Question

In an experiment where data from only two rat species are compared, is there any advantage to using a t-test or an ANOVA? Is there a scenario where you may have an advantage using one test over the other?

Answer 1

In an experiment where there are only two samples, we may use any of the two tests - independent samples t-test or an ANOVA because the probability of a type-I error is 0.05 in both cases. There is an advantage in using ANOVA over multiple t-tests when comparing the population mean of more than two samples. This is because if we have three samples and we apply three pairwise comparisons using t-tests, the probability of a type-I error is higher than 0.05 as below:

P(atleast one Type-I error) = 1 - (No type-I error)³ = 1 - 0.95³ = 0.142625

As we can see, the probability of a type-I error in performing multiple t-tests are 0.142625 but if we run ANOVA, the error rate of Type-I error is controlled to 0.05 thus making us more confident about the significance of the statistical tests.