Hi,

The rule of thumb says that from 50 cases onwards you have to use a K-S test. If it is lower than that it is preferable to use Shapiro Wilk.

But despite of this cutting point If I would to test the distribution of my sample I won't just use this test. I would also check the skewness and the kurtosis of my sample. Moreover, I would check the graphical representation of my distribution. 

As Rainer says, sometimes K-S and S-W tend to tell you that your sample is not normally distributed and if you check further you see that the assumption of normality is not that highly violated. 

In order to give you more ideas, maybe you could share us more information. 

Hope this helps!

You can conduct the tests with every sample size you want, but it may not be useful ;-)

Shapiro-Wilk showed that they had a good sensitivity to detect deviations from normality with n=20. But both test (as well as K-S with Lillefors adjustment) are too sensitive with growing N. I.e., very often you will find a deviation from normal, which has no detremental effects for your analysis. But of course, this depends on your research question. Maybe you could give some additional information?

Hi,

The rule of thumb says that from 50 cases onwards you have to use a K-S test. If it is lower than that it is preferable to use Shapiro Wilk.

But despite of this cutting point If I would to test the distribution of my sample I won't just use this test. I would also check the skewness and the kurtosis of my sample. Moreover, I would check the graphical representation of my distribution. 

As Rainer says, sometimes K-S and S-W tend to tell you that your sample is not normally distributed and if you check further you see that the assumption of normality is not that highly violated. 

In order to give you more ideas, maybe you could share us more information. 

Hope this helps!

For example, I have 1000+ cases. I have to test if distribution in variable Body weight is normal. If I choose K-S test, my question is why this test? Why not S-W test? Concidering large number of cases, is there any difference between this two tests, or is it irrelevant which test will I use?

In their two seminal papers (Shapiro & Wilk, 1965; Shapiro, Wilk, and Chen, 1968) they only simulated data with a maximum N of 50. So they seemed to concentrate on improving the test power for small sample sizes. In turn this means that the K-S seemd to work quite well for large sampe sizes. And this is what is recommended in text books: small sample sizes-> use S-W, large sample sizes -> use K-S(with Lillefors adjustment).

But your quesstion could also be extended: why use K-S or S-W at all, in their 1968 paper, they tested 9 different approaches to test normality. I think it is cumbersome to argue for or against each of them. K-S and S-W are somewhat the standard, but as Juan Carlos and I explained, with large N, they will significant probably almost every time, although the distribution is quite normal. Do not rely only on this parameters, but have a look at the data itself and its distribution.

As Howell for example argued, the K-S test is of no use at all!

Howelll (2013) Statistical Methods for Psychology. Wadsworth.

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality

(complete samples). Biometrika , 52(3/4), 591–611.

Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968). A comparative study of various tests for normality. Journal of the American Statistical Association, 63(324), 1343–1372

Bobane,

As Juan Carlos and Rainer alluded, the differences among the tests rest on the sample size and specifically n = 50 as the cut off. You might find the attached Monte Carlo simulation useful. The authors provide a good overview of literature in the Introduction.

Cheers,

Branko

 Mr. Duesing, Mr. Saravia and Mr. Miladinovic,

Thank you for your advices. Your informations are very useful to me.

for example:

i have study with 6 groups and each group compose of 10 samples, which test of normality i should use? S-W or K-S

I prefer using Shapiro Wilk over KS, regardless of sample size (Article Comparing the performance of normality tests with ROC analys...

However, for large sample sizes i'd avoid using the tests at all. I'd instead plot the distribution of the variable and judge it myself. The reason for this is that with large distributions both SW and KS are very likely to reject the null hypothesis even for small deviations from normality.

Sometimes it seems that the Shapiro-Wilk test is very suitable for samples less than 50. The power of this test increases with increasing sample size, and vice versa, in a small sample number, this test is not satisfactory. The critical points of this test were initially calculated for sample sizes of up to 50 (Shapiro and wilk, 1965) and in another article up to a sample size of 5000. Therefore, in some articles, the power of this test has been evaluated to a sample size of 50, and it is believed that the Shapiro-Wilk test is appropriate for a sample of less than 50.

Also both tests are used to check the normality of the data. The Shapiro Wilk test is appropriate for a small sample size of up to 50, and the Kolmogorov-Smirnov test is appropriate for samples larger than 50, and the Kolmogorov test power is less than Shapiro Wilk's test.