Describe the basic purpose for the analysis of variance and

Describe the basic purpose for the analysis of variance and the general logic that underlies this statistical procedure. Explain when post hoc tests are necessary and the purpose they serve.

Solution

Describe the basic purpose for the analysis of variance and the general logic that underlies this statistical procedure

the purpose of analysis of variance (ANOVA) is to test for significant differences between means.

If we are only comparing two means, then ANOVA will give the same results as the t test for independent samples if we are comparing two different groups of cases or observations, or the t test for dependent samples if we are comparing two variables in one set of cases or observations.

Why the name analysis of variance? It may seem odd to you that a procedure that compares means is called analysis of variance.

The use of ANOVA depends on the research design. Commonly, researchers are using ANOVA in three ways: one-way ANOVA, two-way ANOVA, and N-way Multivariate ANOVA.

Explain when post hoc tests are necessary and the purpose they serve

The examination of differences between pairs of groups after the global analysis is post hoc analysis

It is important to realise that probability theory requires that the number of post hoc analyses be planned and according to good research reasoning, and not undertaken spuriously on a suck it and see basis.

There are many algorithms available to conduct post hoc analysis

post hoc analyses are usually concerned with finding patterns and/or relationships between subgroups of sampled populations that would otherwise remain undetected and undiscovered were a scientific community to rely strictly upon a priori statistical methods