Question

Robust What does it mean when we say that the F test described in this section is not robust against departures from normality?

Short answer

The given statement means that the F test will not give the desired and accurate results if the populations from which the samples are extracted are not normally distributed, irrespective of the sample size.

Step-by-step solution

Given information

It is given that the F test is not robust against departures from normality.

Interpretation of the F-test not being robust

In statistics, robust means that a statistic works well for the given hypothesis test and produces a correct conclusion.

If the distribution of the test statistic is robust against departure from normality, it implies that the distribution is not very strict about the requirement of the population to be normally distributed and will produce accurate results even if the population is not normally distributed.

If the distribution of the test statistic is not robust against departure from normality, the distribution is very strict about the requirement of the population to be normally distributed and will not work well if the population is not normally distributed.

Therefore, the F test is not robust against departure from normality and will not give accurate results if the populations from which the samples are extracted are not normally distributed, irrespective of the sample size.