In assessing the normality assumption we have resorted to box plots and histograms of the data an some hand waving about what appears, and what does not appear, to agree with the assumption of normality. Another graphical display of the data that deals directly with the assumption of normality is the Normal Probability Plot. The basic idea behind a normal probability plot is to plot the data against some reference that depicts a normal distribution. This reference consists of the expected ordered values from a normal distribution. Many statistical software packages create normal probability plots. Not every statistical software package creates normal probability plots in the same way. Some use a probability or percentage scale while others use a normal score scale for the vertical axis. Some put the data on the vertical axis and the normal scale on the horizontal axis. Regardless of how the plot is created, the basic interpretation is the same. If the data correspond to the straight line representing the reference normal distribution then the assumption that the data could have come from a normal distribution is validated. Some normal probability plots include bounds that depict the natural variability one could see in data even when it comes from a normal distribution. If the data depart from the straight line representing the normal distribution (and especially if data fall outside the bounds of natural variability), then the assumption of normality is called into question. Below are some examples of normal probability plots produced by the statistical analysis program, Minitab.

• Data from a normal distribution. Note that the data fall close to the line representing a normal distribution but not exactly on it. All the data do fall within the bounds of natural variability.
   

• Data from a skewed distribution. Note that the data at first rise more sharply than the line representing a normal distribution and then tend to curve off. Many of the data points fall outside the bounds.
   

• Data from a heavy tailed distribution. Note that the data seem to be more clumped in the middle but with a few unusual values in the extremes.
   

• Data from a uniform distribution. Note that the data seem to agree with the line representing a normal distribution. In fact, these data look "more normal" than data generated from a normal distribution.
   

The normal probability plot is another tool for graphically displaying data and assessing the appropriateness of the normality assumption. It is not perfect. Sometimes normal data appear non-normal and non-normal data appear normal. No statistical method is perfect. However, the more data you have the less likely you are going to make a mistake when assessing the appropriateness of the normality assumption. But the more data you have the less important the normality assumption becomes. So it goes ...