anova1, anova2, or ranova?

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Tyler Tuttle 2021-4-23

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https://ww2.mathworks.cn/matlabcentral/answers/810545-anova1-anova2-or-ranova

编辑： Scott MacKenzie 2021-4-29

I have a set of data. I have 1 dependant variable measured 3 times from 5 subjects. Each of the 3 measurements represents a different level (A, B, and C). Based on my understanding, I should use a repeated measures ANOVA because I have multiple measurements from each subject. However, I am unable to get any results. I have tried making each subject a different group, and treating all subjects as the same group. I tried a 1-way ANOVA, which to my understanding treats every measure as a different subject, which seems wrong. I tried a 2-way ANOVA where subjects are treated as an independant variable. Using multcompare after anova1 and anova2 give me unexpected results. Based on the data, it seems pretty evident that column 1 and column 3 should both be significantly different than column 2. However, only column 1 vs column 2 is significant. I am unsure if I am doing something wrong, or if there is a different statistical test I should be using. Any help would be greatly appreciated.

clear,clc
close all
DepVar=[101.053914979877,1.10267662721688,39.9882799952772;216.136311110424,1.25119134782814,70.1362721192365;26.5334559925966,1.54372037819131,81.1211148269482;231.177535625968,0.890020347986787,135.886529812943;140.395359593013,0.00626713939985805,37.2109788038507];
% 1-way ANOVA
[p1,tbl,stats1]=anova1(DepVar);
c1=multcompare(stats1);
% 2-way ANOVA
[p2,tbl2,stats2]=anova2(DepVar,1);
c2=multcompare(stats2);
% RM ANOVA
sub=table([1 2 3]','VariableNames',{'Treatment'});
subject1=['1'; '2'; '3'; '4'; '5'];
t1=table(subject1,DepVar(:,1),DepVar(:,2),DepVar(:,3),'VariableNames',{'subject','A','B','C'});
rm1=fitrm(t1,'A-C ~ subject','WithinDesign',sub);
ranovatbl1=ranova(rm1,'WithinModel','Treatment');
c3=multcompare(rm1,'Treatment');
subject2=['1'; '1'; '1'; '1'; '1'];
t2=table(subject2,DepVar(:,1),DepVar(:,2),DepVar(:,3),'VariableNames',{'subject','A','B','C'});
rm2=fitrm(t2,'A-C ~ subject','WithinDesign',sub);
ranovatbl2=ranova(rm2,'WithinModel','Treatment');
c4=multcompare(rm2,'Treatment');

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Scott MacKenzie 2021-4-28

编辑：Scott MacKenzie 2021-4-28

在 MATLAB Online 中打开

OK, thanks. I've been trying a few things with your data. Like you, I am struggling with how to do analyses on data like these in MATLAB. I've been doing analyses like these with other tools for many years, but not with MATLAB.

The first thing I did was analyse your data in a different tool. Before we get to MATLAB, let's examine results that are known to be correct. Using a commercial stats app, the Anova table is

So, the effect of Bio_Material on Stiffness (kPa) was statistically significant, F(2,8) = 10.439, p < .01. A Tukey/Kramer post hoc multiple comparisons test yields

So, the difference was only significant between the Muscle and Fat conditions (p < .05).

I'm fairly confident these analyses are spot on.

So, the challenge now is to do this in MATLAB. As it turns out, your second approach, using anova2, was the correct one. These statements

DepVar=[101.053914979877,1.10267662721688,39.9882799952772;216.136311110424,1.25119134782814,70.1362721192365;26.5334559925966,1.54372037819131,81.1211148269482;231.177535625968,0.890020347986787,135.886529812943;140.395359593013,0.00626713939985805,37.2109788038507];
[p2,tbl2,stats2]=anova2(DepVar, 1);
c2=multcompare(stats2, 'display', 'off')

yield the following Anova table

Here, we see the same F-statistic, p-value, and MS values. The output also includes the results of a multiple comaprisons tests:

c2 =

1 2 53.236 142.1 230.97 0.0045969

1 3 -18.674 70.191 159.06 0.12062

2 3 -160.77 -71.91 16.955 0.11131

Tukey/Kramer is the default test with multcompare, so this is an apples with apples comparison. The result is exactly the same. The difference between the Muscle (1) and Fat (2) conditions was statistically significant (p = .0046). The difference between the other pairs was not.

Hope this helps.

Adam Danz 2021-4-29

Yes, answers are often developed within comment sections as the question becomes clearer. When a definite solution arises, summarizing that solution or copying it to an official answer makes it more visible to future visitors of the thread whether its accepted or not and it gives users the opportunity to give you credit for your work by accepting or voting for your answer. Plus the thread moves into the answered pool rather than lingering in the unanswered queue.

Scott MacKenzie 2021-4-29