Post-hoc test after Two-Way ANOVA: How to apply Bonferroni in JMP

[#1]

I am currently analyzing multi-group data using a two-way ANOVA (Group × Time), and I would like to know how to perform a post-hoc test using the Bonferroni method in JMP.

Normally, I use Tukey’s HSD for multiple comparisons, I am required to report the results using Bonferroni-adjusted comparisons as well.

I have checked the JMP help documentation and found explanations for multiple comparison methods in one-way ANOVA (Tukey, Dunnett, etc.).
However, I could not find a clear description of how to apply Bonferroni adjustment after a two-way ANOVA, especially from the “Least Squares Means” platform.

Could you please advise on the following points?

When the interaction is significant, what is the correct procedure in JMP to perform simple effects comparisons with Bonferroni adjustment after a two-way ANOVA (Fit Model)?

In nonparametric explanations, Bonferroni is sometimes described as “multiplying each t‑test p-value by the number of comparisons.”
Is this interpretation acceptable in JMP as well, or is there a recommended built‑in method for Bonferroni adjustment?

Any guidance would be greatly appreciated.
Thank you very much.

Best regards,

[#2]

Hi @LossMarmot707 : Yes, “multiplying each t‑test p-value by the number of comparisons.” is the same as the Bonferroni adjustment, no matter what software you are using.  But, why do you want to compare simple effects in the presence of an interaction? This could be very misleading. e.g., there could be a large difference between a pair of groups at each respective timepoint, but when averaged over the timepoints that difference is very small. 

Edit: Or, another way to make the Bonferroni adjustment would be to change alpha (to alpha/k, where k is number of comarisons) in the Fit Model platform (red triangle next to "Model Specification"), and then use the Student's t intervals.

[#3]

Thank you for your comment.

I understand Bonferroni adjustment as a standard approach to control Type I error when multiple comparisons are performed.

Even when an interaction is significant, interpreting only the main effects can lead to a misleading understanding of the overall pattern. For this reason, it is generally recommended to examine the effects separately for each condition (i.e., to compare simple effects), such as at each time point or concentration level.

The presence of an interaction indicates that
“the effect of one factor changes depending on the level of the other factor,”
which means that looking only at the overall averages may obscure important patterns in the data.

Therefore, in the present analysis, I examined the differences between groups within each condition using post hoc comparisons following the two-way ANOVA, in order to clarify these patterns.

In addition, my original question here was specifically about how to perform post hoc tests with Bonferroni adjustment using the statistical software JMP.

That said, as you mentioned, adjusting alpha to α/k and using the Student’s t intervals may indeed be a convenient alternative way to implement the Bonferroni correction.