matter possessed by the various individuals and require of each pupil full use of the talents with which he is endowed.

23. Unreliability of M. A. and I. Q.

[GATES, Arthur I., "The Unreliability of M. A. and I. Q. Based on Group Tests and General Mental Ability," Journal of Applied Psychology, March, 1923, Vol. 7, pp. 93–100.] (Adapted.)

The practice of computing mental ages and intelligence quotients from scores of group tests of general mental ability has been questioned recently on theoretical grounds, and various workers are discovering the unreliability of these measures by comparing the results obtained from different tests. This paper presents data showing that quite ridiculous I. Q.'s may be derived from certain group tests.

The following tests were given on successive days to the pupils of Grades I-VIII inclusive of the Scarborough school:

Dearborn Examination I or II, Haggerty, Delta I or II, Holley Picture Completion or Sentence Completion, Illinois (III to VIII only), Otis, Primary or Advanced, National Intelligence, Forms A and B, (III to VIII only) and Myers Mental Measure. The Stanford-Binet was given during the year to Grades I to VI inclusive. ..

The facts... may be considered with reference to certain important school problems.

1. The entire class of grade I pupils showed brightness, but the degree of brightness varies widely according to different tests.

2. The figures for the lowest I. Q. are fairly uniform, ranging from 92 to 99 but those for the highest are diverse, ranging from 121 to 165. Recommendations concerning sectioning for purposes of promotion would depend very greatly on what test is used.

3. Pupil A is given I. Q.'s ranging from 104 to 165, that is, by one test he would be classified as "average," by another a "genius." It is obvious that the variability of the I. Q.'s obtained by several tests all given within a few days is so great as to make prediction concerning optimum rate of promotion, possibility of completing college, etc., quite out of the question.

Results for Grade II.-For this grade, the group tests, all of them non-verbal, are the same as those used in grade I.

The results are similar. The I. Q.'s yielded by the Myers test show an average deviation from the mean which is more than twice that given by the Otis. One individual receives an I. Q. on one test 76 points higher than that given by another test; the difference between an average intelligence and idiocy. The average range of I. Q. for an individual is 35 points.

Results for Grades III to VIII.-The table shows the ridiculous results which teachers and other workers are likely to obtain from efforts to derive M. A.'s and I. Q.'s from group tests in these grades.

The variability of scores obtained by a given individual becomes greater as the grade becomes higher.

These facts should not be interpreted as a sweeping criticism of the usefulness and validity of group tests of general mental ability. What is urged is a restraint of certain inappropriate uses of these instruments. We should not, it is clear, compute M. A.'s and I. Q.'s from raw scores, but these raw scores themselves may be put to profitable use. It has been shown elsewhere that these group tests, at least those very verbal in content, give substantial correlations with achievement in school work.

The Causes of the Unreliability of I. Q.'s Based on Group Tests.-1. The distribution of native mental ability in the groups upon which the tests were standardized has probably been unequal. . . . Such differences are not necessarily eliminated by mere accumulation of vast numbers of measures; a fact that is now quite generally recognized.

2. The character of school training, especially in reading, writing, and arithmetic, affects the results considerably. For example, if certain grades were backward in arithmetic ... they would obtain lower I. Q.'s in those tests which contained relatively large amounts of arithmetical functions, other things being equal.

Again results will differ depending on the relative amounts of non-verbal material which the particular tests contain. . . . In our results the association between verbal and nonverbal tests becomes less close as the subjects become older.

This fact is a partial explanation of the fact that the disagreement between I. Q.'s is greater in the upper grades.

The factor of greatest importance in our results is practice in group tests. . . . On the whole, the more practice preceding a particular test, the higher the I. Q.'s obtained. . . There are three ways in which practice will cause variations in I. Q. from test to test: First, scores will advance considerably by virtue of general adaptation to test conditions; secondly, the gain will be relatively great in the particular tests which contain large amounts of identical or equivalent exercises; thirdly, the norms for the tests will be high or low, depending on previous practice in intelligence tests as well as on general mental abilities of the subjects on whom the norms are based. . . .

Again, the cumulative procedure of establishing norms probably tends in the long run to produce norms that are too low. . . . Numbers of students fail entirely to understand methods of procedure. They skip pages, lose time through distraction, broken pencils, etc., etc., whereas the factors conspiring for higher scores are fewer. . . .

24. The Accomplishment Quotient

[FRANZEN, Raymond, "The Accomplishment Quotient," Teachers College Record, November, 1920, Vol. 21, pp. 432-440.]

