Some Empirical Results Concerning the Power of Bartlett’s Test of the Significance of a Correlation Matrix
Bibliographic Data
| ID | 8223597 |
|---|---|
| Authors | Thomas R Knapp (University of Rochester, corresponding author), Vincent H Swoyer (University of Rochester) |
| Year | 1967 |
| Volume | 4 |
| Issue | 1 |
| Pages | 13-17 |
| Publication date | 1967-01-01 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | American Educational Research Journal (JOURNAL) |
| Journal identifiers | ISSN: 0002-8312 • E-ISSN: 1935-1011 |
| Publisher | American Educational Research Association (AERA) (PUBLISHER) |
| DOI | 10.3102/00028312004001013 |
| OpenAlex | W1979669257 |
| Language | EN |
| Citations received | 16 |
| References cited | 2 |
Before carrying out a factor analysis of sample data, the investigator should check the sample correlation matrix to see if it is significantly different from the identity matrix, i.e. to test whether or not the off-diagonal correlation coefficients are chance differences from zero. Fortunately an appropriate test exists in the literature, and is due to Bartlett (1950). It can also be found in multivariate texts by Anderson (1958) and Kendall (1957), and has been recommended for use by psychologists in an article by Maxwell (1959). To test the significance of a sample correlation matrix, one computes the expression-[ (N-l) /6 (2p + 5)1] log e RI, where N is the sample size, p is the number of variables, and JIR is the determinant of the sample correlation matrix. This quantity is distributed approximately as x2 with /2 p (p-1) degrees of freedom. If the obtained value of x2 is significant at some appropriate level the investigator should feel reasonably confident in proceeding with the factor analysis. If x2 is not significant, a factor analysis of the correlation matrix should not be attempted, since much or all of the factor structure would be sampling error. Unfortunately this test has rarely, if ever, actually been carried out by factor analysts, or at any rate has not been reported in their research articles. But the purpose of this paper is not to goad factor analysts into using a significance check prior to carrying out their analyses. There are properties of this test which bear investigation. For example, Kendall (1957, p. 96) states: Little is known of the power of such a test, but an intuitive judgment would suggest that its power is reasonably high against normally correlated alternatives. The following discussion is devoted to some considerations of the power of this test
Correlation · Covariance matrix · Econometrics · Empirical research · Matrix (chemical analysis · Physics · Power (physics · Statistics · Test (biology · Advanced Statistical Methods and Models · Advanced Statistical Modeling Techniques · Mathematics · Psychology · Sensory Analysis and Statistical Methods
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| Citations per year | 0.28 |
|---|---|
| Citation span | 1969 - 2026 (58) |
| Highly cited | No |