Question

 

1) Why, how, and when is Anova robust?

2) Why, how, and is T-test robust?

Answer 1

1) The one-way ANOVA is considered a robust test against the normality assumption. This means that it tolerates violations to its normality assumption rather well. As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate. However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options

(1) transform your data using various algorithms so that the shape of your distributions become normally distributed

(2) choose the nonparametric Kruskal-Wallis H Test which does not require the assumption of normality.

There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated

(1) Welch or (2) Brown and Forsythe test. Alternatively, you could run a Kruskal-Wallis H Test.

Anova is robust in terms of the error rate when sample sizes are equal. However, when sample sizes are unequal, it is not robust to violation of homogeneity of variances.

2) t test is robust when distribution of sample depart from the normality. It is fairly well known that the t-test is robust to departures from a normal distribution, as long as the actual distribution is symmetric. That is, the test works more or less as advertised as long as the distribution is symmetric like a normal distribution, but it may not work as expected if the distribution is asymmetric.