Conflicting results of multcompare output c and interactive graph

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Nina Compera
Nina Compera 2022-1-25
回答： TARUN 2025-8-8
Hello,
I am trying to do a multiple comparison using multcompare of my data (SampleData.mat) after having performed a n-way ANOVA with two grouping variables (gMat: materials, gCure:post-processing) to identify significant differences between the groups.
I am using R2019a.
So, my code looks like this:
%Load data
load('SampleData.mat');
%Preselection of data
idx = find(gTime=='48h');
%n-way ANOVA of selected data
[~,~,stats] = anovan(viab(idx),{gMat(idx),gCure(idx)},'model','linear');
%Multiple comparison
[c,~,~,gnames] = multcompare(stats,'Alpha',0.01,'Dimension', [1 2]);
This produces:
c =
1.0000 2.0000 -0.0716 0.0310 0.1335 0.9386
1.0000 3.0000 -0.2115 -0.1089 -0.0064 0.0056
1.0000 4.0000 NaN NaN NaN 1.0000
1.0000 5.0000 -0.0296 0.0729 0.1755 0.1239
...
and the following interactive graph:
So here are my 2 questions:
  1. The interactive graph of multcompare shows that the groups 1 (X=FPMould,X2=Otoflash) and 3 (X=PlasGRAY,X2=Otoflash) are NOT significantly different. However, column 6 of c says that the p-Value is 0.0056 which is smaller than my alpha (0.01), thus suggesting that they ARE different. So, which one is correct now?
  2. Is it possible that column 6 of output 'c' of multcompare does not change when I change alpha to e.g. 0.05?
Has anyone encountered this before? How can I avoid this?
Help on this would be highly appreciated!!!
Thanks,
Nina

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回答（1 个）

TARUN
TARUN 2025-8-8
Hi @Nina Compera,
The mismatch you're seeing happens because the p-values in column 6 of the ‘multcompare’ output (c matrix) do not depend on the ‘Alpha’ value you set. The ‘Alpha’ parameter only affects the:
  1. Width of the confidence intervals. (columns 3–5)
  2. And what gets visually highlighted in the plot.
So, even if the plot doesn't clearly show a significant difference between two groups, you should trust the p-value in column 6.
In your case, a p-value of 0.0056 is below the alpha of 0.01, meaning the groups aresignificantly different, regardless of how the plot appears. To avoid confusion, rely on the p-values for significance, and use the confidence intervals for additional insight.
Please refer to the following documentation to learn more:multcompare: https://www.mathworks.com/help/stats/multcompare.html

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