Dear scholars,
As we know that: the Critical Difference of LSD < Critical Difference Tukey < Critical Difference Scheffe So, I'd like to ask whether the choice of one of the following tests Fisher's Least Significant Difference (LSD), Scheffe’s test,Tukey's Test depends on the accuracy of the results that the researcher wishes to obtain?
Best wishes
Huda
If you are using post hoc tests, then you have already established an overall statistically significant difference in group means using ANOVA. Post hoc tests attempt to control the experiment-wise error rate and they each do it different ways. LSD calculates the smallest significant between two means as if a test had been run on those two means and does not make an adjustment for the fact that multiple comparisons increase Type 1 errors. Tukey is slightly more refined and uses a number that represents the distance between groups to compare every mean with every other mean and so is slightly more accurate. Scheffe controls for the overall confidence level but is customarily used with unequal sample sizes. Bonferroni is possibly the best since it corrects for type 1 errors, but may suffer from a loss of power :)
Thanks Added for your clarification, I agree with you, but all three tests can be used with unequal sample sizes.
Best wishes
Huda
Another aspect of looking at mean differences is to use what we call orthogonal contrasts. In this case you set up a contrast between means and get a balanced (orthogonal) analysis in the ANOVA.
For example I have treatments A,B,C and D.
There could be a very good reason why I wish to compare A with the rest. So if you look into this for your software - you develop a contrast and test that in your analysis. I see this as using pre-planned comparisons which relate to your particular experiment and research question.
SAS has estimate and contrast statements to achieve this.
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