© John Wiley & Sons, Inc.

FIGURE 9-4: Three distributions: leptokurtic (a), normal (b), and platykurtic (c).

A good way to compare the kurtosis of the distributions in Figure 9-4 is through the Pearson kurtosis

index. The Pearson kurtosis index is often represented by the Greek letter k (lowercase kappa), and is

calculated by averaging the fourth powers of the deviations of each point from the mean and scaling by

the SD. Its value can range from 1 to infinity and is equal to 3.0 for a normal distribution. The excess

kurtosis is the amount by which k exceeds (or falls short of) 3.

One way to think of kurtosis is to see the distribution as a body silhouette. If you think of a

typical distribution function curve as having a head (which is near the center), shoulders on

either side of the head, and tails out at the ends, the term kurtosis refers to whether the

distribution curve tends to have

A pointy head, fat tails, and no shoulders, which is called leptokurtic, and is shown in Figure 9-4a

(where

).

An appearance of being normally distributed, as shown in Figure 9-4b (where

).

Broad shoulders, small tails, and not much of a head, which is called platykurtic. This is shown in

Figure 9-4c (where

).

A very rough rule of thumb for large samples is that if k differs from 3 by more than

,

your data have abnormal kurtosis.

Structuring Numerical Summaries into

Descriptive Tables

Now you know how to calculate the basic summary statistics that convey the general idea of how a set

of numerical values is distributed. So which summary statistics do you report? Generally, you select a

few of the most useful summary statistics in summarizing your particular data set, and arrange them in a

concise way. Many biostatisticians choose to report N, mean, SD, median, minimum, and maximum,

and arrange them something like this: