Peter H. Schönemann
Professor Emeritus • Department of Psychological Sciences • Purdue University


Peter H. Schonemann

Power as a function of communality in factor analysis

Bulletin of the Psychonomic Society, 1981, 17, 57-60.


It was recently reported that the likelihood ratio test (LRT) in unrestricted factor analysis "has considerable power even when the sample size is only 10". Here it is shown that

(1) the power of this LRT depends on the communalities (h2),

(2) the average h2 in the simulation on which this conclusion was based far exceeds any found in French's review of 20 years of actor-analysitc work, and

(3) for more realistic h2, the power of the test barely exceeds the alpha level for N = 30 and remains poor for Ns as large as 100.

Prepublication History

The original paper this critique refers to is Geweke, J.F. and Singleton, K. J. Interpreting the likelihood ratio statistic in factor models when sample size is small. Journal of the American Statistical Association, 1980, 75, 133-137. Although the absurdity of the central claim in this paper, that the LRT "has considerable power even when the sample size is only 10", should have been transparent even to the most casual reviewer, the JASA editor steadfastly blocked its correction. The Note therefore had to be published in the BPS.

This goes to show that editors of statistical journals cook pretty much  with the same muddy water as their less illustrious colleagues in the social sciences. Other examples include the File Drawer Problem (briefly touched on in Schonemann, P. H. In praise of randomness. Behavioral and Brain Sciences, 1991, 14, 162-163),  Spearman Hypothesis, and Heritability indices.