# Sample size calculation for parametric test, with large effect expected, small numbers. Should I use parametric or non parametric tests?

I am trying to figure out what would be the best way to analyze data from a randomized double blind trial we conducted. We sought to find if two dosages of a drug were effective for a severe symptom in patients with an advanced stage of a disease in which this symptom is very common (affecting approximately 40% of patients). We used a 100 mm visual analog scale to assess the symptom and decided to include only patients with severe symptom intensity, defined as more than 50 mm on the visual analog scale. A sample size calculation for parametric tests was conducted, using mean VAS and standard deviation from previous studies on the subject. These indicated that the drug had dramatic effects, so a large effect was used in the sample size calculation. The calculated sample size was n=8 per group. Here are my questions:

1. I do not know if I can make a normality assumption. How would I know?

2. If I can make a normality assumption but the sample size calculation gives me small numbers, should I use parametric tests even though the numbers are so small I cannot assume they have a normal distribution?

3. Do normality tests (KS, Shapiro Wilk) make sense on such small numbers? I mean: if such tests do indeed tell me my sample has a normal distribution, are they reliable if the numbers are so small?

4. Is it legit to use non-parametric tests even though I originally calculated the sample using a formula intended for parametric tests?

Thank you!

• 1. It's probably better to separate your questions. Some have been answered already. e.g. see Is normality testing essentially useless which largely addresses one of your questions. 2. don't confuse parametric with assumes normality. – Glen_b Jan 17 at 9:39