we never really questioned why we based all of our inferential statistics on proportions. The reason is that we don't have any better descriptive statistics for binary variables than the proportion. When working with binary variables, the statistics we can use to describe our data are limited to measures of frequency. In theory, we could have chosen the mode instead of the proportion, but the mode doesn't tell us as much about the frequency distribution. The frequency distribution of a binary variable has only two values, and the mode only tells us which value has the higher frequency. In contrast, the proportion tells us the relative frequency of the two values. Indeed, the proportion tells us almost everything we could possibly want to know about the frequency distribution of a binary variable. Knowing only the proportion, we could draw a bar chart for the data, because we would know the relative heights of the two bars. We wouldn't know the absolute height of the bars without knowing the sample size, but we would know everything else about the shape of the frequency distribution. The proportion does a very good job describing the entirety of our data in a single descriptive statistic. In contrast, the mean does a very bad job describing the entirety of our data in a single descriptive statistic. Knowing just the mean, we couldn't possibly draw a histogram of our data. We based all of our inferential statistics in Modules 7 and 8 on the mean, and this is by far the most