Consider the different post hoc tests discussed in the readings and respond to t
ID: 3124844 • Letter: C
Question
Consider the different post hoc tests discussed in the readings and respond to the following:
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
When we get a significant F test result in an ANOVA test for a main effect of a factor with more than two levels, this tells us we can reject H0 i.e. the samples are not all from populations with the same mean. We can use post hoc tests to tell us which groups differ from the rest.
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There are many different post hoc tests, making different assumptions about equality of variance, group sizes etc.
tests are:
The simplest is the Bonferroni procedure.
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A common research model is to compare outcome measurements between multiple groups. If the data is parametric in nature, the Analysis of Variance is usually used. If the data is non parametric, procedures such as the Kruskall Wallis Analysis of Variance Using Ranks are used. The statistical conclusion after these analyses is whether the groups, taken together, are homogenous, or whether they differ significantly from each other.
After the initial analysis however, researchers often wish to know whether any two groups within the study are similar or different. 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, 5 of the more commonly used ones are presented in StatTools. These are explained in the following sections.
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Repeated t test is a lengthy process to identify difference between the means .
On the other hand ANOVA is really a good approach to conclude decision about difference in means for 3 or more variables. But it can not tells us which mean is bigger than another one. At that time we need post hoc test.
Hypothesis for the test is,
H0 : There is no difference between all pairs of means.
H1 : There is difference between all pairs of means.