Relating a Measurement Variable to Another Measurement Variable
In Chapters 12 and 13 we investigated the relationship between a measurement variable and a categorical variable. We took two approaches to this task. The first was to estimate population means for the measurement variable in each of the categories of the categorical variable and attach error ranges to those estimates. The second approach was to use either a two-sample t test (if only two categories were involved) or an analysis of variance (if more than two categories were involved). In Chapter 14 we investigated the relationship between two categorical variables. Once again we took two approaches. The first was to estimate population proportions for one of the variables in each of the categories of the other variable and attach error ranges to those estimates. The second approach was to use a chi-square test to evaluate significance and Cramer’s V to evaluate strength of association. There remains only to investigate the relationship between two measurement variables to complete all the possible combinations, and that is the subject of this chapter. We will see that one approach here is so powerful that we will not really consider alternative approaches.