Research, evaluation, analysis

The Truth about Skew

A statistical term which has recently become what H. W. Fowler called a popularized technicality is skew. Its popular meaning, though, like the meaning of many popularized technicalities, is often different from its technical one.

Skewed is often used as a synonym of distorted or misinterpreted. However, that is not what the term means in data analysis. The original meaning of the term was oblique, and it was adopted in statistics to describe a distribution which had an oblique lean to it (a distribution is simply an ordered list of the number of cases in a sample with each value observed). Distributions of this type are sometimes found in satisfaction surveys when satisfaction is high. For example, you can see the distribution of responses to a satisfaction item administered in a survey conducted by one of my clients by clicking here (use your BACK button to return to this page).

There appears to be a tilt to the distribution in the graph. However, statisticians distrust visual analysis (as they should) and instead use mathematical formulas to define skew. The formulas determine the probability of the tilt in a distribution arising by accident.

A defining characteristic of a skewed distribution is that the mean and the median values will be different. The mean of a distribution of values or scores is more commonly known as the arithmetic average that is, it is equal to the sum of the scores divided by the number of cases. The median is the value or score below which 50% of the values or scores fall.

If a distribution is skewed, you usually are better off not to use the mean as an estimate of the average score. Averages estimate the central point of a distribution. Since the median is the central point, the mean will be inaccurate if it is different from the median. If you want to use a mean (there are often good technical reasons for wanting to), you can transform your data as described in the article on data makeovers.

The Truth About Skew © 2000, John FitzGerald
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