Do I have to conduct a normality test for only one paired sample?

[numbers123]

I have to conduct an action research and I only have one participant. I intend to give the participant a pre-test (before intervention) and a post-test (after intervention). Since this is an action research, I intend to do at least two cycles.

I want to know whether the intervention would make a significant change to the participant or not by assessing:
(i) the difference in pre-test and post-test for each cycle,
(ii) the difference in the post-tests (cycle 1 & cycle 2)
(iii) the increment of scores between the different cycles

What would be the suitable way to analyse the data here? As far as I know, it's either paired t-test or Wilcoxon signed rank test, and it would usually depend on whether there is a normal distribution or not. However, I am not sure if I still have to do normality test since I only have one participant. I have also read that the minimum sample for Shapiro-Wilk normality test is 3. If I just use Wilcoxon signed rank test instead of paired t-test, I would have to give justification on why.

Thank you and any insights would be helpful.

 

[Analyst1981]

You can't do all of these stuff with 1 participant only. Statistics is a summarizing field of science. It summarizes "many" stuff into smaller work or analyses.

I guess in your case. Applying statistics would only be valid if you have several readings of a certain variable taken from that 1-participant. Example: if you track blood sugar level of a person on 30 days. Yes now you can do some statistical work on these 30 values. Something like time-series regression, averages, some statistical tests, etc.

and I guess you should read more about single case statistical designs/methods or single case designs in research, etc.