MATLAB: Does KSTEST not reject the null hypothesis when the P-value is less than the significance level in Statistics Toolbox 6.2 (R2008a)

Statistics and Machine Learning Toolbox

The KSTEST is not rejecting the null hypothesis alhough the P-value received is less than the significance level. I have set the significance level of 0.05 and received a P-value of 0.03, but the null hypothesis was not rejected.

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The function KSTEST by default, performs a two-tailed test. In case of such tests, if the significance level is alpha (0.05 by default), the null hypothesis is rejected if the P-value is less than alpha/2. To account for the tail in the computations, you have to specify the 4th input to the KSTEST function ('tail').

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MATLAB: Kstest and hypothesis rejecting

When in doubt, use help()

help kstest
 kstest Single sample Kolmogorov-Smirnov goodness-of-fit hypothesis test.
    H = kstest(X) performs a Kolmogorov-Smirnov (K-S) test to determine if
    a random sample X could have come from a standard normal distribution,
    N(0,1). H indicates the result of the hypothesis test:
       H = 0 => Do not reject the null hypothesis at the 5% significance

       level. 
       H = 1 => Reject the null hypothesis at the 5% significance
       level.

The null hypothesis depends on your inputs. Again, from the documentation using doc(ktest):

Test the null hypothesis that the data comes from a normal distribution with 
a mean of 75 and a standard deviation of 10. Use these parameters to center 
and scale each element of the data vector since, by default, kstest tests for 
a standard normal distribution.
x = (test1-75)/10;
h = kstest(x)

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MATLAB: Kstest and hypothesis rejecting

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