An Introduction to Statistics in Linguistics (3) Percentages and Ratios

Abstract

Though percentages are widely used to express ratios of numerical data, occasionally, they are inappropriately used. This article summarizes the significance of percentages and important points to bear in mind when using them to express ratios. First, when using percentages in a breakdown of data, it is important to bear in mind that percentages compress information on the numbers of instances when the size of the dataset is greater than 100. Thus it is inappropriate to use percentages with very small datasets or to give more decimal places than precision warrants. When using ratios to compare data for different populations, it is important to be aware of what the ratios are for. Also, a difference in values expressed as a percentage should not be expressed by a percentage itself, but by percentage points. Finally, this article introduces units of ratios other than percentages, including per million words (PMW), which is widely used in corpus linguistics.