# Usage of the Friedman test

I have done an experiment in which I have measured the energy required to chew three different food samples on 10 subjects with 3 repetitions per sample. I am interested therefore in finding out whether there is a difference between samples according to the energy consumed.

I have performed a Friedman test by ranks followed by multiple comparison procedure (Tukey's honestly significat difference for ranks) as Friedman test was significant.

However someone told me that for using that test I should make sure that the error for order effect was not significant, ans I don't fully understand this.

I provided my samples in the same order for all subjects. That is A,B,C -A1 B1 C1 and A3 B3 C3 for each subject.

I will be very grateful if you can tell me

1. whether the test I used (Friedman) is the correct for my purpose?
2. whether the sequence in which I gave the samples affects my result from Friedman test?
3. if what I have done is incorrect, what to do instead?
• Well, if the same individual tries to chew three different food samples then your groups are related/dependent. The Friedman test assumes the dependency and it is a distribution free test. You probably should do the Friedman test followed by post-hoc Nemenyi test (pp.11-12)"proposed" by Schaich and Hamerle. But it is likely your data are normal or try to normalize them to do 1-way RM ANOVA test, a parametric analogue of the Friedman test. IMHO – stan Oct 20 '11 at 10:35
• – stan Oct 20 '11 at 10:40
• Links2: R, R2, discussion. I'm newbie in statistics but I'm also trying to do Friedman+Nemenyi in R... Hopefully this information will help us :) – stan Oct 20 '11 at 10:41
• Friedman's test is likely to assume a single observation, but you did in triplicates. Perhaps this is a vote for 1-way RM ANOVA... – stan Oct 21 '11 at 12:00

1. Given your data, the Friedman test sounds like the right approach. I am not aware of there being any agreement regarding the post hoc testing. One of the commenters refers to the Nemenyi test, but it has pretty low power. Using Tukey HSD on the ranks (which I assume is what you have done), is probably OK but I doubt you will find much academic literature to support that approach.
2. The sequence can have an impact. Imagine that the subject was tired after the first sample. Then, by the time they got to the second sample, it may take longer. Or, even if fatigue was not at issue, something else could occur (e.g., people got bored towards the end of the experiment). Your experiment in its current form confounds the order with which the samples were test with the three different food samples and there is no statistical way of disentangling these and working out whether order did or did not have an impact.
3. The standard approach when conducting sensory research is to randomize the order with people are given the samples (or, use an experimental design and allocate people into different blocks with different pre-determined orders). Then, you can estimate a general linear model or ANOVA which takes into account the order as well as the food samples, permitting you to disentangle the different effects.