENTS SEC. PAGE 1 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 hy 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, Cy and C8, Eii 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 DIS- DIS- tinct tinct Manipulative Tests tests scores Al & 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 C1&C2 Bonser's 2A and 2B 2 2 C3&C4 Woody Addition 1 2 C5&C6 Woody Subtraction 1 2 C7&C8 Woody Division 1 2 Arithmetic Tasks Stated in Words Dl & D2 Bonser's lA and IB 2 2 D3&D4 Starch's Arithmetic Scale 1 2 D5&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 E5 & 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 E15&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 52 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 ID 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 i :45 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 Stenqiiist Construction Test Single Series i 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 lo 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 Head right = 2, nut right = 8, nut toward handle = 4, nut toward head = 2, head wrong and nut right =1, both wrong = 0. Each right link = 1, each half looped Hnk = J4- A Bicycle Wrench B Ten Link Chain C Rubber Hose Clamp D Bicycle Bell E Paper Clip 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. A^ & 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. F Metal Money Safe G Spring Clothespin H Gas Faucet / Electric Push Button J 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 I 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 ^^"^^ Age years, months. Sex Grade School a. Bushing for packing nut of spark plug. h. 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. i. Coping saw blade. j. Cotter pin. k. Curtain rod fixture. /. Cut nail. m. Dowel screw. n. Drive hook. 0. Drill. ■ p. Eight penny finishing nail. -q. Expansion lug nut. -r. Flat head harness rivet. The Interrelations of Mental Abilities — ^. Flat head wood screw. — t. Fuse wire. — u. Gasket or washer for making hose coupling tight. —V. Gimlet. — zv. Glazier's point for fastening glass in window. —X. Hack saw blade. —2. Hinge. * — a\. Insulating plug for electric light wire in lamp. — &1. Jam nut, or first nut for top of spark plug. — cl. Lock washer. —d\. Machine bolt. — e\. Main body of spark plug. —/I. Nail set. — gl. Packing nut for spark plug. — h\. Patent box or mitre frame fastener. — i\. Picture nail. — yi. Pipe reducer bushing. —k\. Plumb bob. —l\. Roller skate wrench and key. — ml. Round head rivet. —n\. Saw screw. — ol. Shade fixture for non-revolving end of shade roller. —p\. Shelf stop or support. — gl. Set screw. — rl. Small hasp. —s\. Soft solder. — ^1. Staple for small hasp. —Ml. Stove bolt. —v\. Tar paper nail cap, to prevent nail head from tearing paper. —w\. Thumb nut. — x\. Trunk caster. — y\. Wedge to prevent window from rattling. —z\. Wedge for tool handles. — a2. Window sash fastener. — &2. Window lift. —c2. Window shade fixture for revolving end of shade roller. A^ & A6 Knot Making Test. Ruger-Mandl Series I and Ruger- Mandl Series II The time for each series is 30 minutes. Source. This test has been designed by Professor Ruger, of Teachers College, and constructed by Mr. M. M. Mandl, a grad- uate student of the Department of Psychology in Columbia Uni- versity, though the writer contributed some thought and energy to the selection of the knots and to the preparation of the ma- terial. Nothing has hitherto been published on these series. Description. The material for this test is contained in a stout manilla envelope 12 inches long and 10 inches wide. Each enve- lope contains fifteen folders, each 11 inches long by 9 inches wide, numbered consecutively from i to 15, inclusive. Each The Tests and Their Administration KNOT MAKING TEST. SAMPLES OF KNOTS. 