What to do when Kolmogorov-Smirnov test is significant for residuals of parametric test but skewness and kurtosis look normal? I have conducted a parametric test in a study, n=290. I want to assess whether the residuals of this test are normally distributed.


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*The  skewness and kurtosis of the residuals are -0.017 and -0.438 respectively. I think this is considered as normal. 

*Unfortunately, the Kolmogorov-Smirnov of the residuals has a p-value of 0.021. I think this is considered not normal. 


Question
What should I do when skewness and kurtosis look normal but Kolmogorov-Smirnov is significant? 
 A: 
In order to make sure that I can use parametric test, I need to make sure that my residual distribution is normal. 

There is really no way to demonstrate that you have exact normality, but that's okay because approximate normality will generally be sufficient for hypothesis tests in regression to work the way you want.

However, when I refer to the value of skewness and kurtosis of the residual, it is -0.017 and -0.438 respectively, where i think this is considered as normal. 

You can obtain values like that with residuals from a simple regression on normal data, but the kurtosis is just significant at the 5% level. 
(Technical aside: I used simulation to assess the significance of the kurtosis of residuals here; not knowing the number of predictors, I did it for both independent normals and for one predictor at the given sample size, both showed essentially the same p-value; results should be similar for regression with small numbers of predictors.)
This doesn't actually suggest a problem with the inference when doing a regression or correlation, however. Your data won't be exactly normal; the essential question is 'are the data so badly non-normal that the inference no longer has the properties you wish?'

Unfortunately, when i do kolmogorov-smirnov, the significant value is 0.021, which indicates the residual is not normal. 

What were the specified population mean and variance of the residuals for your KS test and how did you get such population values?

Could anybody please explain to me what to do. 

I suggest you don't do a hypothesis test to assess the suitability of the assumption of normality, but instead to look at diagnostic displays that show you how badly non-normal the data are.

Some pointers -
See the points here
Also see the discussion on this question
See the comments under this answer,
and the advice in this answer
Consider this advice
A: *

*If you are running one or more tests of normality, a rejection by one of the tests is enough to reject the normality. You can't cherry pick the normality test suite looking for a desired results, it's a dangerous approach.

*Look at this answer Kolmogorov-Smirnov test - reliability on other tests of normality. Basically, KS test is not good to test normality. The tests like Jarque-Bera will use the moments and are better than eye balling the skewness/kurtosis or KS test.
Let's see what is JB test statistics (mentioned in my answer in the above link): $jb=290/6*(0.017^2+0.438^2/4)=2.33$, the critical value at 300 observations and 5% confidence is 3.68, so JB test does not reject normality.
CORRECTION:
My conclusion: assuming that Kurtosis is corrected for 3, there is not enough evidence to suggest that the data is not normal based on JB test alone, but since KS test is rejecting it I'd still reject normality.
