Describe the general rationale behind using post hoc tests (i.e., when they are

Question

Describe the general rationale behind using post hoc tests (i.e., when they are used and why).

One of the advantages of using an ANOVA (compared to using t-tests) is also a disadvantage—using an ANOVA makes it necessary to use post hoc tests if there is a significant main effect. We use a post hoc test because there is one specific advantage in using an ANOVA. Explain why using an ANOVA naturally leads to the need to have post hoc tests (hint: consider what you are examining when you conduct a post hoc analysis).

Conducting a post hoc test is similar to conducting multiple t-tests. As a result, it would seem natural to want to bypass the ANOVA and just use repeated t-tests. Explain why this approach is not necessarily a good idea and why an ANOVA followed by a post hoc analysis is beneficial.

Describe an experimental hypothesis and explain which post hoc test you would use if you find a significant overall effect. Include in your explanation the pros and cons of each test in making your decision.

Explanation / Answer

Answer:

We know that the ANOVA is nothing but the generalization of the t-tests. We use the t-tests for checking the significant difference between the two population means. We use two samples for conduction of t tests, but sometimes if there are more than two samples, we need to perform two sample t tests multiple or several times. Suppose, there are n number of samples, then we need to perform C(n,2) times t tests. So for avoid these multiple tests, technique of ANOVA is used for checking the significant difference between more than two population means. By using ANOVA test, main benefit is to check whether all population means are equal or not. But when we want to check pairwise comparison, then ANOVA do not help us. In this case, we need to perform post hoc tests. Also, if we want to check whether which treatment or sample is statistically significant, then ANOVA do not help us for finding significant treatment. This is the drawback of ANOVA technique. In this case, we need to use different types of post hoc tests. The use of post hoc tests is similar to use multiple t tests for pairwise significance of the population means. Although ANOVA is an easy technique, we do not compare the pairwise differences in the population means. The technique of ANOVA is works for entire significance for overall comparison and it fails to compare pairwise differences. The conduction of t tests is also easy but for more samples it will becomes very lengthy work. Now a day, due to availability of statistical software’s, we can easily conduct several tests.

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