Question

Explain in words and equations , how the ANOVA F test and t test are essentially the same. Show how MSwithin equivalent to SEM, and MSbetween equivalent to mean differences?

Answer 1

The basis of the f-test is F-statisticfollows Snedecor f-distribution, under the null hypothesis. The t-test is used to compare the means of two populations. In contrast, f-test is used to compare two population variances.

The difference between t-test and f-test can be drawn clearly on the following grounds:

1. A univariate hypothesis test that is applied when the standard deviation is not known and the sample size is small is t-test. On the other hand, a statistical test, which determines the equality of the variances of the two normal datasets, is known as f-test.
2. The t-test is based on T-statistic follows Student t-distribution, under the null hypothesis. Conversely, the basis of the f-test is F-statistic follows Snedecor f-distribution, under the null hypothesis.
3. The t-test is used to compare the means of two populations. In contrast, f-test is used to compare two population variances.