# comparing multiple sequences of data over time

##### New Member
Hi, would really appreciate help on how to test my data!

I've three groups (with 5-8 individuals in each group; actually 5 in one and 8 in each of the other two groups), and each of the three groups is undergoing a different treatment. So if we call the three groups A, B and C, I've individuals A1-A5, B1-B8 and C1-C8.

Each day the study parameter is measured for every individual. This parameter is expected to increase over time for every individual, probably in an approximately logarithmic manner, and it's followed over 20 days.

However, the hypothesis is that because the 3 groups are undergoing different treatments, they will differ in the rate of increase: for individuals in one group the parameter may increase rapidly, while for individuals in another, it may rise more gradually.

Within each group, the 5-8 individuals don't seem to vary normally so I guess I need a non-parametric test.

Now, (I think) I can use Kruskal-Wallis to see if my groups differ at each of the various timepoints, e.g. I can do a K-W test to see if there is a difference between the groups on day 2, and I can do a separate K-W test to see if there is a difference between the groups on day 3 etc. In a similar manner I can also use the Mann-Whitney test to see is there a difference between two specific groups at a particular timepoint. That's fine.

But what I'd really like to do is compare the collective sequences for each group over the entire period. So I'd like to take the sequence of repeated measures for group A for days 1-20 and see if, taken as a whole (rather than just looking at a particular timepoint), it differs from the sequence of measures for group B, and that for group C. Can anyone recommend a suitable test to do this?

If it makes a difference, I can track each individual in every group - i.e. I can distinguish the info for subject A1 on day 5 from A2 on day 3, for example; they're not just all lumped in together as five subjects in group A that I can't tell apart.

I'd really appreciate any help! Anything I've seen on repeated measures seems to focus on seeing if there's a difference between the beginning and the end of the sequence; it doesn't compare different sequences with each other. Thanks.

#### victorxstc

##### Pirate
I think a Freidman's test can do it. It is the non-parametric alternative for repeated-measures ANOVA. Using it, you can first check whether each group has had any overall increase over time, or not.

Then if the increase was statistically significant, you should use a Wilcoxon's test to compare the parameter in each group at each sequence with that parameter measured at the other 19 sequences (for the same group only).

##### New Member
Thanks victorxstc.

Looking at the Friedman test, any examples I can find seem to be designed for evaluating any overall change within a group as time passes.
I do want to look at overall change over the time period, taking the 20 days as a whole. But I want to compare the overall change between one group and another.

The parameter being measured is such that it will almost certainly increase within each group as time passes, in an approximately logarithmic fashion (so it's pretty much guaranteed that Friedman would show significance in that respect for each group), but I want to see if the rate of increase is more rapid in Group A compared with Group B or Group C.

So I want to test for differences between independent samples (groups A, B, C), but each sample is in turn made up of a succession of repeated measures which are obviously dependent within each group.

Is there a way of using Friedman to do this too, do you think?

Or another test entirely? Thanks!

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#### victorxstc

##### Pirate
Ur welcome

AFAIK The Friedman's test can be used to check:
a: whether there is any significant changes across the repeated measures within each group
b: whether the trend of changes for all groups are similar or not (between-groups)
So it can be used to test your hypothesis. But I checked some statistical packages and saw none of them could report the between-group difference.

There is another test for your purpose which is an extension to the Kruskal-Wallis test, called Scheirer–Ray–Hare. It can also compute the between-group difference in a repeated measures design. AFAIK the only software which can compute it is BIOMstat. There is also a SAS module designed to calculate this test which computes the between-group difference too. However, I think it needs the sample to be balanced (all the groups must have the same number of specimens). So I think it might give some errors if you force it to compute your non-balanced data.

Thanks

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