using a monte carlo simulation Im just trying to test the null hypothesis for normality in a sample that splits N values into 2, using the first N/2 values to estimate the sample mean and variance, and the second N/2 values to apply the test based on these moment estimates (the Normal distribution tested against will use the sample mean and variance estimated from the first N/2 values). I am using a 95 % confidence interval and when I do 10000 iterations and test all their p values I am getting an acceptance rate of approx 85% and was wondering could some one explain the reason why this is not 95~% and what the reason for the rejection rate is?
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1If you are testing for normality, there are a lot of more specialized tests that are more efficient. Have you looked at a normal probability plot of your data? – Dec 13 '13 at 15:38
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The answer to your question is explained in several answers [here](http://stats.stackexchange.com/questions/45033/can-i-use-kolmogorov-smirnov-test-and-estimate-distribution-parameters) – Glen_b Dec 13 '13 at 16:06