Robustness of t-test and F-test

Abstract

The population phenomenon is studied through a model building of the sampled data. The population could be modelled by assuming some assumptions about population; such as independent observation, normally distributed. There is a situation when the assumptions could not be fitted then the model or analysis could give a different result. If the result is not greatly different from the theoretical one, then we could classify the model or analysis as robust. Two classical statistical analyses will be discussed in this paper, which is the t-test and F-test. The considered assumption in these analyses are independency of observation, normally distribution, and homogeneity of variance. Asymptotically the two methods are robust with regard to departure of the assumptions. Some effect of departures from the assumptions will be discussed as well. Some method to modify the analysis to make them more robust are also presented.