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The answer to questions two and three helps you to decide whether to use a parametric test or its or nonparametric equivalent. Analysis of Variance, the t test, and the correlation coefficient called Pearson’s r are all parametric tests. Parametric tests are more powerful but make more assumptions about the data than do their nonparametric equivalents. (See Chapter 12 of the book for a discussion of power in this context.)
You should definitely consider using a parametric test if the answer to question two is interval, and the answer to question three is yes. The principal assumptions of parametric tests are that (a) the scores in the populations from which your data have been sampled are normally distributed, (b) the variances in these populations are reasonably similar, and (c) the data have been measured on a scale that is at least interval. It is also important that you do not have extreme scores - that is, scores that are exerting a disproportionate effect on the mean.
All of this sounds like a lot, but parametric tests can cope with some violations of these assumptions without going haywire. For instance, in your reading you will come across many studies in which data from rating scales (such as a 7-point scale) have been analysed using parametric tests such as ANOVA. Yet such data are strictly speaking ordinal rather than interval. However the general assumption is that the outcome of such analyses is sensible, despite this violation of one of the assumptions of parametric tests. So, do not automatically reject the use of a parametric test when you have ordinal data. It is worth using parametric tests for their added power (Chapter 12). Get into the habit of exploring your data (see Section 13.9.5 of the book) prior to analysis and checking whether they meet the parametric assumptions reasonably well. Remember, the bottom line is that your analysis must provide you with a meaningful answer to the question you ask. So, do not be afraid to use parametric tests when it is likely that the outcome will be meaningful. |
