Question

Describe a scenario where a researcher could use an F-test for the equality of two variances to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use? Please do not give answer with ANOVA scenario.

Answer 1

F-test for equality of variances is designed to test the null hypothesis that makes an assertion that two populations (assumed to have a normal distribution) have the same variance.

Suppose we are studying machines that manufacture tennis balls. In a city, there are two manufacturers of tennis balls A & B and it is desirable that the variance of the diameters of the balls is not too much for adherence to sports guidelines. A tennis coach wants to test whether the variance in the diameter of the tennis balls sold by the two manufacturers is the same.

To ascertain this the coach collects samples of 30 tennis balls from each manufacturer and records the diameters of the balls. The variables are defined as follows:

X denotes the diameter of the balls produced by the manufacturer A

Y denotes the diameter of the balls produced by the manufacturer B

An F-test can be administered in the given scenario to check if there is a significant difference in the variance of the diameters of the tennis balls produced by the two manufacturers. A significant difference will indicate that the variance in the diameter of the balls produced by the two manufacturers differ.

The F-test is the most appropriate test to use in this scenario because we want to compare the variance between two groups which are assumed to have a normal distribution.