Why is cross-tabulation an appropriate choice for analyzing two variables when both are nominal or ordinal measures but not when one or both are interval or ratio measures?
What will be an ideal response?
Cross-tabulation is the appropriate analysis technique when both variables are nominal- or ordinal-level measures. When the independent variable is nominal or ordinal and the dependent variable is interval or ratio, however, a contingency table would have far too many columns or rows for a straightforward and meaningful analysis. Moreover, a tabular analysis would not take advantage of the information packed in numerical scales. Therefore, other techniques are required. In this situation, we want to compare the means of a quantitative dependent variable (Y) between two or more categories of a categorical (nominal or ordinal) independent variable (X). Intuitively, this approach seems reasonable since a mean is one way to summarize a variable. If the means of various groups or subpopulations differ, then there is possibly a relationship worth exploring.
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