Research, evaluation, analysis

Getting Your Percentage

Percentages are probably the most commonly used descriptive statistic today, so here are a couple of pointers for using them.

Like many others, I was trained not to use percentages if they were based on a sample of fewer than 100. So, for example, if 20 of 40 people were men, you were not supposed to say that 50% were men. There are some sensible reasons for this prohibition. One is that when you are talking about a small sample, a difference of one or two cases can produce a deceptively large difference in percentages. For example, 60% of women students may pass a test while only 40% of men students pass it. However, if only five men and five women took the test, this difference is less impressive than it appears at first glance.

Instead of reporting percentages of a sample of fewer than a hundred cases I often will give an approximate fraction "about a quarter" is often as accurate an estimate as 27%, say. Nevertheless, a percentage is sometimes the most convenient and accurate statistic even when the sample is smaller than a hundred cases; when it is I always report the size of the sample.

Percentages are often presented with one or even two decimal places. For example, if 501 of a sample of 1,000 people were men, the percentage might be given as 50.1%. I abstain from this practice chiefly because I believe it gives a false impression of accuracy. In the example the estimate of 50.1% has the same confidence interval as the percentage of 50% we would get by rounding. Both imply that there is a 99% chance that the percentage in the population is somewhere between 46% and 54%. I suppose whether or not you use decimal places could be considered a matter of taste (and occasionally of significant figures), but why add a decimal place or two when that doesn't improve the accuracy of your estimate?

Getting Your Percentage © 2000, John FitzGerald
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