Re: Lilliefors Test : 40 years

Why one should prefer the Lillifors´s test


An advice (if you allow me) Herman Rubin
Do not make definitive statements before to think closely what the problem is, and do not forget the context, namely that all values are imprecise at Statistical Grounds.
You said:
The Kolmogorov-Smirnov test is a good test if the correct distribution is used. If the population distribution is completely specified, there is no problem. If it is not, the distribution depends on the way parameters are estimated, translated appropriately.
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I add:
The Lilliefors´s Test has critical values that are 2/3 (approximately) shorter than he K-S ones. In consequence using the latter ones the confidence intervals are INCORRECTLY LARGER than they should be, fail to reject H0 (when we REALY should do so) is MUCH MORE PROBABLE than what the chosen K-S ALPHA VALUE seems to indicate.

___|_____________|___________
___Lilli________ K-S: mistaken ALPHA
___| fail to reject___ |

Numerical example (one tail)

____n=4________K-S = 0.565 (alpha=5%)
_______________Lilli. = 0.381

All values of the test statistics in [0.381, 0.656] are INDULLY failed to be rejected.


Good Test (as H.R. says) a Test that one cannot know the true ALPHA value? NO THANKS, I get rid of it!



Luis Amaral Afonso (The Moderator Destroyer)
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