Best test for normal distribution with as little samples / highest accuracy

#1
Hi there,

I only completed one statistics class yet and now struggle with my first project involving statistics. :)

I want to conduct an evaluation where items are rated according to particular scales, leading to a lot of probability distributions, where there is one distribution for each item, scale and several users.

In order to limit the amount of participants required in the evaluation, I am looking for a test which is able to determine a normal distribution with a certain alpha=0.05 and only requires very little sample sizes while still having a high accuracy. I would prefer sample sizes as little as <=10. Given the fact that I have to implement the test in c#, a ranked list of available tests would be of great benefit. The only test I know and tried yet is the \chi^2 one.

Thank you so much for your help!
Christian
 

noetsi

Fortran must die
#2
I am not sure any test works with samples that low (and most normality tests have low power to start with). You might look at a QQ plot that plots your distribution against a theoretical one (in this case normal). If the distribution is normal it will line up very close to a diagonal line that will be superimposed on the plot. You have to have statistical software to generate this.
 
#3
Thanks for your response, noetsi. Unfortunately, I have a lot of distributions, thus I cannot validate them graphically in a manual way. Any other recommendations?
 

noetsi

Fortran must die
#4
All of the statistical tests for normality like Anderson-Darling that I know of have low power. With ten cases your power is likely to be very low anyhow. So whatever the null is for a given test is unlikely to be rejected even if it should be. That makes all these tests doubtful. Other than gather more data (which would be the best solution) the only thing I can think of is to chose one of them and run it. You should note the potential problems with low power (if the person reading it has any statistical background they will know this already, but it is still worth documenting in your comments).

I don't think there is a good solution without more data - just chose a common method like Anderson-Darling that is well known.