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 distributions that do not all come from the same family. And if one of more of the subsamples has a small sample size , the test on the subsample may fail to detect a difference from the hypothesized distribution due to a lack of power . The chi-square statistic may be large due to 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. If you find outliers in your data that are not due to correctable errors, you may wish to consult a statistician as to how to proceed. If the total sample size small, or if there are many cells in the table, then it may happen that no observations are recorded for a particular cell. These zero values in a table are sampling zeroes . However, the actual process that creates the observations may produce cells in the table in which observations can never occur.