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# st: Quantile regression with repeated measures

 From Ingravalle Francesco <[email protected]> To "[email protected]" <[email protected]> Subject st: Quantile regression with repeated measures Date Fri, 11 Oct 2013 15:37:43 +0200

```Dear Statalist,
I have two questions to ask you:
1) when I apply an ANOVA model, the normal distribution of the groups and the omogeneity of variances are basic assumption.
But how can I fit an ANOVA model when I've observed the same value for the dependent variable in one of the group?
2) how can I fit a quantile regression to results obtained by an experiment with repeated measures?
In the following I describe the experiment.
We have split one biological sample in 20 aliquots and we randomly assign these to 4 different tests (so, we tested 5 aliquots with each test).
We repeated this procedure with other two samples; so, in the end, we tested 15 aliquots with each test.
The dataset is the following:
|--------------------------------------|
| sample   test1   test2     test3    test4 |
|--------------------------------------|
1. |      1   0.975   1.254   1.107   1.205 |
2. |      1   0.965   1.254   1.093   1.191 |
3. |      1   0.856   1.254   1.083   1.180 |
4. |      1   0.761   1.254   1.075   1.162 |
5. |      1   0.749   1.254   1.074   1.162 |
|--------------------------------------|
6. |      2   1.167   1.254   1.070   1.219 |
7. |      2   1.158   1.254   1.066   1.217 |
8. |      2   1.157   1.254   1.030   1.201 |
9. |      2   1.141   1.254   1.010   1.191 |
10. |      2   1.122   1.254   1.005   1.185 |
|--------------------------------------|
11. |      3   1.139   1.237   0.819   1.015 |
12. |      3   1.121   1.231   0.722   0.968 |
13. |      3   1.116   1.225   0.716   0.937 |
14. |      3   1.088   1.179   0.683   0.918 |
15. |      3   1.084   1.168   0.624   0.908 |
|--------------------------------------|
Now, I'd like to verify if the results obtained by tests are the same, and I would fit an ANOVA repeated. The main problem is that test2 returned the same value 1.254 (i.e. the maximum value that the instrument is able to quantify) for each aliquots of sample 1 and sample 2.
So, I return to my previous questions: how can I compare test2 with the others? Could the quantile regression with repeated measures a good alternative to ANOVA about this dataset?

Thank you very much
Francesco
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```