8 The Interrelations of Mental Abilities folder contains upon its inside front cover a drawing of the knot to be made, and a loose piece of cardboard, 10.5 inches long by 7.25 inches wide, to which is attached, by two rubber bands, one piece of sash-cord if the knot to be made is single, and two pieces of sash-cord if the knot to be made is double. The knots to be made are arranged in the order of difficulty, as estimated from many preliminary trials. Presentation. The two series were given on different days. To each pupil was given a slip of paper upon which to write his name, etc., and he was asked to place this paper in his envelope. The envelopes were then distributed and placed so that the flap was uppermost and toward the pupil's right hand. He was in- structed upon opening the envelope to take out the top folder, to open it and to make with the piece of cord a knot like the Series A3 Name Number Figure Eight 1 Slip 2 Hitch 3 Reef 4 5 Double Bowline 6 Carrick Bend 7 Weaver's 8 9 Granny 10 11 Fisherman's 12 13 14 15 Series A6 Reef 1 Hitch 2 Weaver's 3 4 Hitch 5 6 Granny 7 8 Bowline 9 Carrick Bend 10 11 Sheepshank 12 13 Chain 14 15 Pieces Length Marks of Cord of Cord, Inches Oorl 17 Oorl 19 Oorl 24 Oorl 24 or 1 or 2 25 0or2 34 0or2 11 each 0or2 34 0or2 30 0or2 24 Oor3 30 or 1 or 2 or 3 30 or 1 or 2 or 3 or 4 1 30 or 1 or 4 34 or 2 or 5 34 Oorl 2 10 each Oorl 20 Oorl 2 10 each Oorl 20 Oorl or 2 19 or 1 or 2 19 0or2 2 11 each 0or2 23 0or3 19 0or2 24 0or2 19 or 1 or 3 30 or 2 or 4 28 or 1 or 2 or 3 or 4 1 34 0or3or S 35 The Tests and Their Administration g diagram and to place the knot upon the cardboard, fastening it there by the rubber bands; then to put the cardboard back into its folder and to put the folder back into the envelope under- neath the others, and then to take another folder, etc. Method of Scoring. Since the knots differ in difficulty the marks vary according to the subjoined scheme, the highest pos- sible score being 35 marks for each series. (See page 8.) Ay & A8 Ruger Puzde Series /,, //, ///, IV Series I. The time for this series is 15 minutes. Source. Puzzles Nos. i, 2, 3, 4, and 5 were designed by Pro- fessor Ruger, of Teachers College, and were shaped and brazed by the writer in the workshops of Teachers College. Puzzle No. 6 was purchased ready made. Puzzles Nos. 7 and 8 were purchased and then modified by the writer. Description. Each puzzle consists of two parts. One part of puzzle No. I is made of No. 7 wire and the other part is made of No. 10 wire. Puzzles Nos. 2, 3, 4, and 5 are made of No. 10 wire. Puzzle No. 6 consists of a finer wire. Puzzle No. 7 consists of a piece of sheet metal shaped like the conventional heart and pierced by six holes through each of which a cord is passed, and then looped and pulled taut. Puzzle No. 8 consists of a metal rectangle pierced by three holes through which a cord is passed and then looped and drawn taut. The ends of each cord are tied by a knot and the knot is secured by sealing wax. These eight puzzles are constructed largely on one principle. The eight are contained in a stout cardboard box 13.5 inches long, 6 inches wide and 1.25 inches high. The box has seven compartments, each containing one puzzle, except the seventh compartment, which contains two puzzles, i.e., puzzles Nos. 7 and 8. The compartments are numbered and the puzzles are arranged therein according to estimated difficulty. Presentation. A slip of paper for the name, etc., and a box of puzzles were given to each pupil with instructions to separate each into two parts, without the use of force. Method of Scoring. One mark was allowed for each puzzle which was separated into two parts without damage to the puz- zle. The highest possible score is eight marks. lo The Interrelations of Mental Abilities Series II. The time for this series is 15 minutes. Source. The metal parts of these puzzles were designed by Professor Ruger and shaped by the writer. The leather parts were made by a neighboring shoemaker. Description. This series consists of three puzzles. The prin- ciple of the three is identical, but the second is much more diffi- cult than the first, while the third is very much more difficult than the second. Each consists of two parts. One part is a leather band about one-fourth inch wide. The other part is made of No. 10 wire. The three puzzles are contained in a stout cardboard box 7 inches long, 5.5 inches wide and i inch high. Each box has three compartments, one for each puzzle. Presentation. A slip of paper for the name, etc., and a box of puzzles were given to each pupil, with instructions to remove the leather strap from the metal part without the use of force. Method of Scoring. Four movements are necessary for the solution of puzzle No. i, nine movements for puzzle No. 2 and nineteen movements for puzzle No. 3. For each movement properly made one mark is allowed. Each pupil, however, re- turned the