Exam 19: Choosing the Right Statistics

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Scales of measurement were first presented in Chapter 1 and reappear repeatedly throughout the book. The distinction between numerical scores (ratio or interval scales) and other scales is most important, although students should also be able to recognize ordinal data because special statistics exist for this kind of data.

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It is unlikely that students will memorize the complete set of statistical techniques.However, they should be able to use the resources in Chapter 19, particularly the flow charts in Figures 19.1, 19.2, and 19.3, to locate the appropriate statistical procedure.In other words, we view Chapter 19 as a review reference/resource rather than a typical chapter that presents "new" material to be learned.

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The first category corresponds to descriptive research, for which the purpose is usually to describe a group of participants or the larger population that they represent. For numerical scores, this typically involves computing the mean and standard deviation. For scores from other measurement scales, the description usually consists of the proportion or percentage of individuals in each category on the scale of measurement.
The second category corresponds to correlational research, for which the goal is usually to describe and evaluate the relationship between variables, specifically to describe the relationship between pairs of variables. For numerical scores, this usually involves computing the Pearson correlation and then evaluating the significance of the correlation. For non-numerical scores, alternative correlations (Spearman, point-biserial, or phi coefficient) can be used to describe the relationship and a chi-square test for independence is often used to evaluate the significance of the relationship.
The third category corresponds to experimental and non-experimental research, for which the goal is usually to describe and evaluate the differences between groups. For numerical scores, this typically involves computing means and standard deviations to describe each group of scores and then using a t test or analysis of variance to evaluate the significance of the mean differences. For non-numerical scores, the differences are often described by comparing the proportions or the ranks from one group to another and the significance of the differences is established with a chi-square test for independence.
If the scores are ranks (or can be ranked), then there are special tests presented in Appendix E that can be used to evaluate the significance of the differences between groups.