e-Statistics

QQ plot

If the size n of sample data is small (n < 30), the t-test procedure requires that the data be approximately normally distributed; otherwise, the result of t-test may not be reliable. The quantile-quantile normal plot (QQ normal plot) is one of the graphical methods to assess the fit of the data to a normal distribution.

QQ normal plot. The values at the horizontal axis are from the sample data, and observed as sample quantile. The values at the vertical axis are given to the corresponding quantiles from the standard normal distribution. For example, the values between -1.0 and 1.0 at the vertical axis consist of approximately 68% of the entire values, which corresponds to the sample data between $ \mu-\sigma$ and $ \mu+\sigma$ (at the horizontal axis) if the empirical rule applies. Thus, the straightness of the QQ normal plot indicates the normal distribution as a reasonable fit.