Help with Shapiro-Wilk Test interpretation.

FrostScYthe

Hi everyone,

I need to make sure that I'm interpreting the Shapiro WIlk test correctly. This is how I'm doing the interpretations:

Set 1
CI = 95%
n = 15
Shapiro W = .92
p = .171

I think this set is distributed normally because p is the probability that it is not normal, so the probability that it isn't normal is 17.1% right?

Set 2
CI = 95%
n = 15
Shapiro W = .95
p = .502

This set is slightly more probable to be not distributed normally because p is 50.2 %

Any help appreciated,

Ed.

Enuma_Elish

Since CI = 95% implies a critical "alpha" value of 5%, the null hypothesis of normality cannot be rejected for either set (at the 5% level of statistical significance).

FrostScYthe

But I can reject Set 1, if I chose an alpha like 20% right?

Enuma_Elish

Correct.

FrostScYthe

Looking at this test more carefully. This test is more for testing whether a sample comes from a population that is not normally distributed.

I mean if the p > alpha then you can't reject the probability that it might be Normal (but it is just a probability, it doesn't tell you how probable is it that it is normal?). What is a good test to determine whether a distribution is Normal or not?

EnumaElish

If p > alpha then you can't reject the NULL HYPOTHESIS that THE DISTRIBUTION IS Normal.

When testing a hypothesis you cannot ever accept the null hypothesis, you can either reject, or fail to reject. There is no statistical test that will tell you the distribution is normal; they can only tell whether you can or cannot reject normality. See this paper.

I suggest using tests based on skewness and/or kurtosis; two examples are the Jarque–Bera test and D'Agostino's K-squared test. If you don't need a formal test result, you can also make a Q-Q plot and decide visually.

FrostScYthe

Thank EnumaElish for clarifying that for me :).