Normal Probability Plots

Detecting normality from a histogram is a difficult job when data sets are not large. Here we view 4 large data sets and corresponding "normal probability plots." If we see how they relate when histograms are easily described (because of the large amounts of data) we can infer how they relate when histograms are not so easy to parse (because of small amounts of data).

Normal Probability Plots

The basic premise is that the plot compares the data with what would be expected of data that is perfectly normally distributed. Then two quantities are compared: The data and idealized normally distributed data. If the two generally agree that means the data agrees with what would be expected from a normal distribution. The normal probability plot is then linear. Otherwise, the plot will not be linear. Of course, no plot will be exactly linear, because data is subject to randomness in it's collection. We llok for a general pattern of linearity.

Data Sampled From a Normal Distribution

Here's a histogram of 100 observations that were randomly sampled from a normal distribution. Below the histogram you see the normal probability plot of the data (generated used the Normality Test in the Stat menu in Minitab for Windows.)

Notice that the normal probability plot (NPP) is basically straight. That's the idea: Normal data = straight NPP. So, when the NPP is straight you have evidence that the data is sampled from a normal distribution.

Data Sampled From a Left Skewed Distribution

For left skewed data, the normal probability plot is generally not straight. In general this sort of curvature in the NPP evinces left skew.

Data Sampled From a Right Skewed Distribution

For right skewed data, the normal probability plot is generally not straight. In general this sort of curvature in the NPP evinces right skew.

Data Sampled From a Bimodal Distribution

For bimodal (two distinct peaks) data, the normal probability plot is generally not straight. In general this sort of curvature evinces bimodality.

Want to see how this works in making conclusions about the normality of small samples?