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Measures of proportion are one of the most basic measures and, as such, are easy to calculate. Such measures include ratios, proportions, and percentages. Their purpose is "to describe the extent to which a single category within a variable characterizes the variable as a whole." (Wallace & Van Fleet, 2012, p. 292) They are meant to summarize data from nominal variables.
A ratio is simply one number divided by another. It can be expressed in several different ways:
The main thing to note is that the value of a ratio is independent of the overall size of the dataset it's calculated from. It's useful for identifying overall trends and comparing categories within a variable.
A proportion is a particular type of ratio where a part is divided by the whole. It is usually expressed as either a decimal (where its value falls somewhere between 0 and 1) or a phrase (e.g. "341 out of 500").
A percentage is merely a proportion multiplied by 100. Its utility is that it is more understandable to a wider range of people than the decimal form of a proportion.
You are replicating one of Mendel's genetic pea crosses. You have 556 peas, with 423 of them smooth and 133 of them wrinkled (pea type is a nominal variable).
The ratio of smooth peas to wrinkled peas would be calculated as 423/133 and could be represented as 3.18 to 1.
The proportion of smooth peas would be calculated as 423/556 and represented as 0.761.
The percentage of wrinkled peas would be calculated as (133/556) x 100 and represented as 23.9%.
The simplicity of these particular measures can be extremely problematic. The fact that they are so common and generally understandable to a layperson means they are also frequently abused. Care needs to be taken so that you don't misrepresent--deliberately or otherwise--your data when reporting these measures. How to Lie with Statistics by Darrell Huff remains one of the best primers on this topic. I encourage you to track down a copy; it's a relatively quick but illuminating read.