Chapter 5 Probability Distributions 201
The Normal Probability Plot
To check for normality, statisticians compute normal scores for their data.
A normal score is the value you would expect if your sample came from a
standard normal distribution. As an example, for a sample size of 5, here are
the fi ve normal scores:
2 1.163, 2 0.495, 0, 0.495, 1.163
To interpret these numbers, think of generating sample after sample of
standard normal data, each sample consisting of fi ve observations. Now,
take the average of the smallest value in each sample, the second smallest
value, and so forth up to the average of the largest value in each sample.
Those averages are the normal scores. Here, we would expect the largest
value from a random sample of fi ve standard normal values to be 1.163 and
the smallest to be 2 1.163.
Once you’ve generated the appropriate normal scores, plot the largest
value in your data set against the largest normal score, the second largest
value against the second largest normal score, and so forth. This is called
a normal probability plot. If your data are normally distributed, the points
should fall close to a straight line.
StatPlus includes a command to calculate normal scores and create a
normal probability plot. Use it now to plot your random sample of normal
data.
To create a normal probability plot:
1 Click Single Variable Charts from the StatPlus menu and then click
Normal P-plots.
2 Click the Data Values button, click the Use Range References
option button, and select the range A1:A101 on your worksheet.
Click the OK button.
3 Click the Output button and type Normal P-plot in the As a New
Chart Sheet box to send the chart to a new chart sheet. Click the OK
button.
4 Click the OK button to start creating the normal probability plot.
Figure 5-15 shows the resulting plot (yours will look slightly different
because you’ve generated a different set of random values).
