Author: Bruce Moreland
Date: 18:40:37 09/04/99
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On September 04, 1999 at 21:05:06, James T. Walker wrote: >Well, don't put words in my mouth. If I had a score of 502-498 I could say that >they are very even with a high degree of confidence. I would not be stupid >enough to say that "A is stronger than B". However if I had a score of 5.0 to >5.0 I would not be so confident that they were even. That's what I mean by >having a higher probability that your conclusion would be correct. By the same >reasoning if I had 600-400 I would be more confident that A is better than B if >the score were only 6-4. So I stick to my statement. More data gives you a >higher degree of certainty. (Just don't mis-interpret the data) It depends upon what you conclude. If the ratio of wins to losses is the same, more data means you can make a more certain conclusion, unless the score is exactly 50%. But if the match is closer, it may be possible that you can say "A is better than B" with less confidence. >>If you play 100 games, and A beats B by a score of 100-0, the statement "A is >>stronger than B", is a very weak statement, it is a conservative conclusion. >>The odds that A really is stronger than B are almost 100% in this case, whereas >>in the previous case the odds that A is stronger than B are only slightly more >>than 50%. > >There would be very little argument in this case but again you are interpreting >the data incorrectly to make your point. But "A is stronger than B" is >perfectly valid and nothing weak about it. If you said "Maybe A is better than >B" that's a weak statement but I wouldn't say that given the above data(100-0). >Even in the face of a small probability that the next 100 might be 0-100. What I mean by "weak" is that it is an understatement, and sorry if I am using the wrong terminology. I am saying that if you weaken what you say, meaning that if you make what you say more conservative, the probability that it is correct increases. bruce
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