puzzles usually wholly apart or wholly together, there- fore very few marks were given for partial solutions. The highest possible score is 32 marks. Series III. The time for this series is 30 minutes. Source. These puzzles (Chinese rings) were purchased ready made, but were later modified by the writer. Description. This series consists of five puzzles, all identical except in the number of the rings. Puzzle No. i has two rings, puzzle No. 2 has three rings, puzzle No. 3 has four rings, puzzles Nos. 4 and 5 have five rings each. In order to prevent the slip- ping of the frame carrying the rings, from the bar to the handle, and thus delaying and probably perplexing the pupil, a piece of strong string was tied around the narrow part, between the bar and the handle, and this string was protected by a thick covering of sealing wax. These five puzzles are contained in a box, similar in all respects to the box of series No. i, except that the boxes for series No. 3 contain five compartments, which are numbered The Tests and Their Administration ii from I to 5. The puzzles are arranged therein according to their difficulty. In order to prevent the rings from slipping wholly off the bar a paper clip, the same as in Test Ai & A2, was placed over the point of the bar. Presentation. To each pupil were given a slip of paper for the name, etc., and a box of puzzles, with instructions to remove first the clip and then to separate, without damaging the puzzles, the frame carrying the rings from the bar, and then to place the clip back on the point of the bar. The purpose of the clip was carefully explained to the pupils. Method of Scoring. For the solution of the two-ring puzzle, two movements are necessary; for the three-ring puzzle, five movements ; for the four- ring puzzle, ten movements ; and for the five-ring puzzle, twenty-one movements. For each movement properly made one mark is allowed. The highest possible score is 59 marks. Series IV. The time for this series is 30 minutes. Source. These puzzles and their boxes were purchased ready made. Several of the puzzles were separated by the writer into their component parts and recombined. Description. This series consists of fifteen puzzles. No two are alike, though three form one group differing only in the number and the arrangement of the parts, while four others form another group likewise differing only in the number or the arrangement of the parts. The boxes are 12.5 inches long, 7.75 inches wide and i inch high. Each box has fifteen compart- ments, that is, one compartment for each puzzle. All these puzzles are made of stout steel wire, nickel plated, except one which is made of cast iron. Presentation. A slip of paper for the name, etc., and a box were given to each pupil, with instructions to separate the puzzles into their parts. The pupils were told that they might use force in separating any, except the puzzle which was made of cast iron. They were told that they might begin the puzzles in any order but were advised that the puzzles at their left hand were on the whole easier than those on their right hand. 12 The Interrelations of Mental Abilities Method of Scoring. The marks allowed varied partly accord- ing to the estimated difficulty and partly according to the number of easily distinguishable movements necessary for the complete solution. Two puzzles were allowed one mark each ; two puzzles were allowed two marks each; five puzzles were allowed three marks each; four puzzles were allowed four marks each; one puzzle was allowed five marks; and one puzzle was allowed six marks. The highest possible score is forty-eight marks. Partial credit was allowed according to the number of correct moves which had been made. Test Aj consists of Series I and Series IV. Test A8 consists of Series II and Series III. Ap & 10 Diagram Matching Test, Two Series: A and B The time for each of these two series is 14 minutes. Source. The writer received the idea for this test and for the next succeeding test from the Binet-Simon series. The pro- totype is given by de Fursac (1913; pp. 437-38), as test No. 54. He calls it a test for imagery of form and assigns it to children A—^ ^r~> ^-v ^N 7 SECTION OF DIAGRAM MATCHING TEST. The Tests and Their Administration 13 of thirteen years. The prototype is given also by Goddard (1911, p. 9) in his revision under the title "Cutting Out," and he assigns it to adults. The writer's purpose was to obtain a non-verbal test for imagery of form, which ( i ) would be much easier than the Binet-Simon tests and which (2) could be given to a large group at one time, and which (3) could be easily scored. The test as modified seems to fulfill all these conditions. 