Frances Swineford

The Bi-factor method

The Bi-factor Method of factor analysis is described and illustrated with a small group of fourteen tests. A detailed illustration is given of how the method may be modified to the case of overlapping group factors. It is advocated that the Bi-factor pattern in unmodified form be used to determine the adequacy of tests for the measurement of unitary traits.

Some comparisons of the multiple-factor and the bi-factor methods of analysis

Bi-factor and multiple-factor analyses of the same data are compared in two respects. First, two criteria are suggested for determining when the factorization is adequate. This problem being more acute for the centroid method than for the bi-factor method, the latter is used primarily for comparison only. It is shown also that the omission from the simple structure of entries smaller than .10 yields a pattern which is a poorer fit to the original correlations than is the bi-factor pattern. Second, the second-order general factor obtained from the intercorrelations of the primaries is found to be highly correlated with the general factor of the bi-factor pattern.

Selected References on Statistics, the Theory of Test Construction, and Factor Analysis

THE following bibliography, with a few exceptions, has been selected from issues of educational and psychological journals from March, 1943, to January, 1944, inclusive. Sharp distinctions do not exist between the fields covered in this list, but, as an assistance to the student with special interests in one or more of the fields, the references have been classified under the following categories: theory and use of statistical methods, problems of test construction, and factor analysis. No articles dealing primarily with the use of tests have been included because these items are distributed functionally in other lists in the cycle, such as those dealing with secondary-school instruction, guidance, etc.

Selected References on Statistics and the Theory of Test Construction

The following bibliography has been selected from issues of educational and psychological journals for March, 1934, to February, 193 5, inclusive. The first part contains items dealing with the theory and use of statistical methods, while the second part includes studies and discussions of problems of test construction. No articles on the use of tests have been included in the present list, since these items are distributed functionally to other lists in the cycle, for example, the lists concerned with secondary-school instruction, educational psychology, and guidance published in other issues of the School Review and the lists concerned with elementary-school instruction and exceptional children published in the Elementary School Journal.

A table for estimating the significance of the difference between correlated percentages.

A table to aid in testing the statistical significance of the difference between correlated percentages is presented. Percentage points which range from .10 to .001 are included.

Graphical and tabular aids for determining sample size when planning experiments which involve comparisons of percentages.

When one knows in advance the minimum percentage difference which will be of practical interest in an investigation, principles of economy suggest the desirability of an accurate estimate of the size of the sample to be used. Charts are presented which eliminate any computation where the two groups involved are to be equal. A table is included for the case where one group will be from one to three times the size of the other. The charts are also useful for determining whether or not obtained differences are statistically significant at the 5 per cent or the 1 per cent level.

FELLOWSHIP RECORD EXAMINATION

This summary contains data from validity studies conducted between October ′46 and July ′49. It is planned that additional supplements will be compiled from time to time in the future. In this connection, suggestions are invited for improving the organization of the material, as are requests for additional information to be included in subsequent summaries.

Further notes on differences between percentages.

In certain problems dealing with percentage differences, it frequently happens that one is interested in a critical value different from zero rather than in the usual hypothesis of no population difference. Moreover, one may be concerned with differences greater than (or less than) a given magnitude, so that only one tail of the distribution of chance values is used. Tables are here presented to facilitate evaluating results of such problems. One per cent and 5 per cent values can be read from the tables, such values corresponding to the more usual 2 per cent and 10 per cent confidence limits.

Factor Analysis in Educational and Vocational Guidance

THE statistical energies of educational and vocational psychologists are currently centered in the field of factor analysis. The procedure is to administer a set of twenty or more tests to at least a hundred individuals, compute the intercorrelations, and eventually arrive at a factor pattern. A factor pattern consists of a set of regression equations, each expressing one of the original tests in terms of usually five or six factors. In case a method has been employed which yields independent (uncorrelated) factors, the regression weights are equivalent to the correlations between the corresponding tests and factors.