0
$\begingroup$

I have to make a statistical analysis of only four (n=4) data pairs. I have tested two specific warm-ups for 4000m Team Pursuit in track cycling, and used a 250 m. sprint test as a meassurement of the warm-ups effect. I only had four track riders available as test subject, så they underwent both types of warm-up followed by the sprint test, on seperate days (repeated meassures). That gives me the four data pairs that i would like to analyse. I first thought of a Wilcoxon signed-rank test, but found out that it required at least six data pairs. I haven't been able to find an alternative test. "Please help Obi-Wan Kanobi (read: stat experts at Cross Validated), you are my only hope!"

ps. all four data pairs show the same warm-up as the most effective.

|cite|improve this question
$\endgroup$
  • $\begingroup$ An exact, permutation-based significance can be done for every nonparametric test of a small sample size. $\endgroup$ – ttnphns May 20 '16 at 9:40
  • 1
    $\begingroup$ @ttnphns The problem is that with 4 pairs the smallest achievable two-tailed significance level is 0.125 ($2(\frac12)^4$). This applies equally to the permutation test as it does to the signed rank test. Similarly, when there are 6 pairs, the smallest achievable significance level for both tests is $2(\frac12)^6=\frac{1}{32}=0.03125$, which is the first one below 5% (this is the source of the "requires six pairs" in the question -- which is actually only true if you insist on a two-tailed test with a significance level of 5%). $\endgroup$ – Glen_b -Reinstate Monica May 20 '16 at 10:11
  • $\begingroup$ @Glen_b, thank you for reminding, and I'm aware of the problem. But could there be a solution for the OP, free of it? $\endgroup$ – ttnphns May 20 '16 at 10:22
  • $\begingroup$ Realistically a non-parametric test with a significance level of 0.05 is silly with n=4 and it would be hard to see how this could be a particularly compelling dataset - perhaps a little pilot trial that should not be overinterpreted? If there is previous data, then identifying a suitable parametric may be possible and may give some power. However, unless you are looking for enormous effect sizes, this is likely not a very conclusive experiment and ideally you should do a better experiment with a sample size suitable to detect realistically plausible effect sizes. $\endgroup$ – Björn May 20 '16 at 10:46
  • $\begingroup$ Hey folks. Thank you for taking your time to answer. As you might can tell I'm not a statistics expert of any kind, but your answers have been useful to me anyway. And Bjørn, you are right, this is a small trial, but smaller then planned to be. I had 8 subjects available to begin with, but injuries and sickness left me with only four and a statistical challenge I had no idea how to handle. Even though I can't say my results are statistical significant, they still show a tendensy which gives me something to elaborate on in my discussion chapter. $\endgroup$ – Thomas May 20 '16 at 11:29
4
$\begingroup$

If you want to be able to use a significance level of 5% and you want a two tailed test, you're pretty much left with parametric tests.

However, this doesn't mean you're stuck with normal-theory tests.

For example you could treat times as (say) gamma-distributed and use a link-transformed sprint-time-for-first-warmup-type as an offset and an intercept-only model (a GLM). e.g. with a log-link you could use log-sprint-time-for-first-warmup-type as offset. Then a test of the intercept would be testing for change in sprint times. (Alternatively, generalized linear mixed-effect models might be used.)

There are numerous other possibilities (e.g. assume differences of log-times are normal).

You might even consider a normal theory test after all, and assume time differences are normal.

|cite|improve this answer
$\endgroup$
  • $\begingroup$ (+1) for the overview of some possibilities. $\endgroup$ – ttnphns May 20 '16 at 10:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.