eelbrain.test.lilliefors(data, formatted=False, **kwargs)

Lilliefors’ test for normal distribution

The Lilliefors test is an adaptation of the Kolmogorov-Smirnov test. It is used to test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution, i.e. does not specify the expected value and variance.

  • data (array_like) –

  • formatted (bool) – Return a single string with the results instead of the numbers.

  • kwargs – All keyword arguments are forwarded to scipy.stats.kstest().


  • D (float) – The D-value of the Kolmogorov-Smirnov Test

  • p_estimate (float) – The approximate p value according to Dallal and Wilkinson (1986). Requires minimal sample size of 5. p is reasonably accurate only when it is <= .1 (cf. Dallal and Wilkens).


Uses the scipy.stats.kstest implementation of the Kolmogorov-Smirnov test.


Dallal, G. E. and Wilkinson, L. (1986). An Analytic Approximation to the

Distribution of Lilliefors’s Test Statistic for Normality. The American Statistician, 40(4), 294–296.

Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov Test for Normality

with Mean and Variance Unknown. Journal of the American Statistical Association, 62(318), 399–402.