How to Interpret a Normal Probability Plot

Normal probability plots plot the quantiles of your data against the quantiles of an ideal normal distribution. The mean and variance of your data is used to derive this ideal normal distribution's quantiles. The main idea of interpreting a normal probability plot is to check your data for normality (i.e. that your data is normally distributed).

Instructions

    • 1

      Check the curvature of the data. If you are lucky, your data should either appear as a straight line or a curve. If your data appears as a straight line all the way through (including the bottom-left and upper-right sides) then your data is normally distributed and you do not need to analyze the plot any further. You can then state that a normal probability plot has given strong evidence to the normality of your data. If your data is curved continue the analysis.

    • 2

      Check the curve's direction. If your data rises sharply at first and then curves downward toward the right of the plot, then your data has a left-skewed normal distribution. If the data rises slowly at the beginning and then curves up sharply at the right of the plot, then your data is right-skewed. If the curve does not follow either of these patterns, then continue the analysis.

    • 3

      Check the curve's overall shape. If the curve is shaped as an "S," then your data is shaped as a short-tailed normal distribution. That is, your data follows a normal distribution but has less variance. If your curve is shaped as an "S" turned on its side, then your data is a long-tailed normal distribution or a t-distribution. If your data's sample size is small, then you can likely interpret your data as being t-distributed.

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