Author: Walter Koroljow
Date: 08:09:02 02/03/01
Go up one level in this thread
On February 01, 2001 at 23:33:10, Uri Blass wrote: >On February 01, 2001 at 22:58:59, Uri Blass wrote: ><snipped> >>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. > >To make it clear you can calculate a probabilty for something that does not >happen and to alculate 1- in order to calculate the probability that it happens >but you assume the same space of events. > >When you say "I assume the null hypothesis" you change the space of events. > >The thing that is called the level of confidence is not something that has no >importance because if the level of confidence is 99% then the probability >(before knowing the result) of doing a mistake by deciding that the winner is >better is at most 1%. > >It means that you get a wrong result in at most 1% pf the cases but it does not >mean that you get right result in 99% of the cases and it is possible that you >get no result in 97% of the cases,get a right result in 2% of the cases and get >a wrong result in 1% of the cases and it means that you are correct only in 2/3 >of the cases that you make a decision. > >Uri On February 01, 2001 at 23:33:10, Uri Blass wrote: >On February 01, 2001 at 22:58:59, Uri Blass wrote: ><snipped> >>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. > >To make it clear you can calculate a probabilty for something that does not >happen and to alculate 1- in order to calculate the probability that it happens >but you assume the same space of events. > >When you say "I assume the null hypothesis" you change the space of events. > >The thing that is called the level of confidence is not something that has no >importance because if the level of confidence is 99% then the probability >(before knowing the result) of doing a mistake by deciding that the winner is >better is at most 1%. > >It means that you get a wrong result in at most 1% pf the cases but it does not >mean that you get right result in 99% of the cases and it is possible that you >get no result in 97% of the cases,get a right result in 2% of the cases and get >a wrong result in 1% of the cases and it means that you are correct only in 2/3 >of the cases that you make a decision. > >Uri Your objection is eliminated if the right hypotheses are used and correctly interpreted. Let We = win expectancy of player A. Then the simplest hypotheses to use are: H0: We >= 0.5 H1: We < 0.5. If we reject H0, we necessarily accept H1. B is the better player at the confidence level of our test. If we choose, as hypotheses: H0: We = 0.5 H1: We (not =) 0.5, then rejecting H0 does show the players are unequal, but does not say who the better player is. By the way, your argument using Bayes' theorem in another post is quite right, but not useful for computation as I am sure you know. One has to assume a value for win probability to begin with. Cheers, Walter
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