For example, if the distribution of the paired differences is not symmetric , a transformation may produce symmetry. Some small violations may have little practical effect on the analysis, while other violations may render the paired t test result uselessly incorrect or uninterpretable. In particular, small sample sizes can increase vulnerability to assumption violations. A lack of independence within a sample is often caused by the existence of an implicit factor in the data. If the data are in a particular order, consider the possibility of dependence.
Outliers are anomalous values in the data.
Outliers tend to increase the estimate of sample variance, thus decreasing the calculated t statistic and lowering the chance of rejecting the null hypothesis . 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. The paired t statistic is based on the sample mean and the sample variance of the paired differences, both of which are sensitive to outliers . In particular, a large outlier can inflate the sample variance, decreasing the t statistic and thus perhaps eliminating a significant difference.