Paired t-test result pre and post intervention only 4 participants completed

#1
I would be really grateful for some advice on the way to present the results from a method development study in which 4 of the possible participants gave complete data. The aim of this part was testing the method. The next part would have a bigger number of participants. However, a reader is bound to ask what about the stats?

1. purpose of the study / research question / hypotheses, if possible, provide some background or context for us. Hypothesis: Symptoms of the behavioural disorder will be reduced by the regular use of this physical exercise.

2. nature of the data - independent and dependent variables Independent variable: Pre or post intervention (physical exercise). Dependent variable: Observer rated symptoms of the disorder.

3. how the variables are being measured The independent variable is categorical. The dependent variable was measured using a rating scale devised, validated and widely used to evaluate symptoms of this specific disorder.

The 4 took part, loved it and the observers saw a marked improvement in behaviour, reflected in the observer-rated symptoms scores. The data meets requirements for normal distribution. So I tried a paired t-test to back the verbal report of improved behaviour. Result of t-test: difference of the two means: p = .06 (two-tailed). For the effect size I calculated Pearson's r = 0.86
The hypothesis is unidirectional is it normal practice to report this as p = .03 (one-tailed)?
I really look forward to your advice,
Nayomi
 

Karabiner

TS Contributor
#2
With n=4 ist is not possible to make reliable statements
about normality (of the differences, by the way). So
the Wilcoxon signed rank test would be the usual option.

Unidirectinal hypotheses usually do not mean that a
one-tailed test is performed. For example, it could well be
the case that an effect is in the opposite direction than
anticipated, and one would make oneself "blind" in that
direction with a one-tailed test.

With kind regards

Karabiner
 
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