Measure of Association

A measure of association is a statistic that indicates how closely two variables appear to move up and down together or to have a pattern of values that observably differs from a random distribution of the observations on each variable. Measures of association fall into two main classes: parametric and nonparametric.

Two cautions precede the measurement of bivariate relationships. First, the sampling used before data collection begins has spatial and temporal limits beyond which it is dangerous to draw inferences (Olsen, 1993; Skinner, Holt, & Smith, 1989). Second, evidence of a strong association is not necessarily evidence of a causal relation between the two things indicated by the variables.

Three main types of association can be measured: CROSS-TABULATION, ordinal relationships, and CORRELATION. For cross-tabulations with categorical data, the available tests include the Phi, Kappa, and Cramér's V coefficients; the McNemar change test; and the Fisher and CHI-SQUARE TESTS. When one variable is ordinal and the other categorical, one may use the MEDIAN TEST, the Wilcoxon-Mann-Whitney test, or KOLMOGOROV-SMIRNOV TEST, among others. When both variables are continuous and normally distributed, PEARSON'S CORRELATION COEFFICIENT offers an indicator of how strongly one can infer an association from the sample to the population. If both variables are ordinal, Spearman's rank-order correlation coefficient or Kendall's TAUb (τb) may be used. Kendall's τb has the advantage of being comparable across several bivariate tests, even when the variables are measured on different types of ordinal scale.

OPERATIONALIZATION decisions affect the outcomes of tests of association. Decisions about technique may influence the choice of level of measurement. In addition, the nature of reality may affect how things can be measured (e.g., categorical, ordinal, interval, continuous, and continuous normally distributed levels of measurement).

It is crucial to choose the right test(s) from among the available nonparametric and parametric tests. Choosing a test is done in three steps: operationalize both variables, decide on a level of measurement for each variable, and choose the appropriate test (see Siegel & Castellan, 1988).

An example illustrates the ordinal measurement of attitudes that lie on a continuous underlying distribution. The example illustrates the use of the paired t statistic; a nonparametric statistic such as the Kolgomorov-Smirnov test for nonnormal distributions would be an acceptable alternative (see Table 1).

Among individuals of various social backgrounds, 154 were randomly sampled and asked how well they [Page 628]would hypothetically have liked a young woman (or a young man) to do a certain type of job or training. Their answers were coded on a 5-point Likert scale that was observed to have different shapes for different jobs. The t-test measures the association between each pair of Likert scales: preference for a young man doing that job versus preference for a young woman doing that job. The paired t-test is often used in repeated-measures situations.

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