This is a very simple explanation of factor analysis primarily for the “factorial layman.” The interpretation of factors and the comparisons of various factor solutions are illustrated with a hypothetical example so designed that the reader can visualize all the relationships in a two-dimensional graph.

A comparison of the “test-retest” and “internal consistency” estimates of reliability coefficients is given, and it is shown that the two methods give different results. Application of the analysis of variance and covariance method reveals that there is not just one but a number of reliability coefficients involved, and that an estimate of each of these may be obtained. The analysis shows that in using the test-retest method the error or remainder effects are not independent on the two trials, possibly because the individuals remember the items and their responses to them on the previous trial.

A simple test of multiple serial response is proposed which makes use of materials that are inexpensive and easily prepared, and that do not get out of order. The test employs twenty-four colored blocks placed in two rows on a table. The total equipment needed consists of the blocks and a watch.

Several sets of learning data furnished by I. Krechevsky have been analyzed in terms of meaningful parameters of the learning curve, and the changes in the frequency distributions of these parameters with changes in the experimental conditions have been studied. One of the parameters represents the animal's initial preference for the light or dark, the other represents learning ability. The analysis shows that destruction of about ten or fifteen per cent. of the cortex, increases the animal's preference for the light and decreases the learning ability slightly. By ordinary methods of analysis, it is not possible to discover that both initial preference and learning ability have been changed by any given factor.

General solutions of the analysis of variance in the case of unequal numbers of observations in the subclasses are presented. If we have k criteria for the classification, there will be k! solutions in making a complete analysis and 2k−1 answers, bearing different meanings, for the sum of squares between subclasses of each criterion. The sum of squares for the interaction of any order, however, will be identical in different solutions of same problem.

Results of 10 trials on 6 tests for 50 subjects were analyzed, first, by applying the centroid method to actual improvement or practice scores and, second, by applying a formula developed by Woodrow for determining factor loadings for practice scores from the differences between factor loadings of initial and final scores. Contrary to expectation, the two methods yielded discrepant results, for the explanation of which a hypothesis is advanced. The operation of a general factor was not demonstrated. Tentative interpretations of the factors extracted by the centroid method are offered.