Question

1. Sam is doing a research project where Sam developed some specific hypothesis about the dose effect of a new drug. Sam predicts that 0 mg dose (control) will be less effective than the 5 mg dose, and the 5 mg will be less effective than the 10 mg. After running an ANOVA, Sam is disappointed that that there was no significant result. However, Sam runs follow-up t-tests anyways, and discovers that there was a significant improvement between the 0 mg and 10 mg doses.
   1. Was this bad science? Justify your answer.
   2. How is it possible to have a non-significant ANOVA, but a significant t-test follow-up.

Answer 1

A. It is not a bad science completely but if the level of significance is not adjusted we will get misleading results and the reason for that is "with independent t-tests the type I error also increases' .do while doing independent t- tests instead of ANOVA, the level of significance should be adjusted.

B. Since The type I error ( that is rejecting True Null Hypothesis of no differences) increases when performing t- tests which lead to significant differences while we may have insignificant difference or Null hypothesis (no differences exist) more often accepted in ANOVA

Hope this is helpful. Thank You