A Discussion of the Index of Formboard Ability
- Author:
Rudolf Pintner,
Ohio State University, and Donald G. Paterson, University of Kansas.
The Seguin Formboard has an interesting history as a mental test. It is now used in routine examinations by most clinical psychologists. There seems to be no disagreement among the many who have used it as to its excellence in differentiating the abilities of the subjects tested. In all the work that has been done, however, no definite index of formboard ability has been proposed which meets with universal acceptance. Time is recognized as the most important feature of the quantitative record. Three trials are usually given and the index is taken to be either the time record of the first trial, or the shortest of three trials or the average of three trials. No other indices seem to have been used by any workers although the third might have some theoretical arguments in its favor. In this article the various methods are subjected to ceitain quantitative treatment which we believe will reveal the relative values of the different methods. Norsworthy1 seems to have been the first to use the test. It was called the Block Test and was given to feebleminded and normal children. A first trial was given and a second followed after a considerable interval. Time was noted in seconds. There does not seem to have been any attempt to get a single index of ability and the results, therefore, were presented for the first and second trials separately. The question as to which of these trials is the more reliable was not raised.
The formboard was given to 271 normal children and 420 feebleminded children by Goddard.2 In this work he used the best of the first three trials as the index of formboard ability and presented age norms of the two sets of subjects tested. Among other mental tests the Goddard formboard was used by Wallin3 in testing epileptics.
1 Norsworthy, N. Psychology of mentally deficient children. Columbia Contributions to Philosophy and Psychology, 1906. Pp. 111. 2 Goddard, H. H. The Formboard as a measure of intellectual development in children. The Training School Bulletin, Vol. IX, June, 1912. Pp. 4. 3 Wallin, J. E. W. Experimental studies of mental defectives. Educational Psychology Monographs No. 7. Baltimore: Warwick & York, 1912. Pp. 155.
On page 62 Wallin states that each subject was given three trials, and then on page 63 he says, “Tests were repeated during the second and third sittings for many subjects, so that frequently the figures utilized are the best single records in from six to nine trials.” On page 74 he varies the index again,?”The averages are based on the best records in three trials (infrequently only two trials).” Although it is difficult to know just what Wallin’s results on the formboard mean it is clear that he favors the use of the shortest trial record. Here as with the case of Goddard’s results no principle seems to have been followed in deciding that the shortest trial record is the proper index. Ten trials were given by Jones1 in applying the test to fifteen children selected at random from the fourth grades of a city school system. He gives the results for both time and errors for each subject for each trial. He also gives the mean or average time for each subject for the ten trials. In this we have the average of a number of trials presented as a possible single index of ability, although Jones does not say whether or not this is the best index of ability. Sylvester2 seems to be the only worker who has attempted to solve experimentally the question as to which index is the most reliable. He decided to use the best time record of the second and third trials as the index of a child’s formboard ability. Whipple in his Manual3 decides in favor of the first trial time record when he says, ” Unless it is evident that there has been some disturbing factor that should have been eliminated, S’s quantitative performance in the first trial may be taken as the measure of his normal unpracticed performance.” This evidently means that the first trial reveals the child’s innate ability to better advantage than do the other possible indices.
The formboard test was given to over 1000 subjects by the Bureau of Analysis, New York State Board of Charities.4 Hall, after a short discussion of the possible indices, decides in favor of the best time record in three trials.
The writers5 in comparing the formboard ability of deaf and hearing children gave the average time and error results for the first three trials and for the average of three trials. In that paper the * Jones, E. E. Individual differences in school children. The Psychological Clinic, Vol. VI, 1913. Pp. 241? 251.
Sylvester, R. H. The Formboard test. Psychological Monographs. Vol. XV, 1913. No. 65. Pp. 86.
? Whipple, G. M. Manual of mental and physical tests. Baltimore: Warwick & York, 1914. Vol. I. Test 25 B, pp. 297-305. i State Board of Charities, Bureau of Analysis and Investigation. Eleven Mental Tests Standardized. Eugenics and Social Welfare Bulletin, No. V, 1915. Pp. 18-25. Results presented under the direction of Dr Gertrude E. Hall. f Pintner, R., and Paterson, D. G. The Formboard ability of young deaf and hearing children. The Pstcholoqical Clinic. Vol. IX, No. 8,1916, pp. 234-237. 194 THE PSYCHOLOGICAL CLINIC. main comparison was made by using the average time of three trials although no reason was advanced which would justify the use of the average as the most reliable index.
