Experimental studies of the successive changes (frequently represented by curves describing laws of learning and other similar functional relationships) in a criterion variable accompanying experimental variations in a given “treatment,” and experimental comparisons of such changes for different populations or for different treatments, constitute a large and important class of psychological experiments. In most such experiments, no attempt has been made to analyze or to make allowance for errors of sampling or of observation. In many others, the techniques of error analysis that have been employed have been inefficient, inexact, or inappropriate. This paper suggests tests, using the methods of analysis of variance, of certain hypotheses concerning trends and trend differences in sample means obtained in experiments of this general type. For means of successive independent samples, tests are provided of the hypotheses: (H1) that there is no trend, or that the trend is a horizontal straight line, (H3) that there is a linear trend, (H5) that the trend is as described by a line not derived from the observed means, and (H7) that the trend is as described by a line fitted to the observed means. Tests are also provided of similar hypotheses (H2, H4, H6, and H8, respectively) for means of successive measurements of the same sample. Finally, tests are provided of the null hypotheses that there is no difference in trend in two series of means: (H9) when each mean in each series is based on an independent sample, (H10) when each pair of corresponding means is based on an independent sample, (H11) when each series of means is based on an independent sample, and (H12) when both series are based on a single sample.

Physical measurements, obtained from several different age-groups and national groups, have been correlated and factorized. The largest of the investigations was based on 2,400 British airmen in the R.A.F., and the most recent included as many as 17 traits. The methods of factorization employed were those worked out in early investigations of mental and scholastic tests, and differed in minor respects from those more recently used by Thurstone in his re-analysis of some of our data. The factor patterns reveal a remarkable constancy from age to age and from one national group to another. The general factor accounts for about the same proportion of the variance as the general factor in cognitive tests. The largest of the bipolar factors classifies traits into longitudinal and transverse, thus in some measure confirming the traditional classification of body-types.

A factorial study of fluency was undertaken to test an hypothesis that at least two fluency abilities would be measured by a battery composed both of word fluency tests used by Thurstone and tests of fluency described by several British investigators. Twenty-eight tests, including ten reference tests for five primary mental abilities, were administered to 181 high-school seniors. Ten centroid factors were extracted, a simple structure was found, and eight factors were interpreted. Five factors defined were the following reference abilities: memory (M), number (N), reasoning (R), verbal comprehension (V), and perceptual speed (P), the last one being somewhat tentatively identified. The main finding is the analysis of fluency into two factors: word fluency (W) and ideational fluency (F). Word fluency is defined as a facility in producing single, isolated words that contain one or more formal restrictions, without reference to the meaning of the words. Ideational fluency is described as a facility in expressing ideas by the use of words and their meanings. Another verbal ability indicated is tentatively interpreted as verbal versatility, the ability to express essentially the same idea by means of several different words or combinations of words.

The concept of test reliability is examined in terms of general, group, and specific factors among the items, and the stability of scores in these factors from trial to trial. Four essentially different definitions of reliability are distinguished, which may be called the hypothetical self-correlation, the coefficient of equivalence, the coefficient of stability, and the coefficient of stability and equivalence. The possibility of estimating each of these coefficients is discussed. The coefficients are not interchangeable and have different values in corrections for attentuation, standard errors of measurement, and other practical applications.

In certain types of experiment it frequently happens that we have a block of data consisting of several trials on the same individuals. Using the methods of estimation provided by the analysis of variance, estimates of reliability are derived for this case, and the conditions under which each is valid are discussed. Various relations between these estimates and the product-moment coefficient of correlation are obtained.

Normal equations, using data in various forms, are presented for securing the regression weights for prediction of a dichotomized criterion, and a simplified equation for the estimation of the multiple bi-serial or multiple point bi-serial, depending upon the proper assumption as to the nature of the distribution of the criterion, on the basis of these maximal weights is given also. The weights, unaffected by the assumption as to the nature of the criterion, are identical (or proportional) to those found by the discriminant function approach based upon analysis of variance. The author holds that the present multiple correlation approach is both easier and more informative than the discriminant function (analysis of variance) approach and suggests that the discriminant function be abandoned in favor of multiple bi-serial and/or multiple point bi-serial correlation and regression.

