The purpose of the present experiment was to examine developmentally the effects of frequencies (4 and 10sec) of intermittent sounds given during the standard time on the reproduced time which was estimated by the method of reproduction. The buzzer was intermittently given for 0.1sec at the intervals of 0.3, 0.5, 0.6, 0.75 and 1.2sec in Experiment 1, and at the intervals of 0.15, 0.2, 0.4, 0.75 and 2.0sec in Experiment 2. These five conditions of buzzer frequencies were at random presented four times respectively for each subject. Besides the pulse rate in the condition of sitting still, the tempo of metronome which was accepted most comfortably and the pace of tapping at his own preferred speed were measured for each subject and the relation of these tempos to the estimated time was examined. The subjects were as shown in Table 1. The results were as follows: Generally the higher the frequency of sounds was, in other words, the shorter the sound interval was, the longer was the estimated time. This finding conforms to the theory of the number of perceived changes stated by Fraisse. And the younger the subjects were, the stronger were the effects of sounds. At the intervals centering around 0.7sec, however, the relation of the sound frequency to the estimated time was not so simple as above mentioned, and the ranges of such frequencies were wider for the older subjects. Besides it was not observed in the older subjects that the estimated time tended to prolong according to the frequency for such high frequencies of sound as 0.2sec and/or 0.15sec (see Fig. 1 & Fig. 2). 2. The smallest mean deviation among the various conditions of sound frequency was obtained for each subject chiefly at the intervals near 0.7sec in all age-groups and it was also observed that the rates of the subjects' pulses and their preferred tempos of metronome and tapping center around the above frequency (see Fig. 2, Fig. 4 & Table 4). These results indicate that these tempos may be the bases of time estimation, so both the mean deviations and the effects of sounds were small for the sound frequencies near 0.7sec And because these tempos might have been firmly established in the adults as the basis of time estimation, the range of the intervals of sounds with such slight effects on time estimation as mentioned in 1 was wide. 3. The reproduced times in those young children who preferred fast tempos of metronome were long, and those young children whose reproduced times were prolonged along with the higher frequencies of sound generally preferred fast tempos of metronome. This relation became looser with age development and even reversal in the adults (see Table 6, Table 7, Table 11 & Table 12).
The “multiple-choice” form of test, in which answer alternatives are given, has frequently met with the objection that an examinee who does not know the correct answer to the item can make a substantial score by chance success. Several methods have been proposed to correct the effect of chance success on items and test statistics. These methods are all based on certain assumptions concerning chance success, which were as follows: (1) An examinee who is ignorant of the correct answer to the item will fail in the free answer form of test, and he will choose the answer at random from the alternatives in the multiple-choice form. (2) All alternatives in an item have the equal probability of chance success, that is, the probability is the reciprocal of the number of alternatives. This study aims at investigating the validity of the above assumptions. Methods: Two parallel mathematical tests consisting of 12 items were prepared, one of which was the “control test” (free answer form), and the other was the “experimental test” of five different forms the 2-alternative form (Form A), the 3-alternative form (Form B), the 4-alternative form (Form C), the 5-alternative form (Form D), and the free answer form (Form E), These tests were given to 3rd grade pupils (N=2, 100) of some secondary schools during October and November, 1964. Ss were divided into two groups: Group 1: A control test was given in the usual way, but the experimental test was given without showing the problems and the examinees were asked to make a pure guesswork on the answer sheets. Group 2: A control and experimental tests were given in the usual way. Results: In the pure guesswork of Group 1, the percentage of response was different among alternatives and the mean score was significantly different from the chance score, contrary to the assumption of the equal probability of choice (Tables 1 and 6-7). The results of Group 2, on the other hand, did not contradict the assumption of chance success. Score obtained were compared with the estimated scores which consisted of the true score and the chance score, and good agreement was obtained. All this is probably due to the fact that the proportion of the chance score in the observed score was so small as to make the difference between the observed score and the estimated score negligible.
Reliability and validity of tests are varied by selection of subjects in some of the tests. The correction formulas have been algebraically derived in Chapters 10, 11, 12, and 13 of Gulliksen's text, “Theory of Mental Tests (1950, John Wiley)” (Chapter 13 is an exception). The same formulas can be derived by the concept of test vectors. It is assumed here as in a conventional model in test theory that a test vector has two orthogonal components, T and E. The length of the test vector is adjusted to be equal to the standard deviation of the test scores in a given group, and the reliability coefficient is defined by the square of the cosine of the angle between the test vector X and its true component T. The correlation coefficient between two distinct test vectors, X1 and X2, is defined by the cosine of the angle between X1 and X2. Change of reliability coefficients. Let R and r be reliability coefficients of a test in an original group and in a selected group, respectively, and σ and s be standard deviations of the test in these two groups. A formula (1-R)σ2=(1-r)s2 can be derived from the assumptions that only the true component of the test vector T is varied by selection and the error component E is invariant under selection. Validity under univariate selection. When the number of explicit selection variables is one and that of incidental selection variables is n, the relationship between the variance-covariance matrix of tests for the original group and that for the selected group is given by C=PTDP, where C and D are the (n+1)-variance-covariance matrices of tests for the original and the selected group, respectively, including an explicit selection variable X in the first entry, and where P=[(σX/sx)(σX/sx-1)(sy1/sx)rxy1(σX/sx-1)(sy2/sx)rxy2…(σX/sx-1)(syn/sx)rxyn 0 1 0 0 0 0 1 0 0 0 0 1] in which σX is the standard deviation of the explicit selection test X in the original group, sx, sy1, …syn are standard deviations of explicit selection test x and incidental selection tests, y1, …, yn in the selected group, and rxy1, etc., are correlation coefficients between tests in the selected groups. The underlying assumptions are that the component of an incidental selection vector which is orthogonal to the explicit selection vector X is invariant under the selection for X and that the component which is parallel to X is changed to the same direction with the same proportion as the change of X. Validity under multivariate selection. The general formulas correcting correlation coefficients under multivariate selection have been given by Aitken (1934, Proc. Edinburgh Math. Soc.) in a matrix form and they are also treated in Chapter 13 of Gulliksen's text, The same formulas are derived from the assumptions below as an extension of the vector concepts referred in the preceding paragraphs. The incidental selection vectors are divided into two components. The first one is normal to the hyperplane spanned by explicit selection vectors and is assumed to be
1. The purpose of the present study was to make clear quantitatively the situational factor in the speech of one-year-old children. The basic data were transcribed lists of the speech of forty normal Japanese children, recorded by a magnetic taperecorder (10min for each child). 2. Situations adopted were the picture-book situation (PS) and the building-block situation (BS.) And in these situations, each mother was asked to play with her child as in their everyday life. 3. The following measures were used to uncover the sequence of functional stages of speech behavior along their development: total number of utterances (Measure I), the number of spontaneous utterances (Measure II), the number of spontaneous-meaningful utterances (Measure III), and the number of spontaneous-meaningful utterances which accord well with the given momentary situations (Measure IV). 4. The main results were: (1) in terms of Measures I and II, speech behavior was more active in PS than BS throughout one-year-old period, and (2) in terms of Measures III and IV, speech was more active in the latter half of the period, besides the fact found by Measures I and II (These differences were all statistically significant at the 1-5% level). 5. Identification of “word classes” of one-word utterances in the primitive sensory-motor level was attempted, with the finding that “representational” words were dominant in PS, whereas “non-inter-personal” words (e.g. action cues) were prevailing in BS (these differences were also statistically significant).