Statistical Methods for Psychology

82 Chapter 3 The Normal Distribution

a. Then create a Q-Q plot for each variable and notice the differences from one plot to the

next. That will give you some idea of how closely even normally distributed data will

conform to the 45 degree line. How would you characterize the differences?

b. Repeat this exercise using n 5 50.

3.21 In Chapter 2, Figure 2.15, I plotted three histograms corresponding to three different de-

pendent variables in Everitt’s example of therapy for anorexia. Those data are available at

http://www.uvm.edu/~dhowell/methods7/datafiles/fig2–15.dat. (The variable names are in the

first line of the file.) Prepare Q-Q plots for corresponding to each of the plots in Figure 2.15.

Do the conclusions you would draw from that figure agree with the conclusions that you

would draw from the Q-Q plots? (Note: None of these three distributions would fail the

Kolmogorov-Smirnov test for normality, though no test of normality is very good with small

sample sizes.)

Discussion Questions

3.22 If you go back to the reaction time data presented as a frequency distribution in Table 2.2

and Figure 2.1, you will see that they are not normally distributed. For these data the mean

is 60.26 and the standard deviation is 13.01. By simple counting, you can calculate exactly

what percentage of the sample lies above or below 6 1.0, 1.5, 2.0, 2.5, and 3.0 standard de-

viations from the mean. You can also calculate, from tables of the normal distribution, what

percentage of scores would lie above or below those cutoffs if the distribution were per-

fectly normal. Calculate these values and plot them against each other. (You have just cre-

ated a partial Q-Q plot.) Using either this plot or a complete Q-Q plot describe what it tells

you about how the data depart from a normal distribution. How would your answers change

if the sample had been very much larger or very much smaller?

3.23 The data plotted below represent the distribution of salaries paid to new full-time assistant

professors in U.S. doctoral departments of psychology in 1999–2000. The data are available

on the Web site as Ex3–23.dat. Although the data are obviously skewed to the right, what

would you expect to happen if you treated these data as if they were normally distributed?

What explanation could you hypothesize to account for the extreme values?

300

200

100

0

Salary

35000.0 45000.0 55000.0 65000.0 75000.0 85000.0 95000.0 105000.0

Frequency

Cases weighted by FREQ

Std. Dev = 5820.93

Mean = 45209.7

N = 589.00

Salaries of Assistant Professors

(1–3 years of service)