What does F-test in ANOVA analysis indicate? When do we use it?

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There are some hypothetical tests we use for statistical interpretations and F-test is one of those. F-test is one of the important tests which is using frequently in SPSS research.

According to the nature of F-test, this test is mainly related to or sensitive to non-normality. However, when do we use this test? If we assume that you have the mean of some means from several normally distributed populations with near standard deviations, then SPSS researchers use this F-test. The F-test is also for Analysis of Variance (ANOVA). On the other hand, it could be said that when a data set follows the nested linear model, we obviously use the F-test.

Now we can explain it mathematically. To do that we assume that there are two variances in a research where one is explained and another one is not explained. Then the formula for ANOVA F-test will be

F = (explained variance / unexplained variance)

On the other hand, for group, if there is more than one group, then we can illustrate the ANOVA F-test in the following way-

F = (between group variability / within group variability)

Addition information is that if there are only two groups for one way ANOVA F-test, the equation will be (in the below equation, t means the sample’s statistic),

F = t2

This F-test is made primarily by one of the greatest mathematician and statistician Sir Ronald A. Fisher in 1920. However, a number of people then worked with this test and this name F-test is given by another mathematician George Snedecor to respect the contribution of Sir Fisher.

However, as there are different types of tests like as f-test, t-test, z-test, you should learn all the tests because when you will be learned about all the tests, you will easily determine which of the tests will be for your SPSS research.

When you are doing an SPSS research and certain assumptions are met, you can use SPSS research methods’ Analysis of Variance (ANOVA) to compare the means of the groups. In SPSS research methods’ ANOVA is actually measured via F-test. In the F test, the total variation in the data is subdivided into variation that is due to differences among the groups and variation that is due to differences within the groups. The within-group variation is considered as the random error. While the among-group variation is due to differences from group to group. The null hypothesis in SPSS research methods ANOVA F-test states that there is no differences in the population means and this is tested against the alternative hypothesis that not all the population means are equal. If in the SPSS research output the corresponding F test statistic registered a p-value (Sig value) of 0.05 or less, one can conclude that there is enough evidence to say that not all the population means are equal.