Statistical Methods for Psychology

2.5 Describing Distributions

The distributions of scores illustrated in Figures 2.1 and 2.2 were more or less regularly

shaped distributions, rising to a maximum and then dropping away smoothly—although

even those figures were not completely symmetric. However not all distributions are

peaked in the center and fall off evenly to the sides (see the stem-and-leaf display in Figure

2.8), and it is important to understand the terms used to describe different distributions.

Consider the two distributions shown in Figure 2.10(a) and (b). These plots are of data that

were computer generated to come from populations with specific shapes. These plots, and

the other four in Figure 2.10, are based on samples of 1000 observations, and the slight ir-

regularities are just random variability. Both of the distributions in Figure 2.10(a) and (b)

are called symmetricbecause they have the same shape on both sides of the center.

The distribution shown in Figure 2.10(a) came from what we will later refer to as a nor-

mal distribution. The distribution in Figure 2.10(b) is referred to as bimodal,because it has

two peaks. The term bimodal is used to refer to any distribution that has two predominant

peaks, whether or not those peaks are of exactly the same height. If a distribution has only

one major peak, it is called unimodal.The term used to refer to the number of major peaks

in a distribution is modality.

Next consider Figure 2.10(c) and (d). These two distributions obviously are not symmetric.

The distribution in Figure 2.10(c) has a tail going out to the left, whereas that in Figure 2.10(d)

has a tail going out to the right. We say that the former is negatively skewedand the latter

positively skewed.(Hint: To help you remember which is which, notice that negatively

skewed distributions point to the negative, or small, numbers, and that positively skewed dis-

tributions point to the positive end of the scale.) There are statistical measures of the degree

of asymmetry, or skewness,but they are not commonly used in the social sciences.

An interesting real-life example of a positively skewed, and slightly bimodal, distribu-

tion is shown in Figure 2.11. These data were generated by Bradley (1963), who instructed

subjects to press a button as quickly as possible whenever a small light came on. Most of

Section 2.5 Describing Distributions 27

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Male Stem Female

Figure 2.9 Grades (in percent) for an actual course in experimental

methods, plotted separately by gender.

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bimodal

unimodal

modality

negatively
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positively
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skewness