If an ANOVA result showed a significant difference among means but during the post hoc tests(Tukey and Bonferroni) there are no significant difference in all pairs. Which result can be safely followed? ANOVA or the post hoc test?
You might find some helpful information and guidance from this previous thread:
https://www.researchgate.net/post/Is-it-possible-to-get-non-significant-results-in-post-hoc-test-when-we-got-the-significant-result-in-ANOVA
In addition to Dr Tomkins great suggestion you might also want to see the attached. Best wishes, David Booth
Excellent resource shared by David Eugene Booth - particularly the section discussing the exploratory vs. confirmatory distinction. At times, you need to step away from the statistics and consider: What is the question I'm looking to answer with test X, can test X actually answer that question, and what is the overall purpose of this study?
P-values and significance thresholds can't give you an answer to any of these questions. Furthermore, ANOVA and post hoc tests are not testing the same thing from the data, thus, they are not addressing the same question.
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