A ten-year-old child whose mental age is ten has progressed at the rate which is normal, and his I. Q. is 1.00. A very exceptional two-year-old child whose mental age is fifteen has progressed just one and one-half times as fast as the former, and his I. Q. is 1.50. Another exceptional ten-year-old child whose mental age is five has progressed at just one-half the rate of the first, and his I. Q. is .50. What we mean, then, by an intelligence quotient is the rate at which a child grows to mental maturity. . . . We can the more readily see the significance of viewing a child's equipment in terms of educational and mental age when we conceive of an educational quotient. This is the quotient resulting from the division of the age level reached in the test in question by the chronological age of the pupil. It is a measure of the rate of progress of the child in the school subject under consideration. Thus a ten-year-old child with

ten-year-ability in Thorndike Reading Scale Alpha 2 would have as his reading age divided by chronological age, 1.00. The division of what is by what would be if the child were normal gives the percentage of normality, the actual rate of progress. Since the I. Q. is the potential rate of progress and the E. Q. is the actual rate of progress, the ratio of E. Q. to I. Q. gives the percentage of what that child could do that he has actually done. Thus a child with an I. Q. of 1.32 whose reading quotient (his R. Q.) is 1.10, though he is doing work which is above normal, is not doing work which is above normal for him.

His

R.Q. 1.10

is whereas if he were progressing at his optiI.Q. 1.32

1.32
1.32.

mum rate it would equal We can, then, measure the approximation to ideal educational performance of any one child in any one elementary school subject through the approximation of this accomplishment quotient to 1.00. One's differences when E. Q. is subtracted from I. Q. are always positive when they are large enough to be significant and small enough to seem spurious when they are negative. Under special treatment one's educational quotients approach the intelligence quotients, that is, the correlation of E. Q. and I. Q. becomes nearer 1.00 when special treatment is given. It is safe, therefore, for practical use to assume that the optimum accomplishment quotient is 1.00. . .

It is a well-known fact that much work must be done in classification to get homogeneity or real conditions of teaching. As it is, most teachers are talking to the middle of their classes. They mystify the lower quarter and bore the upper quarter: they talk to the upper quarter and mystify the lower three-quarters: or they talk to the lower quarter and bore the upper three-quarters. When a child is bored or mystified his educational quotient remains constant. Then his accomplishment quotient becomes less as long as he remains in a position where he is being mistreated educationally. . . .

This accomplishment quotient would to my mind be an ideal school mark. Beside the inaccuracy of marks to-day, which are accurate marks only of the teacher's opinion, biased as it is by the personal equation of the pupil, there is another fault of prevalent school marking. It is based on average work. The mark is the link between education in the school and education in the home. It gives the parents an index of the child's work and allows them to encourage or discourage the child's attitudes

Such indices have no real significance when they are based upon average development, as the parent is generally mistaken about the ability of the child. . . . Such marks as are here advocated would correct this feature of our present system, as well as its accuracy. It is a mark which evaluates the accomplishment of the child in terms of his own ability. A brilliant child would no longer be praised for work which in terms of his own effort is 70 per cent. perfect, in terms of the group 90 per cent. The teacher gives him a mark of 90 while we mark him 70. A stupid child who does work which is marked 70 in terms of the class but 90 in terms of his own, a limited ability, is no longer discouraged. His effort is evaluated, and the praise that he receives from home is merited and consequently economical since the resultant satisfaction cements the bonds of concentration and attention. Such a mark is an actual index of the effort that child is making and consequently forms the proper link between the school and the home.

25. Accomplishment and Educational Quotients [GREGORY, Chester Arthur, Fundamentals of Educational Measurement, pp. 193-194. New York, D. Appleton & Co., 1922.]

5

The accomplishment quotient (A. Q.) of a pupil is found by dividing his educational age by his mental age. It shows the degree a pupil's actual progress approaches his potential progress. This is perhaps the best measure we have of the instruction and the application of the pupil. When a report of this kind is taken home, the parent may form some intelligent idea as to whether the pupil is working up to his optimum capacity. He may find out whether the pupil is progressing at a rate normal for his mental and educational ages. This also becomes a protection to teachers. If they can show that all the pupils under their guidance have progressed at a rate normal to their general intelligence, they have a good defense for adverse criticism of their teaching.

Another unit of measure that is being employed in measuring educational processes and products is the educational quotient (E. Q.), which is the educational age divided by the chronological age. It is the division of what is, by what it would be

5 Special references: Franzen, R., “The Accomplishment Quotient," Teachers College Contributions to Education (Nov., 1920); Ruch, G. M., "The A. Q. Technique," Journal of Educational Psychology (September, 1923); Toops and Simonds, "What Shall We Expect from the A. Q?", Journal of Educational Psychology (December, 1922; January, 1923.)