We have a very small sample (n=7) with a repeated measure deisgn. Therefore we use a non parametric test for repeated measures. In SPSS there is no option for a one tailed test. Divididing the alpha values may be a problem, because we have no normal distribution. How can we handle this problem?
Dear Alexander,
I had this problem in several studies. The first question is: how many groups do you have? Would it be possible to summarize it to 2 groups? Might it be possible to perform the Wilcoxon-test? Please describe a little your tasks in the analysis and a will try to find a solution!
Best regards
Tanja
Dear Tanja
Many thanks for your response. We are conducting a very small pilot study on teacher stress in working and nonworking days, including psychological stress, alpha-amylase; cortisol and heart rate variability.
The purpose of our study is to test a new methodology for the ambulatory assessment of teacher stress during the diurnal course in the field and to investigate the link between psychological stress and teacher’s physiological stress responses (cortisol levels, alpha-amylase and heart rate variability). In a non-clinical sample of 8 primary school teachers in Switzerland we assessed 2 working days and 1 Sunday from their awakening till 2000h. We assessed teacher’s heart rate variability with ambulatory ECG monitoring. 8 samples of stimulated saliva were collected by the teachers immediately after waking up, 30 and 45 min later, at 0800h, 1000h, 1200h 1600h and 2000h. At the same measurement points perceived stress and anger were assessed.
Today we just started with the HRV analysis, starting with the long term components. In a first step we compared for the eight teachers the heart rate variability on the two working days (not aggregated) with the non working day. Due to the small sample we made a Friedman test, which in SPSS can be tested only two-tailed. SDANN is significant (p=.048), SDNN is not (p=.066), HRV triangular not at all.
In a next step we could aggregate the two working days and then just compare the aggregate working days with the non working day, making a Wilcoxon test.
But I just wondered, if there is any reasonable possibility to handle this question with the Friedman test. If the data are not normal distributed, dividing the alphas may be the wrong way. Maybe first we have to check the skewness.
Best regards
Alexander
If you believe you have met all the assumptions for your statistical test, then you can divide the alpha in two to give the proper value for a one-tailed test.
Hello Alexander,
I am curious as to your decision to use tests that reduce data to ranks, because of small sample size. This is new on me. In general, information is lost when reducing data from ratio scale to ordinal scale (ranks). Which means that losing information by reduction to ranks only makes the problem of small sample size (low power) worse.
Turning to your query about the analysis of your data, if your residuals were normally distributed with respect to your your model parameters (2 fixed factor means and 8 random factor subjects) then I don't see the need to consider reducing your data to ranks at the outset. Your design appears to be a 8 subjects crossed with 2 levels--working and non-working-- of a fixed factor. I recommend you look at the residuals from this analysis, before reducing your data to ranks. If the residuals are normal and homogeneous, report the result, report the effect size, and state that the residuals were normal and homogeneous. And use the one-tailed test by halving the p-value, which makes sense in this context.
~David S
Dear Alexander,
I think with this study design, it is not possible to get value results. The problem is, that the parameters you measured have a wide range. In a study with herat failure, we had more than 200 pts. before getting significant results. Would it be possible for you to enhance the sample size? Which sample size you can reach?
Best regards
Tanja
Dear Tanja
Many thanks for your feedback. We plan a study with 40 to 80 teachers, depending on the effect sizes we reach in the pilot study. We will determine the sample size for the main study after completing the analysis of the pilot study with g*power. Because we include also behavior observation, 80 teachers are the limit. Observing 200 teachers would be to expensive.
Hello David
Thank you very much for your most helpful comment. That is a very good idea. We will check the residuals.
Best regards
Alexander
Dear Alexander,
g*power is quite a good software and 80 teachers are a quite good number for a sample size calculation. Good luck!
Best regards
Tanja
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