# ANOVA for repeated measures VS Friedman

#### AEGomes

##### New Member
Hi.
I need to compare means between three or more groups, with dependent and related variables. If the sample has a normal distribution, the ANOVA for repeated measures statistical test is used. In this test, not only it is possible to verify the statistical significance between the tested groups, but also to study the influence of other factors. That is, it calculates the interaction between continuous variables (example: weight measured at different times) and also the influence of (one or more) ordinal variables (example: sex or age). Alternatively, if the distribution is non-parametric, the Friedman test is used. And if the Friedman test gives a statistically significant difference, it is possible to find out in which pair of groups this happens using the Wilcoxon test. However, I cannot find any non-parametric test (for related continuous samples) that allows the assessment of the statistical significance between means, while studying the influence of other factors (such as ANOVA for repeated measures that calculates the interaction between continuous and ordinal variables). Are there any tests that allow me to do this? Or will I have to perform the test for each one of the ordinal variables? Can someone help me, please. I would really appreciate it.
Best regards, AEGomes

#### Karabiner

##### TS Contributor
Hello.

I would like to clarify some things.

If the sample has a normal distribution, the ANOVA for repeated measures statistical test is used.
This is not correct. If the POPULATIONS from which the samples are drawn are normally distributed, then this might be of interest.
The sample data just can give us some idea whether that assumption should be rejected or not.

But: the normality assumption is only interesting if the sample size is very small (n < 30 or so). If the sample size is not very small,
then the analysis of variance is considered robust with regard to non-normality.

ordinal variables (example: sex or age).
Most would consider sex as categorical, and age as interval scaled (if it is not categorized into age groups).

Alternatively, if the distribution is non-parametric,
There are no non-parametrc distributions. There are non-parametrc tests, i.e. tests which do not make teh same
distributional assumptions as "parametric" tests.

the Friedman test is used.
Mind that the Friedman test is based on the ranks of the data, therefore it does not compare means.

However, I cannot find any non-parametric test (for related continuous samples) that allows the assessment of the statistical significance between means, while studying the influence of other factors (such as ANOVA for repeated measures that calculates the interaction between continuous and ordinal variables). Are there any tests that allow me to do this?
No. But since the normailty assumption is the least important or even unimportant in ANOVA,
you might consider using repeated-measures analyis of variance, especially if your sample size is
n > 30.

With kind regards

Karabiner

#### AEGomes

##### New Member
Hello.

I would like to clarify some things.

This is not correct. If the POPULATIONS from which the samples are drawn are normally distributed, then this might be of interest.
The sample data just can give us some idea whether that assumption should be rejected or not.

But: the normality assumption is only interesting if the sample size is very small (n < 30 or so). If the sample size is not very small,
then the analysis of variance is considered robust with regard to non-normality.

Most would consider sex as categorical, and age as interval scaled (if it is not categorized into age groups).

There are no non-parametrc distributions. There are non-parametrc tests, i.e. tests which do not make teh same
distributional assumptions as "parametric" tests.

Mind that the Friedman test is based on the ranks of the data, therefore it does not compare means.

No. But since the normailty assumption is the least important or even unimportant in ANOVA,
you might consider using repeated-measures analyis of variance, especially if your sample size is
n > 30.

With kind regards

Karabiner
---------
Dear Karanbiner,
I learned a lot from you with this reply. Thank you very much for your attention. I am very sorry for the mistakes I made throughout the text. I am still a beginner. Once again, thank you.
With my best regards,
AEGomes