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 100 diagrams which compose tests A9, Aio, An, A12 were drawn at one time in such a way that the 100 diagrams are really twenty-five groups of four each, these four being identical with each other except in orientation. For the Matching tests twenty groups were selected and from each group one was taken for series A9 and another was taken for series Aio. The test consists of two sheets of paper. One sheet contains twenty diagrams, which are symmetrical, so far as their quarters are concerned. This sheet contains blank spaces for the name, etc. The other sheet contains the Upper Left Hand Quarters of the diagrams of the first sheet, but the order of the figures in the two sheets is quite different. The Upper Left Hand Quarters are numbered consecutively. Presentation. Two diagrams, which are not in these series, were drawn on the blackboard, and also their Upper Left Hand Quarters. The tests were explained and described from the blackboard. The pupils were told that they would be required r r _^ ^ 1% ry- Rv T N^- R> ^ r 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. All & 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 I T""i \""\ I i" ill i 11 T \ \ '[ j "i I L_i_.i._J.....] i....L...i L.J i i i--l-l I. 'T I i i ! \""r'\ r J i !._..i. .L...U._i. QZLlZi rilEIIZi PZlIZI [TXII] -r- i I I I I I i I ! ! ! ! i ! :• i ! i 1 • J i T i..4— i j-4 1-4 1 1 1 1 i- I {..-1.-4 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. Ais & 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 A 14. 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 i6 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 Bi Superposition Test The time for this test was 2 minutes. Source. This is a modification, for the sake of simplification, by Miss Rogers,^ 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. ^Rogers, A. L., Tests of Mathefnatical 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 (i 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 Hne to the right. Imagine the card moved along this black Hne 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 VA r7v\ The Interrelations of Mental Abilities Page 2 \:\ r7v\ £7 n \ LJ V\ 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. B^ & 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 Aliss 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 — r= 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. 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. 1. A motor boat sails up a straight canal midway 1. between the banks. Draw in the space opposite the path of the boat. 5. 5. 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 ^4 North. 7. Show by a drawing in the space opposite, how a road would have to be constructed so as to be everjrwhere 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 pubHshed in 1913.^ Description. The test consists of four odd figures and eight pairs of figures. The members of a pair are ahke 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.^ 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. iiA as printed in Bonser (1910, p. 2) 1 and No. 35 in Briggs (1913. P- 34)-^ 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. iiB 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. Cj & 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 (1916).^ ^Bonser, F. G., Reasoning Ability of Children in Grades 4, 5, 6, Teachers College, 1910. ^Teachers College Record, September, 1913. ^Woody, C, Measurements of Achievement in Arithmetic, Teachers College, 1916. The Tests and Their Administration 23 Description. The test has 38 questions. It embraces the addition o£ 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. C7 & 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 lA 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. Dj & D4 Arithmetic Scale The time for this whole test is 20 minutes. Source. This test is by Dr. Daniel Starch (1916, p. 213).