For example, measurements for females may follow a normal distribution, and measurements for males may also follow a normal distribution, but the measurements for the entire population of both males and females may not follow a normal distribution. Depending on the relative proportions of sampled data from each underlying normal distribution, and on the means and variances of each distribution, the composite mixture distribution may appear to be skewed , or to have nonnormal kurtosis , or both. Of course, an implicit factor may also separate the data into different nonnormal distributions. And if one or more of the subsamples has a small sample size , the test may fail to detect nonnormality due to a lack of power . Values may not be identically distributed because of the presence of outliers .
Outliers are anomalous values in the data.
They may be due to recording errors, which may be correctable, or they may be due to the sample not being entirely from the same population. Apparent outliers may also be due to the values being from the same but nonnormal , population. However, if there are only a small number of data points, nonnormality can be hard to detect with any of these methods. If there are a great many data points, the normality test may detect statistically significant but trivial departures from normality that may be of no practical importance. Moreover, with small samples, nonnormality is difficult to detect even when it is present.