Author: Walter Koroljow
Date: 14:16:00 02/04/01
Go up one level in this thread
On February 04, 2001 at 13:28:03, Uri Blass wrote: >On February 04, 2001 at 12:48:36, Walter Koroljow wrote: > >>On February 03, 2001 at 18:58:36, Uri Blass wrote: >> >><snip> >> >>>Assume level of confidence 97% in all of your tests. >>> >>>If you reject H0 in 3% of the times then it is possible that you are always >>>wrong when you reject H0(for example when always We=0.5). >>> >>>If you reject H0 in 50% of the times then you are wrong only in at most 6% of >>>the cases that you reject H0(to be more exact I need to say if the probability >>>to reject H0 is 50% but the probability is something that you do not know and >>>the % of the cases that you rejected H0 practically is something that you know). >>> >>>Uri >> >>If I interpret you correctly, I disagree. Let us work at the 97% confidence >>level with H0 as before. >> >>We agree that the highest Type I error rate (false rejection of H0) occurs if, >>for each test we run, we have We = 0.5. In fact the error rate will be exactly >>3% then. If We = 0.8, the error rate will be less -- assume 1% for convenience. >> Let me make my case by example. >> >>Suppose that in the population that we test repeatedly we have: >> >>34% We = 0.5 (H0 true) >>33% We = 0.8 (H0 true) >>33% We = 0.2 (H0 false). >> >>Then the Type I error rate for the case H0 true is (.34*3% +.33*1%)/(.34+.33) = >>2.01% >>This is less than 3%. I cannot see how the error rate could ever exceed 3% for >>any mix of We. >> >>For the case We = 0.2, a Type I error is impossible since H0 is false. So the >>overall Type I error rate >>will be: >> >>(.34*3% + .33*1% + .33*0%)/(.34+.33+.33) = 1.35%, of course also less than 3%. > >Basically I guess that we agree and there is some misunderstanding in the >language > >I will try to explain it more clearly only by math. > >From my post: >"If you reject H0 in 3% of the times then it is possible that you are always >wrong when you reject H0(for example when always We=0.5)." > >Explanation: > >If P(You reject H0)=0.03 then it is possible that >p(you are wrong| you reject H0)=1. > > >From my post: >"If you reject H0 in 50% of the times then you are wrong only in at most 6% of >the cases that you reject H0(to be more exact I need to say if the probability >to reject H0 is 50% but the probability is something that you do not know and >the % of the cases that you rejected H0 practically is something that you >know)". > >Explanation: > >If p(You reject H0)=0.5 then >p(you are wrong| you reject H0)<=0.06 > >Uri O.K., I agree. Maybe we should just talk mathematics. Spoken language is very vague.
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