Question

1. What are the differences between planned contrasts (or planned comparisons) and post hoc tests? Why are they used after performing a one-way ANOVA? How do you decide which to use of the two types of follow-up tests?

2. What are the main differences between between- and within-groups one-way ANOVAs? What determines which type of test should be used? Which is a stronger test and why?

Answer 1

1) Planned contrasts tests can be pre-defiened. post hoc tests are done after completing the experiment.

Here are some differences between Planned contrasts and Post hoc Analysis.

Difference between planned contrast and Post hoc tests

Planned Contrast Post hoc Analysis 1 This method is used for further comparison of means for different levels when results are may or may not be significant in first analysis. Here we can do all comparison of k - 1 levels. This method is used for further comparison of means for different levels when results are significant in first analysis. Here we can do all comparison of pairs. 2 Here in earlier stage, one can decide which comparisons need to be done. Here number of comparisons are decided after results of analysis significant.

In one way ANOVA, we do compare if three or more means are equal or not. This method tests if a given variable differes significantly in three or more levels of factors.

In ANOVA first we see significance of all levels of factors. Planned contrasts and post hoc analysis are used after one way ANOVA because we need to compare specific possible combinations of mean pairs. To see which means are differ with each other and which means are at same level.

In one way ANOVA Planned contrasts use linear comparisons of the differences between pairs of means. With help of contrast we can compare two means at a time. For the planned contrast of ANOVA , we can do total k -1 test of comparions. so for example, in one way ANOVA with 4 levels there can ne k -1 = 4-1 =3 contrasts are possible. mostly orthogonal contrast is used.

In one way ANOVA, post hoc analysis is done after ANOVA is significant. We can take all possible combinations of levels and do comparions betwen them. These tests can be planned in advance. Some examples are Bonferonni test, Scheffes test, Tukeys test.

Planned comparisons are dcided in advance before looking at the data set. At the time of design of experiment with help of scienfic reasoning, planned comparions are decided. Post of test are decided after significance of experiment hence this is decided after looking at the data set. we can do as foolow up tests.

2) In between group comparison, we do check variability between different factors in a sample. in within group comparison, we do check variability of specific values in factors of sample. For examples. The variation due to different factors is explained variation in between group. The variation due to particular factor is error variable in within group.

Between group variation is due to indepedent variables in different group. Within group variation is due to differences in same group, here indepdent variable is not responsible.

F Ratio from ANOVA is obtained with help of between group variation and within group variation.

Variability in given data and Statistical significance decides which type of test need to be used. Experimental design is also important to decide about test.

Planned comparison are designed before analysis of data which can help increasing power of tests. Post hoc analysis is decided after significance of the analysis. Hence we get more precision to work on data set. Here we have less chance of doing type II error. Hence post hoc tests are more stroger tests than planned comparison. In case of planned comparison our arbitrary choice of rules may fail.