On Cliff's Formula, the Kaiser-Guttman Rule, and the Number of Factors
| Autor: | Henry F. Kaiser |
|---|---|
| Rok vydání: | 1992 |
| Předmět: |
geography
geography.geographical_feature_category 05 social sciences 050401 social sciences methods 050109 social psychology Experimental and Cognitive Psychology Guttman scale Sensory Systems 0504 sociology Cronbach's alpha Decision matrix Principal component analysis Statistics Cliff 0501 psychology and cognitive sciences Reliability (statistics) Mathematics |
| Zdroj: | Perceptual and Motor Skills. 74:595-598 |
| ISSN: | 1558-688X 0031-5125 |
| DOI: | 10.2466/pms.1992.74.2.595 |
| Popis: | Cliff (1988) has presented a formula for the reliability of a principal component which is different from my long-known formula (Kaiser, 1957, 1991) for coefficient alpha of a principal component. Cliff claims that his approach is “correct” and mine “is the result of a misapplication of the formula for internal consistency reliability” Actually, both developments are correct but are based on different premises: Cliff considers measurement error within—but not between—attributes, while I consider measurement error between—but not within—attributes. The application of my formula to the knotty problem of the “number of factors”—the Kaiser-Guttman Rule—appears often to give the “right” result, when “right” means agreement with the subjective judgment of factor-analytic grandmasters. But when it fails it is approximately equally likely to overfactor as to underfactor. Cliff's formula, on the other hand, when used to establish the number of factors, almost invariably overfactors and, in the limit, as the within-attribute reliabilities all approach one (as with, say, physical attributes), nonsensically will declare all principal components perfectly reliable no matter how small their associated eigenvalues, yielding an absurd answer if used to establish the number of factors. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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