Wallin’s1 most recent work with the formboard advances some arguments, based upon experimental results, in favor of the shortest of three trials. He states, (p. 24) “Properly to gauge psycho-motor capacity by the formboard it is advisable to give the test at least three times; first, because the average score improves from test to test; and, second, because the effect of repetition varies somewhat according to the intelligence, type, age, and sex of the subjects. Girls make a poorer initial attack than boys and, therefore, gain relatively more from repetition. Intelligent and more mature children make a better initial adjustment than less intelligent and younger children, and, therefore, improve less from repetition; and epileptics very frequently do poorer in the second or third trials than in the first. For these and other reasons the fairest single index by which to gauge the psycho-motor efficiency of an individual by this formboard is the best record in the three trials.” It is not at all clear that the reasons Wallin puts forward are those which really favor the shortest trial. The arguments seem, lather, to apply against the use of the first trial or against the use of any one trial as the single index. To the writers the arguments seem to favor the use of the average of three trials, in this way eliminating idiosyncrasies of various types of subjects in responding to particular trials of the test. Young2 in his standardization of a new modification of the formboard accepts as established Sylvester’s conclusion that the shortest of three trials is the most reliable single index of the subject’s formboard ability. He therefore presents his standard age norms in terms of the shortest of three trials.
To recapitulate, we find that of nine different workers two favor the use of the first trial record, two the average of three trials and five the shortest of three trials. This is not veiy significant, however, as workers in this field as in other fields tend to follow the beaten track and because the first important study (Goddard, 1912) adopted the shortest of three trials as the index, we find later workers doing likewise.
Sylvester’s3 work devotes considerable attention to the problem of the determination of the most reliable index of formboard ability. He compares the distribution of the time records of the first trial, the 1 Wallin, J. E. W. Age norms of psycho-motor capacity . Journal of Educational Psychology, Vol. VH, No. 1, Jan. 1916, pp. 17-25.
? Young, H. H. The Witmer formboard. The Psychological Clinic, Vol. X, No. 4, June, 1916, pp. 93-112. ?Sylvester, R. H. Op. cit., pp. 26-34. third trial, the shortest trial, and the aveiage of three trials. The following criterion is then proposed for the determination of the index, ” That standard which gives the lowest and most regular variability is probably the best.” The shortest of three trials is chosen as fulfilling this condition although the average of three trials shows a very smooth curve. In a thorough mental examination of individual children he found that, “in many cases the shortest trial index was found to be unsatisfactory and in some cases it was quite misleading.” On the contrary Sylvester after subjecting the average of three trials to the same kind of correlation with the results of thorough mental examinations, says, (p. 33) “Without doubt, the average of three trials is a more reliable index to the mentality of a child than is any other single numerical index.” In spite of this conclusion, however, he returns to the shortest trial record of the second and third trials. It does not seem to the writers after a review of the efforts to solve this question that the last word has been said. Theoretically the shortest time record is open to serious criticism. It is coming to be a recognized principle of differential psychology that no one test is a true measure of ability, that in fact we need a variety of tests for such measurement. This is true for two reasons, first to allow of a balancing or compensating of the many specific abilities possessed by the individual, and secondly to reduce to a minimum the influence of large fluctuations of attention due to especially facilitating or inhibiting factors operative in the course of the experiment. To take the shortest time record is to violate this latter principle. Further, we cannot see why a reduction in the variability of the distributed results fiom age to age should be the criterion of the proper index. So far as we are aware it rests upon no definite piinciple. The reverse might be held with as much justification in logic. Thus we might argue that that measure which gives the greatest variability in the distributed results is the best measure because it is making finer dif~ ferentiations among those tested.
From the consideration of the principle of eliminating the influence of chance fluctuations of attention, above referred to, we might conclude that the average of three trials is the best index of a child’s formboard ability. It measures the child’s average ability without giving undue weight to extreme fluctuations of attention and possibly other accidental factors which might be operative to produce one exceptionally short trial.
The first trial record seems to us to be especially significant. It falls in line most closely with the now commonly accepted definition of general intelligence as the rapidity and accuracy with which the organism can adjust itself to relatively new situations. The common objection urged against the first trial is that the instructions and meaning of the situation may not be understood by the subject. This is really no objection at all if one will but consider the instructions, which should at all times be standardized and rigorously adhered to, as a part of the test. This principle does not seem to have been thoroughly grasped by some workers in the field of standaidization. So far then, theoietically, the time of the first trial as well as the average time for three trials might be held to be reliable indices of formboard ability. With this exposition of the question we believe we have demonstrated that no particular index has as yet been shown to be the most reliable either on theoretical or experimental grounds. However, we believe that an acceptable criterion can be found. If we make the assumption that individuals within a group develop while maintaining relatively their same differences of ability, we might say that that measure is the truest index which yields the highest correlation between the rankings of the same individuals from one period of time to another. By the use of correlational formulae the various indices in question can readily be submitted to this test.