^ 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. D§ & 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 5 is The answer to 6 is ^Starch, 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 ^ 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 8^4 dozen pencils cost at the rate of $J4 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 15^4 gallons and the next day 9J^ 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 IJ^ times what he paid for them. He sold C and D for 1^ 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., i, 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., i, 2, 7, 11, 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 Adfninistration 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. £j & E4 Grammatical Scales: A and C The time for A was 12 minutes and for C 6 minutes. Source. These tests are by Starch (191 5, p. 615 and p. 620).^ 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. £5 & E6 Mixed Relations. Two Series The times was about i 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 1 Light 2 Birds 3 Chalk 4 Sun 5 Summer 6 Cats 7 Emerald 8 Water 9 Father 10 Hat 11 Chair 12 Fast 13 Cup 14 Man 15 Write 16 Lamp 17 Daily 18 Hair 19 Food 20 Clothes 21 Air 22 Barn 23 Month 24 Far 25 July 26 Opaque 27 Thermometer 28 Potato 29 Light 30 Sight 31 City 32 Slipper 33 Present 34 Work 35 Water 36 Factory 37 Fat 38 Bread 39 Live 40 After 41 Sparrow 42 Picture 43 Happy 44 Ounce 45 Mail 46 Complex 47 Linen 48 Victory 49 Cheap 50 Pencil day fly_ white shines hot scratch green drink son head wood fastest saucer husband stories oil newspaper black eat tear birds hay week near month wood temperature vegetable dark blind mayor shoe knoM^n problems glass workman heavy flour die before bird frame laugh pound write difficult cool defeat many write Dark Fish Carbon Wind Winter Bees Ruby Air Mother Shoe Stove Great Knife Woman Draw Stove Monthly Eyes Books Dishes Water Library Day There Friday Transparent Clock Veal Dry Hearing State Cap Future Play Coffee Store Thin Candy Life Earlier Mosquito Field Sad Inch Telephone Simple Wool Success Costly 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. Ey & 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).^ 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 — hook handle — knife fire — hums 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. Eii & 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 i, 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. £15 & 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). ^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 fiozver," etc. Method of Scoring. This was in terms of penalties. Score = Errors-f-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. E17 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 pubUshed 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. Same 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. ^Loc. cit. 34 The Interrelations of Mental Abilities Fj & 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, Rah, and 36 The Interrelations of Mental Abilities R'ab) Dr. Spearman writes (1914, p. 109): "The significance of Rah 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. Rah 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 Rah. The matter is simplified by the easily demonstrable fact that if Rah is = I 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'ah." Formulae m = a measure of an individual in a test. n = the number of individual w's in a group. S or 2 = Summation. A = Arithmetic average. jf or y =z the deviation of any m from A. A. D. = Average Deviation from A. S.D. or (T r= 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. Rah = The Correlation of the respective correlations in two columns. R'ab =z Rab corrected for the Sampling Errors of pax and phx by the Spearman formula (/). pax — Deviation of each value of rax from the mean of rax. phx = Deviation of each value of rbx from the mean of rbx. ^ax — P.E. of rax. %bx = P.E. of rbx. a^ax =z mean value of "Si^ax -^ .6745^. a^hx = mean value of '^^bx -^ -6745^. aax abx = mean value of Sa.*- '^bx -i- .6745^. The Tests and Their Administration 37 Formulae Arithmetic Average = '^mn (a) A.D. = Arithmetic ^x/n or Arithmetic Sjj//w (&) . or S.D. = M^ or ^^ or ^II^ - A' (c) n n n ^^+xy')—^i-xy) o-2fl,+j/ — o-\ — <7^v ,,x ^xj/ = ^=^ or ± (rf) Modifying formula forf _ r,,,. ■ r ,,,, ■ r ,,,, ■ r ,,, , attenuation usmg g^o-y ^v — r^ \^ ) metrical averages L ^^^^"^ ' ^^^"^^ Modifying formula fori _ r,, ,, + ^.1 ..