Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.


When comparing means of two independent samples one often encounters the situation of unequal variances, thus preventing the standard two-sample t test from being applicable. However, in the case the samples are from normally distributed populations, an adapted t-test can be applied. The adaption is based on the adjustment of the test statistic and the adjustment of the number of degrees of freedom. Please note that the Welch test is an approximate solution, since the problem of unequal variances cannot be solved exactly.

In order to apply the Welch test you have to carry out the following steps:

Hint: Some statistical programs don't round down the number of degrees of freedom df but use the exact value of the formula above. This may result in slight differences between the statistical programs.

Last Update: 2012-10-08