phall
02-20-2007, 12:41 PM
In the K-S test section, it is stated after equation 14.3.8 that "the significance level of an observed value of D (as a disproof of the null hypothesis that the distributions are the same) is given approximately by the formula" P(D>observed)=Q_KS([f(N_e)D]).
Shouldn't that be "proof", not "disproof"? If D=0, the distributions must be the same, and P(D>observed)=1; i.e. 100%. If D goes to infinity, P(D>observed)=0; i.e. 0%. So the significance level given by Q_KS is the significance level that the null hypothesis has been proved, not the significance level that it has been disproved.
As it says in ksone on the next page, small values of P(D>observed) indicate a difference between the distributions being compared. It's 1-P(D>observed) that gives the significance at which the null hypothesis of the distributions being the same is disproved.
Shouldn't that be "proof", not "disproof"? If D=0, the distributions must be the same, and P(D>observed)=1; i.e. 100%. If D goes to infinity, P(D>observed)=0; i.e. 0%. So the significance level given by Q_KS is the significance level that the null hypothesis has been proved, not the significance level that it has been disproved.
As it says in ksone on the next page, small values of P(D>observed) indicate a difference between the distributions being compared. It's 1-P(D>observed) that gives the significance at which the null hypothesis of the distributions being the same is disproved.