Correlation of the Witmer Formboard and Cylinder Test
- Author:
Mary Hoover Young,
Graduate Student, University of Pennsylvania.
In the spring of 1915, the cylinder test was given by two advanced graduate students in psychology to 47 men and 28 women undergraduates in Psychology 2c at the University of Pennsylvania. The following fall, this same test as well as the Witmer formboard was given by advanced students in psychology to 55 men and 59 women undergraduates in Psychology lc. These tests were employed to give the students an insight into mental testing, and to begin the accumulation of data with the view of establishing norms for adults. As such tests come in the group generally known as mechanical or manual tests it has seemed advisable to treat them together.
The cylinder test consists of eighteen wooden cylinders of graduated depth and diameter, modelled after the larger Montessori insets with duplications omitted, and fitted into eighteen cylindrical recesses set in a circular wooden frame. The experimenter removed the cylinders in the presence of the subject by beginning with the smaller blocks and lastly placing the larger blocks on the top of the pile in the inner space of the cylinder board. The subject was then told to replace the blocks as quickly as possible. The time was taken to fifths of a second by means of a stop watch from the moment the subject touched the first block until the last one was correctly replaced. Each subject was given three trials by the same method in as rapid succession as possible. The shortest trial time is taken as the index of the subject’s cylinder ability.
TABLE I. NUMBER OF CASES AND TIME VALUES IN SECONDS?CYLINDER TEST. Number of subjects. Mean Standard deviation. Minimum Lower quartile Median Upper quartile Maximum Min 2c 47 32.1 5.86 17.8 29.0 31.4 36.0 54.0 lc 55 34.9 7.67 22.0 29.0 34.0 ? 39.0 60.0 (112) Combined 102 33.6 7.21 17.8 29.0 33.0 38.0 60.0 Women 2c 28 35.5 6.39 18.4 33.2 36.6 39.2 47.4 lc 59 35.0 7.89 21.0 29.0 33.0 41.0 57.0 Combined 87 35.2 7.34 18.4 30.0 34.0 38.0 57.0
Table I contains the results of the cylinder test for both classes. The first column of figures contains the time values for the men in Psychology 2c; the second, for the men in Psychology lc; the third the combined results for the men of both classes; the fourth, the time values for the women in Psychology 2c; the fifth, for the women in Psychology lc; and the sixth or last, the combined results for the women of both classes. In explanation of the meaning of the time values given in the table, it may be stated that the mean is the average time for the group; the standard deviation indicates variability and the reliability of the mean; the minimum is the shortest time record of the group; the lower quartile is that record below which twenty-five per cent of the cases fall; the median is that record above and below which fifty per cent of the cases occur; the upper quartile is that record above which the highest twentyfive per cent of the cases occur; and the maximum is the highest or longest time record of the group.
Reference to table I shows that there is a close agreement between the results for the two classes, and that the standard deviations are fairly constant. It would thus appear that the record for either of these groups is fairly representative of what could be expected of all similar groups. On the whole there is a tendency for the men to be superior to the women on this test. The students of Psychology lc were tested on the Witmer formboard by the standard method described by Mr. Young in the present issue of The Psychological Clinic. Each student was given three trials according to the standard method, and the shortest trial was taken as the index of his formboard ability. Immediately after these three regular trials were completed, the subject was given a fourth trial in which he was required to keep his eyes closed during the time the blocks were being removed by the experimenter, and TABLE II. NUMBER OF CASES AND TIME VALUES IN SECONDS?FORMBOARD. Number of subjects. Mean Standard deviation. Minimum Lower quartile. Median Upper quartile Maximum Mbn Standard Method 55 11.8 2.72 7.4 9.8 11.2 14.0 20.0 Eyes Closed 55 156.0 83.94 49.0 90.0 134.0 184.0 447.0 Women Standard Method 59 12.6 2.81 6.0 10.8 12.0 14.6 20.4 Eyes Closed 59 152.0 97.62 49.0 80.0 119.0 185.0 499.0 while he himself replaced them. The time was taken in seconds by means of a stop watch from the moment the subject touched the first block until the last one was correctly replaced.
Table II includes the results of the undergraduate students in Psychology lc on the Witmer formboard. The first column of figures contains the time values for the men tested by the standard method; the second column, for the men tested with the eyes closed; the third column, for the women tested by the standard method; and the fourth or last column, for the women tested with the eyes closed. The time values in table II have the same significance for their respective groups as those in table I. By the standard method the men are slightly superior to the women in formboard ability, but with the eyes closed the reverse is true.
The standard deviation is relatively much larger where the formboard is worked with the eyes closed than where it is worked by the standard method. The large standard deviation in the former case is apparently due to the fact that in a few cases an unusually long time was required to complete the test. Such a distribution is to be expected, for while there is a minimum time below which the test cannot be worked, there is not such an upper limit. For the men the difference between the median and maximum is 3.7 times that between the median and minimum, while for the Avomen the difference between the median and maximum is 5.4 times that between the median and the minimum.
