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 Result interpretation of 2-way ANOVA RM

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Tryphon Posted - 09/11/2018 : 10:51:45 AM
Hello,

I am confused on the result interpretation after execution of the Two-way ANOVA repeated measures process on my data.

Let me expose the context.
I use the factors Time and Genotype to explain the response in my experiment. The Time factor is a repetition factor (4 levels) related to the repeated measures of the response. The Genotype factor is not a repetition factor (2 levels).

I use Indexed input data, Significance Level = 0.05 and I ask for Interaction computation and Means Comparison using Holm-Bonferoni method.

Now I am trying to understand the worksheet results I get reading in parallel the example found there : https://www.originlab.com/doc/Tutorials/2WayRepeatedMeasuresANOVA

In the Multivariate Tests table I see only the rows Time and Time*Genotype which is okay for me since I have only one repetition factor (Time).

In the Mauchly's Test of Sphericity table I get only one row named Time.

Question 1 : Why I cannot see the Time*Genotype row?

In the Tests of Within-Subjects Effects table I see 3 rows : Time, Time*Genotype and Error(Time).

Question 2 : How to choose the right correction for sphericity violation since I did not get the Mauchly's test for Time*Genotype ?
Anyway, all the corrections presented in the Tests of Within-Subjects Effects table shows a non significant Time*Genotype interaction (for my data).

In the Tests of Between-Subjects Effects table, I see the Genotype row which indicates a significant difference between the two genotype levels.

At the end I see 3 tables : Time/Pairwise Comparison, Genotype/Pairwise Comparison and Time*Genotype/Pairwise Comparison which are all populated.

For the first two Comparison tables (main effects), all combinations are significant and this is okay in my study. However, post-hoc test results for Genotype within Times are not presented and I expected them in this table since I got Time*Genotype interaction not significant.

Question 3: Why post-hoc test results for Genotype within Times are not computed?

Question 4 : Could you explain why the Time*Genotype/Pairwise Comparison table is populated since the Time*Genotype interaction was found not significant? In this situation, what is the meaning of the post-hoc tests showed there?

Now comes the Holm-Bonferoni test results for Genotype within Time (4 levels)in the Time*Genotype/Pairwise Comparison table. I tested many set of data which show no significant interaction. For some data sets, the Alpha column shows values less than the signicant level I choose (0.05) and this is okay to manage errors of type I. But for other data sets, Alpha is exactly 0.05 at all Times which is not expected according to the Holm-Bonferoni method (as far as I know). I saw this strange behavior with the Bonferoni method also.

Question 5 : Could you explain why this happens sometimes ?

Thank you.

Origin 2018b (64 bits) b9.5.5.409
Operating System: Windows 8.1 64 bits
3   L A T E S T    R E P L I E S    (Newest First)
Echo_Chu Posted - 09/18/2018 : 03:03:23 AM
Hi,

Sorry that I did not realized that you have further questions.

1) the tutorial does not explain further. But you can still look at the results in Month * Gender branch if you perform analysis according to the tutorial

2) Alpha is the significant level to be compared, for the results of Bonferroni method, please look at Prob>|t|. As you can see in the tutorial, they are close to 0 and are much less than 0.05(alpha value), so the means are significantly different.
Tryphon Posted - 09/12/2018 : 09:05:39 AM
Thank you, your link helped me for some questions. Question 3 and 5 remain regarding the SPANOVA example given in this link. I ask them again for this example.

1) Knowing the fact that Weight*Gender interaction is not significant in this example, why I cannot see post hoc tests for the Gender at each Weight level? This could help to see at which Weight level the Gender effect is precisely significant since it is shown significant in the Tests of Between-Subject Effects table.

2) In the Weight/Bonferroni Test table, why Alpha is always equal to 0.05 when I expected it to be lower than 0.05 according to the Bonferroni method?

Thank you for your help.
Echo_Chu Posted - 09/12/2018 : 04:03:14 AM
Hi,

As one of your factor is not repetition factor, we call it mixed designed ANOVA.

Please refer the tutorial below for the detailed explanation of results for such case

https://www.originlab.com/doc/Tutorials/2Way-Mixed-Design-ANOVA

Echo
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