We have said that we are comparing a continuous variable across categories. But what about the continuous variable are we measuring and comparing across the categories?

Most commonly, we wish to know if the average (mean) of the continuous variable differs across the categories. For this reason, we often call these techniques “comparison of means.”

Now, we have already looked into this question of whether a mean of a variable differs across groups. You will find such an analysis in Chapter 8, where we get descriptive statistics of a variable across categories. This chapter takes this analysis further, however, by testing whether any difference in means between categories is statistically significant, which is a question we did not ask previously.

For instance, in Chapter 8, we looked at whether Sales (the dependent variable in the main textbook example) differs significantly across License categories (Freeware vs Premium). We will now analyze these differences in averages by asking whether the difference is statistically significantly different from zero.

Other than the commonly-used mean, you can also compare other statistical features of the continuous dependent variable across categories, such as medians, spread (standard deviations), maxima and minima, etc. These techniques are mostly omitted from this book; the interested reader can reference intermediate and specialist texts.