Count Data vs Proportion

Counts are non-negative whole numbers and they depend on how big the group is, which is why comparing raw counts across groups of different sizes misleads. For example, 45 walkers in a 300-student school is a larger share than 60 walkers in a 600-student school, since $45 / 300 = 0.15$ beats $60 / 600 = 0.10$. Converting each count to a proportion or a rate is the fix. Counts are also what chi-square procedures require, because the test compares observed counts to expected counts; entering percentages instead produces a meaningless statistic.

A proportion rescales a count so that groups of different sizes become comparable, and because it is a part of a whole it can never fall below 0 or rise above 1. In symbols $\hat{p} = x / n$, where $\hat{p}$ (p-hat) is the sample proportion, $x$ is the count in the category, and $n$ is the sample size; the population version is written $p$. For example, if 45 of 300 students walk to school then $\hat{p} = 45 / 300 = 0.15$, or 15 percent. Proportions carry no units, which is what separates them from rates such as 7 cases per 1,000 people per year.