Experiment!: Planning, Implementing and Interpreting

7.6 Normal Probability Plots

It can be difficult to see if data are normally distributed in a histogram, especially if the sample is small. Normal probability plots, or normal plots for short, are complementary graphical tools that can be used for this purpose. Apart from checking the normality of the data they can also point to individual values that do not originate from a normal distribution. This is why they will be important when we introduce experimental design in Chapter 9. In experimental data, some part of the variation is due to measurement error and some part to our deliberate experimentation. We hope that at least some effects of the experiment are greater than the measurement noise. Such effects do not follow the normal distribution of the error and normal plots can thereby be used to detect them.

In normal plots the data are essentially plotted against a theoretical normal distribution. If the data are normally distributed they will plot on an approximately straight line. Figure 7.10 shows such an example. The x-axis represents the data in the sample, roughly scattered between zero and 35 with most values in the middle of this interval. The y-axis represents the cumulative probabilities of a theoretical normal distribution. To aid the eye, the figure also contains a straight line drawn through the upper and lower quartiles. Figure 7.11 shows a normal plot of a right-skewed sample. Recall that the distribution of such a sample has a tail extending to the right. Since ...