Statistical Methods for Psychology

symmetric, unimodal distribution, frequently referred to as “bell shaped,” and has limits of

6`. The abscissa,or horizontal axis, represents different possible values of X, while the

ordinate,or vertical axis, is referred to as the density and is related to (but not the same as)

the frequency or probability of occurrence of X. The concept of density is discussed in fur-

ther detail in the next chapter. (While superimposing a normal distribution, as we have just

done, helps in evaluating the shape of the distribution, there are better ways of judging

whether sample data are normally distributed. We will discuss Q-Q plots later in this chap-

ter, and you will see a relatively simple way of assessing normality.)

We often discuss the normal distribution by showing a generic kind of distribution with

Xon the abscissa and density on the ordinate. Such a distribution is shown in Figure 3.5.

The normal distribution has a long history. It was originally investigated by DeMoivre

(1667–1754), who was interested in its use to describe the results of games of chance

(gambling). The distribution was defined precisely by Pierre-Simon Laplace (1749–1827)

and put in its more usual form by Carl Friedrich Gauss (1777–1855), both of whom were

Section 3.1 The Normal Distribution 69

Behavior Problem Score

35.39.043.047.051.055.059.063.067.071.075.079.083.087.0

0

11.015.019.023.027.031.0

Std. Dev = 10.56

Mean = 49.1

N = 289.00

Frequency

30

20

10

0

Figure 3.3 Histogram showing distribution of total behavior problem scores

Behavior Problem Score

35.39.043.047.051.055.059.063.067.071.075.079.083.087.0

0

11.015.019.023.027.031.0

Std. Dev = 10.56

Mean = 49.1

N = 289.00

Frequency

30

20

10

0

Figure 3.4 A characteristic normal distribution representing the distribution of

behavior problem scores

abscissa

ordinate