The formboard worked by the standard method gives results which lie within a narrower range of distribution than the results for the cylinder test, while the formboard worked with the eyes closed gives a much wider range of distribution than either of the above mentioned tests. The minimum record for the cylinder test is several seconds below the maximum record for the formboard worked by the standard method, while the maximum record of the cylinder test is only several seconds above the minimum record of the formboard worked with the eyes closed. From this it is readily seen that most of the time records of the cylinder test lie between the maximum formboard record obtained by the standard method and the minimum formboard records obtained with the eyes closed. Just what the significance of these differences is has not been determined, but it is certain that they indicate the varying difficulties of the tests. These three tests represent a series of progressive difficulties; the formboard worked by the standard method is a simple test, the cylinder test is a stage higher in difficulty, while the formboard worked with the eyes closed makes a very difficult test, because the individual is facing a new problem and feels himself in a strange environment.
Since three trials were used in working these tests, it would naturally be expected that the majority of the best records would occur on the third trial, for here practice would tend to shorten the time. The percentage of cases where the best records occurred on the first, second, and third trials respectively, was determined.
TABLE III. DISTRIBUTION OF SHORTEST TRIAL TIME RECORDS. Trial. Formboard. Cylinders. . Men 2% 7% 11% 34% 87% 59% Women 14% 7% 10% 33% 76% 60% Table III shows these percentages for both the men and the women in working the cylinder test and the formboard by the standard method. Thus 11 per cent of the men made their best record on the second trial of the formboard, and 34 per cent made their best record on the second trial of the cylinder test.
Since it is the general assumption that the different mechanical or manual tests, such as these, test the same factors or qualities in an individual, it would be only natural to expect that success on the one would mean success on the other. In reading over the present literature we find the formboard listed as a test of powers of recognition, discrimination,- memory, muscular co-ordination, and trainability by some clinicians, while others consider it a test of form perception, rate of movement, and ability to meet a new situation, and still others use it as a test of constructive capacity, intellectual ability, or so-called general intelligence. From casual observation, although the cylinder test is more difficult, it would appear to test the same factors. Such tests as the formboard are generally considered simple and are supposed to involve only a few of the simpler mental processes. On this account they are generally referred to as mechanical or manual tests. If these tests were simple and involved the same factors they should show a high correlation. To determine the facts of the case, a correlation was worked out between the results obtained from each test.
From the class in Psychology lc in the fall of 1915, 55 undergraduate men and 59 undergraduate women took the formboard test by the standard method and with the eyes closed during one recitation. The following recitation the same students took the cylinder test. These tests were not given as group tests. Each individual was tested by himself so that no student saw any other work the tests. The results are presented in the preceding tables and are here correlated by Pearson’s product moment method of correlation. Table IV gives these correlations.
TABLE IV. CORRELATION.
Correlation between: Cylinders and Formboard by the Standard Method. ” ” ” with the eyes closed Formboard; Standard Method and eyes closed Men +0.466 +0.570 -0.008 . Women +0.067 +0.186 +0.415
These correlations are scarcely what one would have expected from such apparently closely allied tests. In no instance is there a high correlation. Just as interesting as the lack of a high correlation, is the fact that there is no agreement in correlation between the sexes. A significant correlation between two tests for the one sex does not accompany an equally significant correlation between the same tests for the other sex. Thus the cylinder test and the formboard by the standard method which give the positive medium correlation of 0.466 for the men, have the very low positive correlation of 0.067 for the women. Then the formboard by the standard method and the eyes closed, which gives the insignificant negative correlation of 0.008 for the men, has the positive medium correlation of 0.415 for the women.
Assuming that the number of cases presented is sufficient to give fairly reliable results, what are we to conclude about the above tests? It does not appear that they are as simple as is generally assumed, and furthermore it does not appear that they test the same mental factors. The formboard worked with the eyes open and with the eyes closed gives two distinctly different sets of results for the men, while for the women it seems to set more nearly the same problem. The reverse is true for the cylinder test and the formboard by the standard method. They appear to set somewhat the same problem for the men, but different problems for the women. There appears to be sufficient evidence to conclude that each of these tests sets a different problem for each of the two sexes, and tests different factors in each. If this is true, success on the formboard by the standard method means one thing for a man and a very different thing for a woman. This may help to explain why different investigators use the same test in approximately the same manner to test very different factors. They consider the test to be simpler than it really is, and thereby stress one phase to the neglect of others of probably equal importance. The sex differences here demonstrated deserve further investigation and indicate the need of further analysis of performances and of more careful interpretations.
Disclaimer
The historical material in this project falls into one of three categories for clearances and permissions:
Material currently under copyright, made available with a Creative Commons license chosen by the publisher.
Material that is in the public domain
Material identified by the Welcome Trust as an Orphan Work, made available with a Creative Commons Attribution-NonCommercial 4.0 International License.
While we are in the process of adding metadata to the articles, please check the article at its original source for specific copyrights.