+^0.. »+^x. ,. ... attenuation using arith- >-^ ^^v — ^r T \~ ^^ ^ metical averages J ^Krx^x2^ ry^vz) ^^ , .6745(1— r^) , , P.E. of r = ± ^ {9) \n /.6745 \ — =^ — P- E.r {h) .67 AS VV^ / R^ab = — (;) M 1 2(p2„.) - («- l)OeOWCOCO'*INCOQO(MM>0<»010COCOCOCCCO^-)t-*CJOOrteOrHOOM®eO |M <] iH r-l CO ocOWOOW(MOOt-incOOrHCON^t-®05T-tTtH^'*05IM-*'*®OIP>OC^C1t-COt-«5rH I© <) r-i 1-1 " T-( ^ rHWM*W®t-OOaOrH^M^W«J:;»30HS^COM;WOt500gOjHCQCO^K.gt5 64 The Interrelations of Mental Abilities r-i I e<^I-((^^ost-oOr-(^-(t-«ooor-((^^oOI-^t-oo5^-r^ooOM^oooo(^^I-lOSr^T-l(^^^-^ 1 >o ^ I i-lrHiH T-liHrHr-l T-l iH i-l i-l tH iH rt t-It-I tH rH tH i-( i-I rHiHiHiH K Q >Q WOTjCI-*(NeOrHr-ICO-*«<3-*tHMMlOU30'*eO-<*'W IIQ M I WlOlOCO'*TtllOlO?D®inW*>nlOO I -* 1 C0iMIO03'*-*IO I •<*< to to 10 IM ■* IM Tjt to I T« iM I iMeoincoco(MC]-*ioiOT-ieoi-i-*cocoiMco-*Mc^iirocococoTf*(rt'<*(eorH»irD [■^jt-* ton U Q ' ' S3 02 I ^ 55 OOiHlMOOOinOOrHr-IOleOOTtlt- I O O OS i-( t-H 03 Tft © OJ Oi la) pi OcOCOCOlMCNiMCOCOWCOCOINiM IcNMlMCOCOCMlMC-liMCOlMC^iMCOCOIMCOCOC^COCOMM jcS o S • E^ I int-00©Nin l iMtH-* I 01t-©OTHTHOOr-ll>t-0000050©r-l05l-(M0005010eC>© I CD a W I W(N(NlMCOCv| I CO CO CO I IN C* N CO CO CO CI IM IM a)INrHO5THailniN-*iHt~r-l©T)T-(Oine->-*inrH001 I lO0>iHrH©C0a5THi-IC0C»i-IC5»HO00C0 01ini-tiNTt(01 I © ^ U I C\| CO IN CO COO) CO CO CO CO IN IN I C) iN CO CO CO CO M CO CO CO Ol CO C^l CO CO IN CO Cv) IN CO CO CO IN I g M TtlCOTHinaitilN©«OTtteOeOeO(Nt- I 2J rj CO CO CO C) CO CO CO IN CO CO CO IN IN CO Ol CO CO CO CO CO IN CO C^ CO CO CO CO IN CO CO CO CO CO CO CO CO CO I 00 < I- CO I nTti'*co'*coincoiN-*co-*cococococ^ini-(cocoiNN'*iH'* I loo i g 5'*incococoincoco'*i-(r-(OcoiniNvnTjHiNiNcooioioeO'»*t i co'^ it; ' p to I ®«-*CO-*-5t<10lNt003IN-* I e0-*l»O-*t--*r-|iK>«DTtiiN I | ©tO-*«OeO(NC0 I lO-*C0lM I 00m I CO I 0000r-(l>00?0 05i-H(N00lOO OS i-i •*■*■* Ti< in ■*•*•*•*■* lo •* »o ■*•* ■*!■*(■* ■* I TjtTti I ■* I ■* ■* lo -*( ■* -j< -.ji T*< in Tt< ■* m o " I r-t t- mrH-*COl-00'*lOtD»OrHCOOO'MrHOOQO'*VfflM>OffO(MMlf3 0000>OTHiM-*05t-01©-*01 I 00 i-H O05©rHO05©0;05OOC5O01050005rHt-©C500t-OO0505©0i©©05©05©0300 rH ^i-HHr-l 1-1 i-lrHTH iHi-l iHi-l r-li-(rHi-(i-( «D W C»5moO>OeO«30-*-*T-l«Oira-*i-l05MCO I •**t:~t~t-ai^QOt~'Ot-QCt~t~t~ I t-5DiK>l>t:-l>t-l--?OCOI>t-t-t-t-00THC0rH'*li-liHMO5CDiMlOO5©iMOii-(eO CO S "-I OCDOOt-t-t-OJIOt-OlOOt-OSOOOlOOt-OSWt-t-t-OOt-COOOlOCOl-OOCOt-t-QOOOOJOO Ifl o ' =^ ^ ■* lft00010 0000t-0005tHt-lf5H tH i-i iH tH iH iH I 00 V I O iH I NIO- cj c^ Oa005COeOeO?000©Ttl05^-005«0-*050l— Cgci0203000>t>©iHlOCiaOCOO©«CO I oj g CO I-I CO eg d eg CO iH tH CO c) eg eg CO eg eg eg eg r-i eg eg eg eg iHci eg coci coco eg eg coco com g lO OOJTtO I CI 05 OS CI r-l-* lO I l>©O5O5;*b-t-O5e0 I M M 1 egi-( I cgegcjr-ie-iegegrHegrHr-iegegrHr-i I r-ir-icir-icirH I iHcgr-ir-icgegr^r-ieg eg eg ©000000005C50500©t-05-*00-tlCJ©©t:--*t--*OOOOr-lrHt-t-t-COi-l05t-000005t- | jH ^ rH r-l 1-1 r-lr-lrH rH r-l rH O n iHe^eo'*>o«ot-aoo50i-tegeo-*ioMii-ooo50rHegeo-*iO«ot-oo©OrHegco-»t2 25 24 16 08 26 14 —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 AlO 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 A14 —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 oa 04 09 —07 —04 02 —07 —02 —03 —04 27 —03 02 08 02 07 TABLE 52 RAW CORRELATIONS OP 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 34 34 34 23 42 TABLE 56 RAW CORRELATIONS OF THE LOGICAL TESTS Boys Fl P2 F3 F4 Girls Fl F2 F3 F4 Fl 30 21 36 32 30 02 P2 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 00 005r-l*(lMme0^e 1-1 OT-l(MiMOrHi-(THOr-IC)rHOOOOO (Nj-IOOlMCO-*-*03CaCO 8 I I P _j ThrtlCD-^OOt-IMOSCOC^ iH O IM 05 CD iH lO PH Jh •*THOOCO-*iHiHrHCO COMMCOC^IrHIM ^ El P> " H t-, iHC^05 05CO(Mi-ICOO iM (M O O O t- IM O r3 ^ lOcoocqinioiHTtf-ii cocoiH-*iocoiMi-i H <-) g COC-lOiHCO-^CO-Tl ■"*! r-l tH OJ 10 O Tt< (M O Or-lp ^ « II I § ' ^ ^ M O 00 W- iH CO CI 00 lO 05 1- C5 ■*! CO 05 IN CO IH H COCOOOt-'^CO -^-^rHiMlM ■*■*-* IM 1-1 ri i-i©iHOlfflCD00 COCOtHCItH-^i-^IN-*-* H " I ^ H t- t-00O5©CO!M iniMi-llMCOCOIMeOOOOlM OOOiHIMiMCO (MiHmiOCOW-*OCOt-t- S fH iHfNOCjTjH-* C0C0iHi-lJ t- 05 ■* O C-llO ^ lO OIOCDCOCO COCOIMiM Q0OC005CD t-QO 53 inclOOCD ■*Ttc*lOrHCn iittiHIMOO •CO»ncoiM^lOlOlC-*0 i-lr-ICOri C0l'-10'*»0C0Tt<-*CDt-CDOiM K5 ' ' n tH OOi-I 0005OiH"*lO5Tt-*i-it-iot:-iH-*ooi>ioiM05coo