Author: KarinsDad
Date: 20:39:44 03/03/99
Go up one level in this thread
On March 03, 1999 at 17:15:26, Don Dailey wrote: >On March 03, 1999 at 14:30:44, KarinsDad wrote: > >>On March 03, 1999 at 12:40:05, Don Dailey wrote: >> >>[snip] >>> >>>I'm tired of speculating however. The truth of the matter is >>>that Deep Blue won. The only scientifically valid conclusion >>>you can draw from this is that it is slightly more likely that >>>Deep Blue is the better match player. >> >>Actually, this conclusion is just as speculative as a conclusion in the other >>direction. > >Woops, a little mistake by you, better review your theory. Ok, I will. > >If you do an ELO rating of the match you will discover that Deep Blue >will get the higher rating. What does this mean? It means you there >is small degree of statistical confidence that Deep Blue is a better >player. Not much, but some. And this is EXACTLY what I said. Actually, you did not say this at all. You said and I quote "The only scientifically valid conclusion you can draw from this is that it is slightly more likely that Deep Blue is the better match player". This is different than what you said in this message: "It means you there is small degree of statistical confidence that Deep Blue is a better player" (this was a little garbled, but I think I got the gist). I agree that there may be a small degree (note the words may and small) of statistical confidence (not evidence) that Deep Blue is a better match player. But a statistical conclusion (which is what you originally stated) on this cannot even be considered. There is major difference between a statistical conclusion and a statistical confidence. Also, consider that after 1 game, Kasparov was in the lead. Through games 2 through 5, they were tied. So, if the sample size would have been smaller, you may be using the exact same logic to argue that there is a small statistical confidence that they are virtually equivalent players. > >Saying that it is just as likely that Kasparov is better because he >LOST (huh???) indicates to me that you might need to brush up on >probability and statistics. I never said this. Please do not put words into my writing. I said that a statistical CONCLUSION in one direction is just as speculative as in the other direction. > >Your comment does exposes a very common misconception that people have >when it comes to probability and statistics. Your next comment >exposes the roots of this, where you seem to indicate that the size of >the sample tells you whether you can say something conclusively. You >say, "Scientifically speaking, the sample set for either conclusion is >too small to be conclusive." This is actually true, but the sample >size has nothing to do with it unless the sample size is INFINITE and >I don't think you meant that, especially if you don't even understand >basic probability theory. Actually, I might surprise you with the amount of probability theory I know as I used to teach it. As to the size of a sample, it is commonly understood in statistical theory that you do not need an infinite sized sample to come to a conclusion. A relatively large sample size (or statement) will do in most cases. In actuality, for random samplings, it is normally considered that the smallest number of samples that can even be considered is 5 and the largest is several hundred. But, of course, it depends on what you are trying to measure and either extreme is undesirable. If you use too large of a sample set, it can result in insignificant effects being measured and assigned significance. For example, let’s say that Kasparov played Deep Blue 500 times and it was determined that Kasparov loses 1.7% more times when the games are played before 12 noon than after 12 noon. This information may be worthless, but worthless or not, it may not necessarily even be observed in the 6 game match. If you use too small of a sample set, it can also result in insignificant effects being measured and assigned significance. Let’s say that you flip a coin six times and you come up with heads 4 times and tails 2 times. If from this sample set of data you come up with the conclusion that heads will turn up more than tails, you are mistaken. Even if you state that you have a statistical confidence that heads would show up more times than tails, you would be mistaken (assuming the coin is balanced and flipped from random positions, heights, etc.). > >Now it's possible you are using the gray definition of "conclusive." >You know, the one where you play Kasparov a 24 game match and he beats >you 24-0. Then we might say, "he has proven conclusively that he is >the better player." He hasn't REALLY proven he is better, but almost >any fool would bet on him for the second match! But it doesn't matter >which definition you use, it doesn't invalidate my assertion that >based on the result of the match, it is SLIGHTLY more likely that Deep >Blue is the better player. Again, this is not what you wrote. You may have meant this, but this is not what you wrote. In fact, it appears that you were using a "gray definition of conclusive" and really meant that you had a confidence when you first mentioned it. > If you don't understand this, then you >just don't understand that a 2800 player will probably beat a 1200 >player and you shouldn't be trying to correct people. My error. I thought I knew the difference between the two. > > >I don't mind being corrected if I am wrong, but at least make sure you >know what you are talking about. I don’t mind being corrected if I am wrong, but at least make sure you know what you are talking about. KarinsDad :) :) > >- Don > > > > > >>Scientifically speaking, the sample set for either conclusion is too small to be >>conclusive. Statistically, there isn't enough evidence to determine the better >>match player. >> >>KarinsDad > > > > > > > > > >>> Anything more than this >>>is a very fallible judgement call and speculation. >>> >>[snip]
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