Q-Q plot

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In statistics, a Q-Q plot ("Q" stands for quantile) is a tool for diagnosing differences in distributions (such as non-normality) of a population from which a random sample has been taken. One plots the k/(n + 1)-quantiles of the comparison distributon (i.e. the normal distribution) on the horizontal axis (for k = 1, ..., n), and the order statistics of the sample on the vertical axis. For a sample from the comparison distribution this approximates a straight line, especially near the center. In case of substantial deviations from that appearance, the statistician rejects the null hypothesis of sameness.

Q-Q plots are similar to rankit plots, also called normal probability plots. The difference is that in normal probability plots, instead of the k/(n + 1)-quantile of the normal distribution, one plots the expected value of the kth order statistic from a normal distribution with expectation 0 and variance 1. Only when n is small is there a substantial difference between a Q-Q plot and a normal probability plot.

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