# Mean Comparison test for 3 related samples

I have ratio scale data for 3 related samples. What is the statistical test that I can use to check whether there's any significant difference between the 3 groups? (I tried Friedman, but I'm doubtful whether it can be used for ratio scale data.)

https://statistics.laerd.com/spss-tutorials/friedman-test-using-spss-statistics.php

This cite says Friedman test can be used for continuous scale data as well, but I need to make sure about it as this is the only place I found that fact. In every other place, it speaks about ratio scale data.

NOTE: I collected data from 15 people. i.e. sample size is 15. The same 15 people faced the 3 different situations where we need to compare

• related = dependent samples – Dovini Jayasinghe Oct 1 at 16:28

In a comment you clarifies

collected data from 15 people. i.e. sample size is 15. The same 15 people faced the 3 different situations where we need to compare

that is information that really needs to be in the post itself! please edit. So one simple model for your situation is $$y_{ij}=\mu+\tau_i+\beta_j+\epsilon_{ij}$$ with $$i=1,2,\dotsc,15$$ indexing the persons and $$\beta_j, j=1,2,3$$ indexing the groups. As written this is a mixed model and could be analyzed as such, or traditionally as repeated measurement ANOVA. If you use R, you could start with something like

lme4::lmer(y ~ groups + (1 | person), data=your_data_frame)


with data in long format. Also search this site for repeated measures, and read up on mixed models!

• Thanks a lot. I did the edit as you requested. Mixed models are new to me. Will check further on it – Dovini Jayasinghe Oct 2 at 17:57

Since your data is a ratio scale data why don't you try to use ANOVA for testing. It is a parametric test as compared to the non-parametric Friedman.

• If OP has data collected according to a block design, Friedman might be OK. But you would have to specify carefully what kind of ANOVA to use. – BruceET Oct 1 at 2:18
• Cannot use ANOVA, since the samples are not independent. They are related (dependent samples) – Dovini Jayasinghe Oct 1 at 16:32
• If you really want to use the Friedman test, then look at the example at the end of the R documentation for that test. You have a design just like the baseball example, except you have 15 subj as 'blocks' (not 22 players) and you have three methods to compare. The hypothesis test will compare your 3 groups. // However, if your data have nearly normal residuals, you can use the ANOVA model suggested by @Kjetilbhalversen (+1). Maybe make a normal probability plot of residuals at the end to verify their near normality. – BruceET Oct 2 at 0:08
• Is normality the only requirement for ANOVA? Don't the data should be independent? – Dovini Jayasinghe Oct 2 at 17:53
• sites.ualberta.ca/~lkgray/uploads/7/3/6/2/7362679/… – Dovini Jayasinghe Oct 2 at 17:54