Should I follow up a oneway ANOVA with a t-test or only a post hoc test like a tukey?
To determine whether you should follow up a one-way ANOVA with a t-test or a post hoc test like Tukey's test, you need to consider the nature of your research question and the specific hypotheses you want to test.
A one-way ANOVA is used to compare the means of three or more groups to determine whether there are statistically significant differences among them. If the ANOVA yields a statistically significant result, indicating that there are differences among the groups, you may want to perform further analyses to identify which specific groups differ from each other.
Tukey's test is a commonly used post hoc test for ANOVA that allows for pairwise comparisons between all groups to determine which pairs are significantly different. It controls for Type I error rate by adjusting the p-values for multiple comparisons.
However, if your research question or hypotheses have specific pairwise comparisons that you are interested in, you may choose to perform t-tests instead of a post hoc test. A t-test would compare the means of two specific groups to determine if they are significantly different from each other.
Here are the steps to decide whether to choose a t-test or a post hoc test after performing a one-way ANOVA:
1. Determine your research question and hypotheses: What specific comparisons are you interested in making among the groups?
2. Check the assumptions: Make sure that the assumptions of ANOVA are met, such as the normality of the data and homogeneity of variances among the groups.
3. Conduct the one-way ANOVA: Perform the ANOVA analysis to assess overall group differences.
4. Interpret the ANOVA results: If the ANOVA results are statistically significant, indicating differences among the groups, proceed to the next step.
5. Choose between t-tests and post hoc tests:
- If you have pre-planned specific pairwise comparisons, perform t-tests between those groups to determine if they are significantly different from each other.
- If you want to compare all possible pairwise combinations or if you did not have specific pairwise comparisons planned, conduct a post hoc test like Tukey's test to identify significant differences between groups while controlling for Type I error rate.
In summary, the decision between using t-tests or post hoc tests like Tukey's test after a one-way ANOVA depends on your specific research question, hypotheses, and whether you have pre-planned pairwise comparisons.