This note suggests that the reflection of residuals in the centroid method of factor analysis should be continued, whenever possible, after all the sums of the columns in the correlation matrix, excluding diagonal values, are positive. A criterion is given for determining whether further reflection is possible in such cases.

A table is presented which directly gives phi coefficients accurate to three places when entered by the proportion of one sub-group responding in a specified manner and the proportion of a second sub-group responding in the same manner. The table gives coefficients identical with those obtained by formula if the sub-groups are equal in number. The phi coefficients can readily be expressed, if desired, in terms of critical ratio or chi square. The table is more accurate than the use of abacs and eliminates the use of time-consuming formulas. Accurate determination of item validity on the basis of statistically rigorous techniques can be made more quickly by means of the table than validity determined by less efficient methods which have previously been used to save time.

P-technique, a method employing intra-individual correlation, is tried out for the first time. As part of the general design it uses some variables the same as those in a coordinated R-technique study and a second, parallel P-technique study with a clinical case. Definite factors are obtained among the psychological and physiological variables, which can be mutually matched. One is a fatigue factor, but the rest are general personality factors readily identifiable with those obtained in past R-technique researches.

This paper shows the formulation of nine methods of estimating the unknown communalities. Each of these methods has been used on experimental data and the results tabulated for comparison. The results show that the most accurate approximations are obtained from the Centroid No . 1 and the Graphical methods.

Under controlled flight conditions, the distance between a navigator's report of position and his actual position is a criterion of success in dead reckoning navigation. Students' logs were evaluated for five separate missions by comparing the students' entries with standards determined by experts. The reliability of this technique is indicated by the fact that mission to mission intercorrelations of error scores were low, while the intercorrelations between legs of the same mission were moderately high. The intercorrelations between the error scores for the different navigation variables were computed and analyzed by using both factor analysis and multiple regression techniques. Both analyses indicated that a major portion of all dead reckoning error could be attributed to errors made in determining magnetic deviation. As a result of these analyses, recommendations were made for changing the instruction in dead reckoning and alterations in the equipment used were suggested.

In connection with a study bridging rating, questionnaire, and objective test factors, confirmation was sought with respect to the twelve personality factors previously found for young adult men. Variables were chosen to clarify and discriminate the nature of related factors. Ratings of and by 373 students were obtained, and the present study describes the separate factorization for the 133 men among them. Factorization yielded eleven factors, of which, on “blind” rotation for simple structure, 9 or 10 proved to be identical with those of the previous study. A new factor M is described.

Results of an experiment to obtain data on the consistency of the items of two forms of an Activity Preference Blank are presented. Both Form I and Form II, which was a revised edition of Form I, were administered twice, so consistency data are available for both forms. A sub-item is said to be consistent if a high proportion of men marked it the same way, M for preferred Most and L for preferred Least, on both administrations of the test. The data of the experiment were investigated to see what happens to the consistency of sub-items when the items are changed in context, when the number of sub-items in an item is reduced, and when the time-interval between the administration and the re-administration of the test is increased. The author also gives data on the consistency of the responses made to particular combinations of sub-items and data on item consistency when all sub-item combinations are taken into consideration.

A technique of analysis utilizing frequencies of differences is described and applied to a hypothetical experiment involving two methods of instruction. A nomograph is provided for computing the chi-square values applicable to the method.

Several of the more popular statistics texts used in psychology are reviewed with respect to their treatment of the measurement and interpretation of skewness. Some areas in psychology where measures of skewness of distributions may yield significant information are indicated. Tables of 1%, 2% and 5% points of moment measures of skewness and tables of the 1% and 5% points of the difference in skewness of two uncorrelated distributions are presented. These tables are approximations based on the approximate normality of skewness in large samples from normal populations. The limited confidence with which these tables can be used in the absence of exact knowledge of the distribution function of the underlying statistics is indicated.

In this modification of the Aitken Pivotal Condensation Method for obtaining partial regression weights and multiple correlation coefficients, the unit matrices used by Aitken are eliminated, with a resultant decrease in the computational work. Through a simplified arrangement of successive matrices, each one is reduced by the same simple rule. Other modifications also contribute to ease of computation and facilitate checking.

The KG Index described below is proposed for evaluation as one approach to the problem of providing an index giving comparable values for items (1) of equal discriminative power at all levels of difficulty and (2) of different numbers of alternative responses.