Does anyone know how to run a post-hoc test in a two way ANOVA (especially 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 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.
It is well known that the acceptable Type 1 error for a comparison to be = 0.05
But the problem when you do a multiple comparisons you inflat this Type 1 error. For example, if you have 3 means (A, B and C) and you want to make all possible piarwise comparisons i.e. A vs B, A vs C, and B vs C (i.e. 3 comparisons), then the total (Familywise; FW) type 1 error will be 0.05*3 = 0.15
Therefore, some post-hoc test come with a solution to this problem by making the familywise error rate to be 0.05, i.e. 0.016 per comparison (in case you have 3 comaprisons). But again the drawback of these tests it make you loss power.
There is no rule for which test to use, but there are some guidlines that may be helpful:
LSD test: if you comparing between just 3 means.
Bonferroni: if the number of comparisons more than degree of freedom of your groups (No. of groups - 1).
Tukey's HSD: if you comparing between more than 5 means and you want to check all possible pairwise combinations.
BUT AGAIN THERE IS NO RULE!
Best of luck!
Hello dear Safri
You can do mean comparison for interaction effects. You must wright the interaction effect together in a new column e.g we wright a1b1 effect as 11 and ...
then you can comparison with this new variable with LSD, LSR and ...
in this situation you can only use from mean comparison table only and you cant use ANOVA table.
with best regards
Hello Safri,
For a two way anova you can use post hocs such as Tukey or Bonferroni. These type of post hocs are widely accepted for two way anovas and can be easily performed on statistical packages such as Graph Pad Prism or JMP. As well, you can perform this in R (not so easy, but possible).
There is a trial version of Graph pad prism (just google it) and I can give you the links of some ppt tutorials (screenshoots with explainations) I have on the web for performing this type of analysis. As well I have the codes for performing the two way anova with post hoc and the interaction plot in R. Let me know through e-mail ([email protected]) if you are interested.
Best regards,
Karla
Thanks all..
I have a licensed Minitab Software, that is why I specifically asked for the Minitab procedure. I found out from a colleague that I can use the generalized linear model instead of two way ANOVA to do the post hoc multiple comparisons.
Karla, It would be interesting to compare the results with the other software.. I will get in touch with you..
I am a minitab user, version 16, I tend to use the GLM ANOVA option. In that you have a tab called comparisons in which you can set the particulars of the post hoc test. The results for main effects are given as groups defined with letters (no shared letter implies a significant difference between levels). I haven't ever tried to perform post hoc tests on interactions but it'd be worth giving it a try using the same coding as in the model.
Thanks Simon.. I am using version 15, but I don't think there are much difference between version 15 and 16..
I'm happy to chat further about it if you have any more questions ([email protected]). Cheers.
There is an ability to get coefficients for each level of a factor in Minitab. This will give you the ability to see what is going on.
What type of comparison do you want to do? How is your data structured? That will really tell you what you need to do.
It is well known that the acceptable Type 1 error for a comparison to be = 0.05
But the problem when you do a multiple comparisons you inflat this Type 1 error. For example, if you have 3 means (A, B and C) and you want to make all possible piarwise comparisons i.e. A vs B, A vs C, and B vs C (i.e. 3 comparisons), then the total (Familywise; FW) type 1 error will be 0.05*3 = 0.15
Therefore, some post-hoc test come with a solution to this problem by making the familywise error rate to be 0.05, i.e. 0.016 per comparison (in case you have 3 comaprisons). But again the drawback of these tests it make you loss power.
There is no rule for which test to use, but there are some guidlines that may be helpful:
LSD test: if you comparing between just 3 means.
Bonferroni: if the number of comparisons more than degree of freedom of your groups (No. of groups - 1).
Tukey's HSD: if you comparing between more than 5 means and you want to check all possible pairwise combinations.
BUT AGAIN THERE IS NO RULE!
Best of luck!
Dear Safri
You can create new variable ( called it int. for example ) represent the combination treatments ( interactions ) in the data setting , you will need to perform the analysis two times , the first in normal procedure without the new variable ( int. ) and in 2nd performed with the new variable only ( int. variable) , you will get the comparisons of interactions with duncan and tukey or other post hoc
But you must perform the two time with the same design and must get the same MSE in ANOVA
Good Luck
You can try by
Two-way ANOVA in SPSS Statistics analysis
https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php
I also have the same problems in my data analysis. all the interactions and main effects are statistically significant (p
Iranzi Emile Rushimisha you can do it easily by Minitab. If you want to do it by minitab I am ready to help you.
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