Friday, September 23, 2011

Student's t-Test, Normality, and the Bootstrap

Is Student's t-statistic still t-distributed if the data are non-normal? I addressed this question - in fact, an even more general question - in an earlier post titled "Being Normal is Optional!". There, I noted that the null distribution of any test statistic that is scale-invariant, will be the same if the data come from the elliptically symmetric family distributions, as if they come from the normal distribution.