Hi everybody, sorry if this is a daft question but it's one I'm struggling to find an answer to (have googled etc. before posting here). I'm trying to up my stats knowledge to beyond "push this button  ifthisthenthat", and I've been reading more about the various statistical tests for normality. I understand a bit about their limitations with large sample sizes, but the particular dataset I'm working with is small, so I would like to understand a bit more about how to interpret various figures.
My specific questions are:
a) what are the pros/cons of using z scores of skewness/kurtosis versus the KolmogrovSmirnov/ShapiroWilk tests to make a judgement about normality? As far as I can tell, they're both indications of the probability of a distribution being nonnormal, but I'm not sure exactly how they work differently.
b) what does it mean/what should you do if they give different results (i.e. one suggests significant skew/kurtosis and the other doesn't? I get that it's useful to use one to confirm the results of the other, but what if the result is disconfirming?
To give an example for question b, I have a variable that returns the following result:
Skewness: .767
ZSkewness: 1.82
Kurtosis: .364
ZKurtosis: 1.37
KS value: .172 (p = .020)
SW value: .910 (p = .013)
So as far as I understand it, the z scores suggest that the variable isn't significantly nonnormal (because the z values are less than 1.96), but the KS/SW tests suggest that it is significantly nonnormal? What does this pattern of values mean, and which is better to go with? Have attached an image of the histogram & descriptives if that helps to make sense of it......
Many thanks for your help.
My specific questions are:
a) what are the pros/cons of using z scores of skewness/kurtosis versus the KolmogrovSmirnov/ShapiroWilk tests to make a judgement about normality? As far as I can tell, they're both indications of the probability of a distribution being nonnormal, but I'm not sure exactly how they work differently.
b) what does it mean/what should you do if they give different results (i.e. one suggests significant skew/kurtosis and the other doesn't? I get that it's useful to use one to confirm the results of the other, but what if the result is disconfirming?
To give an example for question b, I have a variable that returns the following result:
Skewness: .767
ZSkewness: 1.82
Kurtosis: .364
ZKurtosis: 1.37
KS value: .172 (p = .020)
SW value: .910 (p = .013)
So as far as I understand it, the z scores suggest that the variable isn't significantly nonnormal (because the z values are less than 1.96), but the KS/SW tests suggest that it is significantly nonnormal? What does this pattern of values mean, and which is better to go with? Have attached an image of the histogram & descriptives if that helps to make sense of it......
Many thanks for your help.
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