Question

Provide an example scenario for which you would use ANOVA and explain what the calculated F value tells us.

Answer 1

Suppose we decide to analyse the SAT scores of students from 4 different colleges appearing for the SAT exam.

Each college will have a different mean SAT score based on the students appearing for the SAT exam from the respective colleges.

Here, an ANOVA test is conducted on the sample scores collected from the 4 different colleges.

Here, this is a single factor ANOVA where the factor is the SAT score and 4 groups are the 4 colleges

F-value is calculated.

The F-value is the ratio of the variation between the sample means and the variation within the sample means

If the observations for each group are close to the group mean, the variance within the samples is low. However, if the observations for each group are further from the group mean, the variance within the samples is higher.

In general, an F-value is a ratio of two quantities that are expected to be roughly equal under the null hypothesis, The null hypothesis assumes that the means of all groups are equal.

If F-ratio is sufficiently large, we can conclude that not all means are equal

In case of our example, if F-ration is sufficiently large, we conclude that atleast one college has an average SAT score different from the other three.