Fortunately, we have the records of thirty-two children (18 deaf and 14 hearing) tested in October 1914 and again in October 1915. In an article1 presenting those results the fact was brought out that the rank correlations based on the aveiage of three trials showed a Pearson r of +.64 for the deaf children and +.88 for the hearing children, although the correlations were computed from records taken one year apart. We here present similar correlations for five indices, the time for the first trial, for the second trial, for the thiid trial, for the shortest trial, and for the average of three trials. We have ranked the deaf and hearing children as a group and have omitted the record of one child whose record showed a gain from one year to the next out of all proportion to the gains of the rest of the children. This gives us 31 children whose records serve as the basis of the correlation. Spearman’s foot-iule or R-method was used and converted into Pearson r values by reference to Whipple’s manual.2 Table I gives the results of these five correlations. The first trial records in 1914 were used in ranking the children and then these ranks were correlated with the first trial lecords in 1915. The same procedure was used in determining the correlations for the other indices. Column 1 of table I gives the index used for purposes of correlation, column 2 the Spearman R value, column 3 the Pearson r value, column 4 the 1 Pintner, R. and Patcrsoa, D. G. Op. eit.
1 Whipple, G. M. Manual of mental and physical tests. Baltimore: Warwick & York, 1915. Vol. I, pp. 42-44.
probable error (P. E.), and column 5 the reliability of r, i. e. the ielation between the size of the r and the P. E.
TABLE I. CORRELATIONS OF FIVE INDICES OF FORMBOARD ABILITY. The Index First trial 1914 with first trial 1915 Second trial 1914 with second trial 1915…. Third trial 1914 with third trial 1915 Shortest trial 1914 with shortest trial 1915 . Average of three trials 1914 with average of three trials 1915 R value + .46 + .43 + .30 + .44 + .56 r value + .66 + .62 + .45 + .64 + .77 p ? Reliability of r .0863 .0863 .1133 .0863 .0688 7.6 7.1 3.9 7.4 11.1 The correlation of the first trial ranks in 1914 with the first trial ranks in 1915 yields us an R of +.46, an r of +.66 with a P. E. of .0863. The r is 7.6 times the P. E. and is fairly reliable. The third trial record produces the lowest correlation (r = + .45) and according to our criterion would be the least desirable as an index. This is interesting for it fits in with the impression one gets as he gives the test. A child usually tries to make his best record on the third trial and in his haste he makes errors or else fails to put the blocks in on the first attempt thus wasting time. In other words, “Haste makes waste.” The first trial record, the second trial record and the shortest trial record seem to yield about the same coefficient of correlation and we would hold are of the same reliability as indices of formboard ability. The average of three trials gives the highest correlation of all (r = +.77). The r is 11.1 times the P. E. and is very reliable.
These correlations show us that regardless of the index used (with the exception possibly of the third trial record) we find that the children maintain their relative ranks from one year to another although all the children made great gains in formboard ability. Leaving out of consideration the second and third trial records we find that of 13 individuals making a gain in rank from 1914 to 1915 in their first trial records, only six of them gained in position when measured by their shortest trial record while ten gained in their average trial records. Thus the gains probably represent true gains in ability as compared to the other children. If our assumption with which we started out is correct then the average of three trials is the most reliable index of formboard ability for it shows the highest correlation. This result is not strange for it fits in well with the general a priori considerations outlined above.
We would conclude, then, that the average of three trials is the best index because it shows the highest correlation from one period of time to another and because it does not give undue weight to fluctuations of attention although it rightly takes them into consideration, and further because it allows for the influence of the measure of the child’s first attack upon the “new situation.” In short, all three trials are of importance in determining the child’s formboard ability. The average of three trials is the only single index which gives weight to all these factors. A priori considerations, the evidence of the close correlation of the average of three trials with the results of thorough mental examinations (Sylvester, op. ext., p. 33), and the fact that the average gave a much higher correlation than did any of the five possible indices, all point to it as the most reliable index of formboard ability.
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