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. If you are unsure whether your samples are independent, you may wish to consult a statistician or someone who is knowledgeable about the data collection scheme you are using. 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 skewed or heavy-tailed population. Outliers tend to increase the estimate of sample variation, and might lead to an incorrect conclusion that the dispersions or variances of the samples are not equal if the outlier is the result of a recording or measurement error. Because the statistic for the Kruskal-Wallis 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.