wcD-*05oococo'''S£J SS?52!r:SS 5 COOCO^lOT-ICOCOWTH'tKNCO'^INrHO i-ICIi-d-tCOi-li-IOi-lOOe'Jr-lThidWIM P OiHC-JCOTtilOCOt^OO ,53 C>iHiMeO-*lOCOt~00 b rHIMeO-*lOCDl~0005iHTHiHrHrHiHi-(r-li-l fci iH IM CO •* lO CO t^ 00 05 tH rH rH iH rH rM tH rH iH 76 The Interrelations of Mental Abilities TABLE 57 CORRELATIONS OF THE PAIRED TESTS CORRECTED BY THE FORMULA FOR ATTENUATION BOYS GIRLS Al-2 A3-4 A5-6 A7-8 A9-10 All-12 Al-2 A3-4 A5-6 A7-8 A9-10 All-12 Al & 2 39 53 57 42 25 75 48 69 58 06 A3 & 4 39 29 59 35 29 75 14 30 12 07 A5 & 6 53 29 57 63 63 48 14 34 76 64 A7 & 8 57 59 57 37 25 69 30 34 55 25 A9 &10 42 35 63 37 47 58 12 76 55 51 A11&12 25 29 63 25 47 TABLE 58 06 07 64 25 51 ] BOYS GIRLS Bl-2 B3-4 B5-6 Bl-2 B3-4 B5-6 Bl & 2 33 49 35 —07 B3 & 4 33 84 35 10 B5 & 6 49 /4 TABLE 59 —07 10 BOYS GIRLS Cl-2 C3-4 C5-6 C7-? ! Cl-2 C3-4 C5-6 C7-8 CI & 2 42 38 37 31 64 75 C3 & 4 42 132 124 31 36 47 C5 & 6 38 132 105 64 36 83 C7 & 8 37 124 105 TABLE 60 75 47 83 BOYS GIRLS Dl-2 D3-4 D5-6 Dl-2 D3-4 D5-6 Dl & 2 112 81 95 85 D3 & 4 112 137 95 76 D5 & 6 81 137 TABLE 61 85 76 Boys B1&2 E3&4 E5&6 E7&8 B9&10 B11&12 E13&14 B15&16 B17&18 El & 2 —34 70 59 100 72 27 52 21 E3 & 4 —34 20 13 -32 —14 12 26 160 B5 & 6 70 20 74 93 55 76 92 66 B7 & 8 59 13 74 56 31 52 67 21 E9 &10 100 —32 93 56 48 51 91 63 E11&12 72 —14 55 31 48 42 45 34 E13&14 27 12 76 52 51 42 78 64 E15&16 52 26 92 67 91 45 78 57 E17&18 21 160 66 21 63 34 64 57 Girls Bl & 2 14 50 37 139 74 97 108 364 B3 & 4 14 35 17 17 00 —03 17 —01 E5 & 6 50 35 77 88 73 74 88 84 E7 & 8 37 17 77 75 48 65 57 96 B9 &10 139 17 88 75 66 71 82 105 E11&12 74 00 73 48 66 49 52 53 E13&14 97 —03 74 65 71 49 75 106 E15&16 108 17 88 57 82 52 75 103 E17&18 364 —01 Boys F3&4 84 96 TABLE 105 62 53 106 Girls F3&4 103 PI & 2 120 61 Individual and Composite Scores 77 TABLE 63— BOYS RAW CORRELATIONS OF THE COMPOSITES Non-Verbal Non-Verbal Computa- Verbal Very- Manipulative Spatial tion Arithmetic Verbal Logical (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) Manipulative (1) 90 55 65 18 18 —05 —08 25 27 03 —19 (2) 90 , . 60 61 24 36 11 02 33 34 01 —13 Non-Verbal Spatial (1) 55 60 .. 55 12 20—05 09 23 24 07 09 (2) 65 61 55 .. 07 09 04 02 08 17 07 07 Non-Verbal Computa- tion (1) 18 24 12 07 . . 70 60 61 29 26 —33 —22 (2) 18 36 20 09 70 . . 53 31 40 29 —33 —09 Verbal Arithmetic (1) .—05 11 —05 04 60 53 . . 56 17 33 —11 —25 (2).— 08 02 09 02 61 31 56 .. 18 18—07—09 Very-Verbal (1) 25 33 23 08 29 40 17 18 .. 82 38 26 (2) 27 34 24 17 26 29 33 18 82 .. 51 12 Logical (1) 03 01 07 07 —33 —33 —11 —07 38 51 . . 39 (2) —19 —13 09 07 —22 —09 —25 —09 26 12 39 . . TABLE 64— GIRLS Manipulative (1) 77 03 32 04 22 01 00 31 22 09 09 (2) 77 .. 12 14 39 51 28 26 33 39 12 00 Non-Verbal Spatial (1) 03 12 . . 17 —04 08 13 18 05 20 30 32 (2) 32 14 17 .. —04 26 16 26 30 29 13 39 Non-Verbal Computa- tion (1) 04 39 —04 —04 . . 69 52 52 28 48 12 —11 (2) 22 51 08 26 69 .. 68 67 47 63 32 05 Verbal Arithmetic (1). 01 28 13 16 52 68 .. 70 55 64 12 28 (2). 00 26 18 26 52 67 70 .. 50 68 34 28 Very-Verbal (1) 31 33 05 30 28 47 55 50 .. 80 31 48 (2) 22 39 20 29 48 63 64 68 80 .. 48 39 Logical (1) 09 12 30 13 12 32 12 34 31 48 .. 25 (2) 09 00 32 39 —11 05 28 28 48 39 25 . . TABLE 65— CORRELATIONS OF THE COMPOSITES CORRECTED BY THE FORMULA FOR ATTENUATION Boys #A #B #A 86 29 01 #B 86 18 05 #(J 29 18 80 #1) 01 05 80 #lfl 34 25 41 31 #F —11 16 —41 —24 #C #D #B #F Girls #A #B #C 34 —11 25 16 30 41 —41 29 31 —24 19 49 39 49 10 #B #c #D #E #F 30 29 19 39 10 14 50 46 128 14 86 61 21 50 afi 79 57 46 61 79 92 128 21 57 92 SECTION VII BIBLIOGRAPHY BoNSER, Frederick G. (1910) The Reasoning Ability of School Children of the Fourth, Fifth, and Sixth School Grades. (Contributions to Education, No. 37.) Teachers College, Columbia University. Briggs, Thomas Henry (1913) Formal English Grammar as a Discipline. Teachers College Record, September, 1913. Burt, Cyril and Moore, Robert C. (1912) The Mental Differences be- tween the Sexes. Journal of Experimental Pedagogy, 1912, pages 273 to 284 and 355 to 388. DE FuRSAc, J. Rogues (1913) Manual of Psychiatry. John Wiley and Sons. GoDDARD, Henry H. (1911) The Binet-Simon Measuring Scale for In- telligence. Revised Edition. Hart, Bernard and Spearman C. (1912) General Ability, Its Existence and Nature. British Journal of Psychology, Vol. V. Spearman, C. (1904) General Intelligence objectively