Kurtosis

Kurtosis is commonly thought of as a measure of the “pointyness” of a frequency distribution. This is because kurtosis is the degree to which scores cluster in the tails of a frequency distribution: A platykurtic distribution has many scores in the tails (often called a heavy-tailed distribution) and so is typically quite flat, whereas a leptokurtic distribution is relatively thin in the tails and so looks quite pointy. Figure 1 shows both leptokurtic and platykurtic distributions. The leptokurtic distribution is pointier than a normal distribution; conversely, the platykurtic distribution is flatter than a normal distribution.

Kurtosis is typically measured using a scale that is centered on zero (the value of kurtosis in a normal distribution). Negative values of kurtosis represent platykurtic distributions, and positive values indicate leptokurtic distributions. If a frequency distribution has positive or negative values of kurtosis, this tells you that this distribution deviates somewhat from a normal distribution.

Values of kurtosis have associated standard errors, and these can be used to convert the value of kurtosis to a z score using the standard equation for a z score,

The mean value of kurtosis in the population is zero, and so the equation reduces to

The utility of this conversion is that deviations from normality can be assessed using conventions that can be applied to any data set (regardless of the unit of [Page 523]measurement). For example, if the z associated with the value of kurtosis is greater than 1.96 (when the plus or minus sign is ignored), it is significant at p < .05; if it is above 2.58, then it is significant at p < .01; and if it is above 3.29, it is significant at p < .001. Although these criteria for “significant” deviations from normality can be useful, large samples will give rise to small standard errors; therefore, when sample sizes are big, significant values of kurtosis will arise from small deviations from normality. Field suggests that although these criteria can be applied to small samples, if the sample size is larger than about 200, it is more important to look at the shape of the distribution visually (using a histogram) and to look at the value of the kurtosis statistic rather than calculating its significance.

Figure 1 A Leptokurtic (top), Normal (middle), and Platykurtic (bottom) Distribution