I am testing the hypothesis, "there is no difference between 3 materials", with a small sample size. I have 3 materials and 2 DVs (test 1-2). They also have a different number of replications as seen below. Six material-1, two material-2, and two material-3. Unfortunately this is all of the data that I will get due to the difficulty of the tests.
Material Test1 Test2
________ _____ _____
'mat1' 5 3
'mat1' 4 7
'mat1' 8 7
'mat1' 8 2
'mat1' 2 2
'mat1' 5 5
'mat2' 5 10
'mat2' 7 4
'mat3' 8 6
'mat3' 8 3
I am using Matlab to run a MANOVA analysis using the repeated measures function with 95% confidence. The output from the analysis is shown below;
Within Between Statistic Value F RSquare df1 df2 pValue
________ ___________ _________ _______ _______ _______ ___ ___ _______
Constant (Intercept) Pillai 0.11538 0.91304 0.11538 1 7 0.37113
Constant (Intercept) Wilks 0.88462 0.91304 0.11538 1 7 0.37113
Constant (Intercept) Hotelling 0.13043 0.91304 0.11538 1 7 0.37113
Constant (Intercept) Roy 0.13043 0.91304 0.11538 1 7 0.37113
Constant Material Pillai 0.20218 0.88696 0.20218 2 7 0.45359
Constant Material Wilks 0.79782 0.88696 0.20218 2 7 0.45359
Constant Material Hotelling 0.25342 0.88696 0.20218 2 7 0.45359
Constant Material Roy 0.25342 0.88696 0.20218 2 7 0.45359
It seems to clearly show that the null hypothesis holds true. I want to make sure that I went through the process correctly and I used the "best" method for the data I have. Should I do separate t-tests for the materials because of the small sample size? Is there some post-hoc analysis I should be doing? I am giving myself a crash course in statistics over the last few weeks, so any help is greatly appreciated.
manovafunction. You cannot reject the null in this case. However, the correlation between your two outcomes is zero; combined with the low sample size, it is diffcult to conclude. – chl Oct 22 '20 at 18:21