Note on Measures of Association
| Autor: | A. J. Magoon, Victor R. Martuza |
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| Rok vydání: | 1972 |
| Předmět: | |
| Zdroj: | Psychological Reports. 30:920-922 |
| ISSN: | 1558-691X 0033-2941 |
| Popis: | Summary.-Glass and Hakstian (1969) recently presented a very convincing argument against the indiscriminate use of several proposed "measures of association." The emphasis in this note is on where and when these indices would be appropriate, an issue not clearly delineated by the earlier critics. An example is included, and an extension made to multivariate applications. Glass and Hakstian (1969) recently presented a very convincing argument against the indiscriminate use of several proposed "measures of statistical association," e.g., Kelley's e%nd Hays' 2, in fixed-effects analysis of variance designs. They argue that, in most fixed-effects experiments, the independent variable is "a conglomerate of treatments (e.g., instructional methods) with no conceptually meaningful or practically important characteristic in common" (p. 408). The factorial and conceptual complexity of a variable so defined makes it virtually impossible to select a random sample of treatment levels for inclusion in an experiment. As a result, the researcher typically selects, quite arbitrarily, the levels of the "independent variable" to be included in the experiment Since measures of association like these tend to encourage many to make inferences concerning the rela tionship between the "independent variable" and the dependent variable, their use is potentially misleading and, hence, ought to be avoided. They offer the analogy that "the calculation of either coefficient [Kelley's E~ or Hays' wZ] for a fixed-effects factor in an experiment is like calculating rz, on a selected, unrepresentative sample of cases" (p. 411). The argument is a sound one. Indeed, the indiscriminate use of indices like E~ and w2 can be quite misleading. This does not mean that indices like these are totally without value: the principal problem is not with the index, but how it is used. An example is presented at this point to illustrate one instance where such an index seems quite appropriate. Suppose the officials of a particular school district want to evaluate the relative effectiveness of several "instructional methods" in facilitating student achievement in, say, science. Although it may be argued that there are an infinite number of levels of "instructional methods," it is frequently the case that only a very small number of such methods (e.g., lab, lecture) is of interest to the officials in that district because of the practical constraints within which they operate (e.g., the amount of money available, the number of teachers). In such a case, the sweral welldefined teaching methods to be compared completely define the population of levels of the "independent variable" for that school district at that time. If all of these levels are included in the experiment, then a descriptive measure of association between the independent and dependent variables seems justified. This is not too different from calculating r,, for a restricted set of population |
| Databáze: | OpenAIRE |
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