statistical power of lillietest

In order to asses normality of data, I run a lillietest on the following two variables A and B:

A       B    
0.000   0.125
1.500   0.125
2.375   1.125
2.375   0.125
5.625   0.250
4.250   0.000
0.750   0.000

p=0.37  p=0.008
H0=1    H0=0

Responses accept H0 for A and rejects H0 for B.

Given the small size of sample (N=7), how can I check the statistical power of this test? I see there is a function for this, called sampsizepwr . Is it the right function? In positive case, what type of argument 'testtype' should I furnish? 'z' 't' or 'p'? Thanks, Valerio

Answer 1

[Anshuman]

Hello,

To check the statistical power of the Lilliefors test, using a function like "sampsizepwr" in MATLAB would not be a good idea as this function is typically used for calculating sample sizes or power for hypothesis tests such as z-tests, t-tests, or proportion tests. It may not be directly applicable to the Lilliefors test for normality.

Here's what you can do:

• Simulate a large number of datasets from a known distribution (normal and non-normal) with the same sample size (N=7).
• Run the Lilliefors test on each simulated dataset.
• Determine the proportion of tests that correctly reject the null hypothesis when the data is non-normal (this gives you the power of the test).

Hope it helps!