Cross-Sectional Research

Measures of Association

There are many measures of association between pairs of variables (‘bivariate correlation’) that depend on the ways in which the variables are measured. The most widely recognized, the Pearson product-moment correlation coefficient (r), is used when both variables are continuous (either interval or ratio). Other correlation coefficients arise when the IV and DV are other types of scales (e.g., the phi coefficient is used when both variables are dichotomies) or combinations of scales (e.g., the point-biserial correlation is used when one variable is continuous and the other is a dichotomy). However, the textbook formulas for these coefficients are simply special cases of the Pearson r.

One important consideration in estimating the degree of association between two variables is whether the obtained correlation coefficient has been attenuated by unreliability in the variables or diminished by variance restriction. The maximum observed correlation [Page 207]between X1 and Y is limited by the reliabilities of the two variables. Thus, it is extremely important to measure variables as reliably as possible. This can be achieved by rationally constructing multi-item scales for both variables, pretesting these scales, conducting item analyses to refine the scales, and reporting the scales' reliability coefficients (e.g., Cronbach's α) in the study results. Variance restriction occurs when a floor or ceiling effect produces a skewed distribution of very low or very high scores, respectively. A very high proportion of low scores results when using an ability test that is too difficult or an attitude inventory whose items are too unpopular. By contrast, a very high proportion of high scores results from using an ability test that is too easy or an attitude inventory whose items are too popular.

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