PROPHET StatGuide: Examples of normal probability plots

Normal probability plots can reveal:

Suspected outlier(s): For data sampled from a normal distribution, the X-Y values in the normality plot will lie along a hypothetical straight line passing through the main body of the X-Y values. If this is generally true, with a few points lying off that hypothetical line, those points are likely outliers, as with the smallest data value and, perhaps, the largest two data values in the hypothetical example shown here:

Skewness to the right: If both ends of the normality plot bend above a hypothetical straight line passing through the main body of the X-Y values of the probability plot, then the population distribution from which the data were sampled may be skewed to the right. Here is a hypothetical example of a normal probability plot for data sampled from a distribution that is skewed to the right:

Skewness to the left: If both ends of the normality plot bend below a hypothetical straight line passing through the main body of the X-Y values of the probability plot, then the population distribution from which the data were sampled may be skewed to the left. Here is a hypothetical example of a normal probability plot for data sampled from a distribution that is skewed to the left:

Light-tailedness: If the right (upper) end of the normality plot bends below a hypothetical straight line passing through the main body of the X-Y values of the probability plot, while the left (lower) end bends above that line (an S curve), then the population distribution from which the data were sampled may be light-tailed. Here is a hypothetical example of a normal probability plot for data sampled from a distribution that is light-tailed:

Heavy-tailedness: If the right (upper) end of the normality plot bends above a hypothetical straight line passing through the main body of the X-Y values of the probability plot, while the left (lower) end bends below it, then the population distribution from which the data were sampled may be heavy-tailed. Here is a hypothetical example of a normal probability plot for data sampled from a distribution that is heavy-tailed:

Mixtures of normal distributions: Data may be sampled from a mixture of normal distributions. Depending on the means and variances of the component normal distributions, and on the relative proportions of the data that come from each distribution, a mixture of normal distributions may produce a variety of normal probability plots.

Here is a hypothetical example of a normal probability plot for data sampled from a mixture of two normals with the same mean but different variances:

Such a mixture of normal distributions may be hard to distinguish from a symmetric, heavy-tailed distribution.

Here is a hypothetical example of a normal probability for data sampled from a mixture of two normals with the same variance but different means:

Such a mixture of normal distributions may be hard to distinguish from a light-tailed distribution.

Truncated normal distributions: The normal probability plot for data sampled from a truncated normal distribution will resemble one for data from a skewed distribution.

Here is a hypothetical example of a normal probability for data sampled from a normal distribution truncated at the left:

This may be hard to distinguish from a normal probability plot for a distribution skewed to the right.

Here is a hypothetical example of a normal probability plot for data sampled from a normal distribution truncated at the right:

This may be hard to distinguish from a normal probability plot for a distribution skewed to the left.

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Last modified: February 20, 1997

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