Not sure why you would want to test normality and the power will be low with n=4, but also what do you want to test? If a variable x, and say you want to use the Shapiro-Wilks test, you can download R for free and: shapiro.test(x). You might want to add more background information.

It depends on what you plan on doing with the data. If you have collected qunatative data and your goal is to use a parametric test such as t test, ANOVA, Pearson's correlation, etc., then you would need to check for normality before you can go ahead with the test. In case the data is not normally distributed, you can opt for non-parametric tests such as Kruskal-Wallis test. I have two papers published in SAGE and Taylor and Francis journals where I have used this test.

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Daniel Wright I completely understand that, but I am wondering why there are parametric and non-parametric tests then for single case design analysis? I have chosen Nonoverlap of all pairs (NAP) for exploring the effect size of the intervention which falls into non-parametric test.

s. Rama Gokula Krishnan Thank you for your comment but I am lookinf for analysis for single-case designs and not group statistics.

Hemangi Narvekar can you say more about your analysis strategy for your design? What are you planning to do? Where did you find the assumption of normality and in which context? Please clarify.

Rainer Duesing The main analysis is visual inspection that is available for single-case designs. Apart from that I wanted to perform numerical analysis for exploring the effect size of the treatment. Some of it is mentioned in this article: https://files.eric.ed.gov/fulltext/EJ1127772.pdf

Hemangi Narvekar thank you for the article. I didn't see anything about normality. Maybe you should think about the reason for the normality assumption in a lot of analyses. There is no universal "law" that the "data" has to follow a normal distribution. Normality needs to be assumed if you use inferential statistics, where confidence intervals and hence p-values are calculated and you need a distributional assumption for the parameter of interest (e.g. mean, mean differences, regression coefficients etc.). And it is not about the data itself (which will most often not be normally distributed) but about the deviation of the observed values from the true value (error), which can be assed with residuals, which in turn are the deviation of the observed values from the estimated parameter of interest.

Therefore, if you do not use such techniques, there is no need for a normality assumption. Describe the data as they are.

Rainer Duesing Thank you so much for the information. This is helpful.

As per my knowledge, you can't apply the normality test on a single case.

Sanjay Chandwani Thank you.