Author: Amir Ban
Date: 02:27:27 02/02/01
Go up one level in this thread
On February 01, 2001 at 22:58:59, Uri Blass wrote: >On February 01, 2001 at 17:26:30, Amir Ban wrote: > >>On February 01, 2001 at 17:18:46, Uri Blass wrote: >> >>>On February 01, 2001 at 17:08:36, Amir Ban wrote: >>> >>>>On January 31, 2001 at 20:17:17, Bruce Moreland wrote: >>>> >>>>>I expressed very forcefully that a 10-0 result was more valid than a 60-40 >>>>>result. >>>>> >>>>>I've done some experimental tests and it appears that I'm wrong. >>>>> >>>> >>>>No, you were right the first time. Check again. >>> >>>The question is what is the meaning of a more valid result. >> >>Valid in the sense of demonstrating who is stronger. >> >> >>> >>><snipped> >>>>10-0 gets better than 99.9% confidence for the winner to be better. >>>> >>>>60-40 has about 95% confidence. >>> >>>I agree but the word confidence is misleading because you may ask the question >>>what is the probability that the winner is the better player and the confidence >>>does not give an answer to it. >> >>That's exactly what it answers. >> >>Amir > >From your previous post: > >"you assume the null hypothesis, which is that the >result is NOT significant and is a random occurrence between equals." > >You cannot calculate the probability that the winner is the better player by >assuming a model that does not exist. > This is what is taught in universities and is written in textbooks. If it doesn't work, then statisticians have been talking nonsense for centuries. It makes simple sense: You find the significance of an event by calculating the probability that the event is insignificant. >I can give a simple example: > >Suppose that the better program has 51% chance to win and 49% chance to lose >when the results of games are independent and the only missing data is which >program is better. > This is a completely artificial assumption. Where does it come from ? What you show is that if the two opponents are almost equal, then both have about the same probability to win 10-0. This is true, but not relevant, because the question is whether the opponents are equal to start with. Amir >Suppose you also see 10-0 result. > >you need to calculate p(the winner is better /the result is 10-0) > >You do it by base rule > >You know that: > >1)p(the result is 10-0)=0.51^10+0.49^10 >2)p(the better player is the winner and the result 10-0)=0.51^10 > >The probability that the winner is the better player after you see 10-0 result >is not the level of confidence but 0.51^10/(0.51^10+0.49^10). > >Uri
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