determined and measured. American Journal of Psychology, Vol. XV, No. 2. (15114) The Theory of Two Factors. Psychological Review. Starch, Daniel (1915) The Measurement of Achievement in English Grammar. Journal of Educational Psychology, December, 1915, p. 615ff. (1916) A Scale for Measuring Ability in Arithmetic. Journal of Educational Psychology, April, 1916, pp. 213ff. Thompson, Helen B. (Mrs. Woolley) (1903) Psychological Norms in Men and Women. University of Chicago Contributions to Phil- osophy, Vol. 4, No. 1. Thorndike, Edward Lee (1914) Educational Psychology, 3 vols. Teach- ers College, Columbia University. (1914) The Measurement of Ability in Reading. Teachers College Record, September, 1914. Woodworth, R. S. and Wells, F. L. (1911) Association Tests. Psycho- logical Review Monographs, Vol. 13, 1911, No. 57. Woody, Clifford (1916) Measurements of Some Achievements in Arith- metic. (Contributions to Education, No. 80.) Teachers College, Columbia University. ACKNOWLEDGMENTS The thanks of the writer are due to: Mr. J. H. Smallen, principal of the school in which the tests were given; the Misses E. M. Hammer and A. S. Sainsbury, the teachers of the two classes, and several other teachers, all of whom showed kindness and a spirit of cooperation toward the writer. The members of the New York State Commission on Ventila- tion : Messrs. C.-E. A. Winslow, D. D. Kimball, F. S. Lee, J. A. Miller, E. B. Phelps, and E. L. Thorndike, who were kind enough to permit the writer to use some of the records which had been obtained for them from the same pupils. The tests, which were given, scored, and tabulated under the direction of this committee, are C3, C4, C5, C6, C7, C8, D5, D6, E7, E8, E9, Eio, E13, E14, E15, E16, and E18. Miss Agnes Low Rogers, of Goucher College, who presented, scored, and tabulated four tests : Bi, B2, B3, and B4. Dr. Marvin James Van Wagenen, of the University of Minne- sota, who presented, scored, and tabulated two tests : E5 and E6. The members of the thesis committee : Dr. H. A. Ruger, assistant professor of educational psychology, Teachers College, who designed the Puzzles tests ; the late Dr. Naomi Norsworthy, associate professor of educational psychology. Teachers College; Dr. Robert Sessions Woodworth, professor of psychology, Co- lumbia University, and for general assistance and advice, espe- cially Dr. Edward Lee Thorndike, professor of educational psychology, Teachers College. VITA Frederick William Steacy was born in Ottawa City, On- tario, Canada, on the 22nd day of April, 1871. He attended a public school till April, 1883, when, owing to the death of his father, he was compelled to leave school and to begin work. In October, 1892, having attended night school for some months, he entered a school to prepare for college entrance. He matriculated into McGill College, Montreal, June, 1893, and graduated, with honors in Latin and Greek, in April, 1897. Dur- ing these four years he studied theology in the Montreal Diocesan Theological College (Church of England), and without complet- ing all requirements for the diploma was ordained to the Diaco- nate in June, 1897, and was appointed to the parish of Papineau- ville, Quebec. He was ordained to the priesthood in December, 1897. In 1899, he was appointed to the parish of Mille Isles, Quebec, and in 1902 to the parish of Adamsville and East Farn- ham, Quebec, and in 1909 to the parish of Glen Sutton, Quebec, In this year he completed (extramurally) the requirements of his theological college and received its Testamur (diploma). In Sep- tember, 1912, he resigned the parish of Glen Sutton for the pur- pose of beginning postgraduate studies, and was appointed hon- orary assistant to St. Edward's parish, Montreal, which position he still holds. In May, 1913, he received the A.M. degree in classics from McGill University, and in September, 1913, com- pleted the requirements for the degree of Bachelor of Divinity under the Board of the Church of England Universities and Col- leges of Canada. During the Winter Session, 1913-14, he studied Education and German in McGill. He attended Columbia Uni- versity and Teachers College from 1914 to 1917, receiving the Teachers College Diploma of Instructor in Education in 1917. He became lecturer in Elementary Education, Macdonald College, Province of Quebec, in 191 7. LIBRARY OF CONGRESS 019 842 761 5