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 signed rank 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.
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 skewed or heavy-tailed population. Outliers may lead to an incorrect conclusion that the distribution of the paired differences is skewed. Because the statistic for the signed rank test is resistant , it will not be substantially affected by the presence of outliers unless the number of outliers becomes large relative to the sample size. 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.