Skewness

If a person says that there is a car parked ‘askew’ in a lined parking space, then we know the car is not parked straight and is closer to one side than the other. This common usage of the idea of skewness carries over into the statistical definition. If a statistical distribution is skewed, then more of the values appear in one end of the distribution than the other. Skewness, then, is a measure of the degree and direction of asymmetry in a distribution. Skewness is also called the third moment about the mean and is one of the two most common statistics used to describe the shape of a distribution (the other is kurtosis). Skewed distributions have values bunched at one end and values trailing off in the other direction. The most commonly used measure of skewness is the Pearson coefficient of skewness.

There are three types of skewness: right, left, or none. Often, these are referred to as positive, negative, or neutral skewness, respectively. Often, people are confused about what to call the skewness. The name of the type of skewness identifies the direction of the longer tail of a distribution, not the location of the [Page 975]larger group of values. If a distribution is negatively or left skewed, then there are values bunched at the positive or right end of the distribution, and the values at the negative or left end of the distribution have a longer tail. If a distribution is positively or right skewed, then there are values bunched at the negative or left end of the distribution, and the values at the positive or right end have a longer tail.

Figure 1 Negatively Skewed Distribution

Figure 2 Neutrally Skewed Distribution

Figure 3 Positively Skewed Distribution

The most commonly known distributions and their type of skewness are given in Table 1.

Often, skewness is used to help assess whether a distribution being studied meets the normality assumptions of most common parametric statistical tests. While the normal distribution has a skewness of 0, it is important to realize that, in practice, the skewness statistic for a sample from the population will not be exactly equal to 0. How far off can the statistic be from 0 and not violate the normality assumption? Provided the statistic is not grossly different from 0, then that decision is up to the researcher and his or her opinion of an acceptable difference. For most typically sized samples, values of the Pearson coefficient of skewness between −3and +3 are considered reasonably close to 0. To accurately measure the skewness of a distribution, sample sizes of several hundred may be needed.

If a researcher determines that the distribution is skewed, then reporting the median rather than or along with the mean provides more information about the central tendency of the data. The mean is sensitive to extreme values (those skewed), while the median is robust (not as sensitive).