Proportion vs Rate

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.

A rate answers how many per unit of something else, so unlike a proportion its numerator need not be part of its denominator and its value can exceed 1. For example, 84 emergency room visits in a town of 12,000 people over one year is $84 / 12000 = 0.007$ visits per person per year, normally reported as 7 visits per 1,000 people per year. Speed works the same way: 60 miles per hour is a rate, and no proportion could ever equal 60. Always state the base and the time window, because 7 per 1,000 per year and 7 per 1,000 per decade are very different claims.