Post Hoc test for two way ANOVA

Hi all,

Does anyone know how to run a post hoc test in a two way ANOVA in Minitab? I am aware that we can use Tukey, Dunnet, Fisher LSD or other post hoc test directly for one way ANOVA, but still struggling how to do the test for two way ANOVA. I found one website how to run the test in SPSS but couldn't find one for Minitab..

I have some experimental data which showed significant interaction between the two factors that I investigated and found that each of the main factors are significant (p < 0.05) and the interaction is also significant (p < 0.05). What I want to know is:
1. Which level at each of the factor different significantly with each other?
2. Which level of the factors that interact and gave the best result?

Thanks..

You will have to use Stat > ANOVA > General Linear Model > Comparisons. The options for Post-Hoc comparisons are Tukey, Dunnett, Bonferroni and Sidak.

The GLM menu is more complicated than the Two-way ANOVA menu because it is more flexible, but the results should be identical albeit with a little more information.

remember that statistical significance doesn't mean practical importance. in addition to the excellent answer that Miner provided on statistical tests using Minitab, I woudl recommend plottting your data - all of the data points not just the means.

if you post your data we can provide more insight...

Hi Miner and Bev D,

Thank you very much for your answer. I already found the analysis in GLM.

I better explain my experiment. The purpose was to see whether there is a change in concentration of a particular compound after storage at different temperature and addition of supplement over time. So, we took sample from three subjects, give them supplement, and store it at different temperature and analyze the compound at three time points. We consider the subjects as replicate. So, there are actually three factors here Time, supplement and temperature. we are still not sure whether this is a repeated measures, since different explanation about this subject. When I checked minitab supplement, they don't have examples where the analysis is conducted at different time points from the same subject. The example they gave is a subject given different treatment at different time point. I managed to use GLM to get the ANOVA table, but the post hoc test couldn't work. Attached is the Minitab project file. I hope you can give me suggestion. Thank you very much for your kind help.

IF I correctly understand your design and treatment structure, the attached file should provide what you desire.

I used Sidak, because Bonferroni's is overly conservative.

Hi Miner,

Thank you for your help. However, Looks like something wrong with the file. I couldn't open the file.. I have Minitab 15 version. Do you use newer version? when I tried to open the file Mintab says it is an "unsupported file format". Any idea what can I do with this?

I saved it as a Release 15 in this attachment.

Thanks so much Miner.. I can open the file now.

There are two ANOVA table that added to the file. I assume that the second one is the one that I should pick. Can I just add more questions to it?
1. I noticed that Subj factor nested in Suppl. What is the main difference if I do not nested the factor ?
2. You mentioned that Benferoni test is overly conservative. Would you mind tell me what conservative here means? I already read some article mentioned about conservative of the test, but still can not get what it means. Do you think Tukey test can not be applied for this case?
3. The third question is very technical. I noticed in your analysis results, there is a grouping information under the post hoc test result (indicating means that do not share a letter are significantly different). I tried to find the command for this in Minitab 15, but couldn't find it. Is this function only applied for Software above Minitab 15? If this also applicable in Minitab 15, would you mind let me know? This is very helpful, since I often confused to make the groping after the post hoc test.

I actually have another question about repeated measures, but I guess I better make a new thread.

Thank you so much for your kind help. It really help me in my project.

Best regards

Yes, the first one had subjects as random effects, but this prevents the use of Post Hoc tests, so the second changes them to fixed.

If you do not nest, Minitab will not analyze this as a repeated measure design. This is a requirement of the repeated measures model in Minitab.

All three methods (Tukey, Bonferroni and Sidak) correct for family-wise Type 1 error rates in different ways. The stronger this protection, the weaker the power of the test, increasing the Type 2 error rate. This tradeoff varies by method. So, Sidak provides equivalent family-wise protection against Type 1 error at a slightly higher Power. Regarding the choice of Sidak vs Tukey, Tukey has greater power with a large number of comparisons, while Sidak has greater power with a small number of comparisons. However, I cannot find a breakpoint for when to switch from one to the other. You may want to run both for comparison.

The grouping was an addition to Minitab 16.

Thank you so much for the detail answer... really helpful..