Author: Joseph Ciarrochi
Date: 19:29:51 02/04/06
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Hi allesandro Yes, the big jumps do tend to be more likely at lower sample size. This has to do with the limited number of distinctions between scores at lower N size and the fact that scores don't convenientty begin and end at our various cut-off leves. For example, in a sample of 10, there are twenty distinctions, with intervals at 5% (e.g., difference between 7 and 7.5. You can't have a 7.2). In contrast, at higher sample sizes, the distinctions are finer. With a sample of 100, the intervals are at .5% (77 versus 77.5). Ok, so with a resampling procedure, what you do is draw x number of samples of size n. with sample of 10, you might get an output that looks something like this. percentile Score 9% 6.5 8% 7 7% 7 6% 7 5% 7 4% 7 3% 7.5 2% 7.5 1% 8.0 I would like to use a 5% cut-off, but if i choose 7 as the cut-off, as you can see that value or greater occurs more than 5% of the time. So i go up one to 7.5. this conservative cut-off garentees that 5% or less of the scores occured at that level in a sample of ten, "going up 1" means a 5% shift, wheras in a sample of 100, it means only a .5% shift. thus, The discontinuities you observe should reduce with increasing sample size. I think i'll redo the whole table and try takeing 100,000 samples. I'll see if this smooths things out a little, though the discontinuity issue is still going to be there. best Joseph On February 04, 2006 at 18:51:05, Alessandro Scotti wrote: >On February 03, 2006 at 21:12:59, Joseph Ciarrochi wrote: > >>On February 03, 2006 at 20:10:23, Alessandro Scotti wrote: >> >>>On February 03, 2006 at 19:26:43, Joseph Ciarrochi wrote: >>> >>>>Here is the stats table i promised Heinz and others who might be interested. >>> >>>Hi Joseph, >>>I find this information very useful and would like to put it on my site >>>(http://www.ascotti.org/programming/chess/chess.htm), with proper credit of >>>course. Would that be ok? > >Thanks Joseph! :-) I have put your post in the following page: > >http://www.ascotti.org/programming/chess/two_engines.htm > >There is one thing that puzzles me though. If I do the difference between the >value in the third and second columns, I get the following: > >10 games -> 10 >20 games -> 5 >30 games -> 3.3 >40 games -> 5 >50 games -> 3 >75 games -> 4.7 > >I know pretty much nothing of statistics, but intuitively I cannot account for >those big "jumps"... why they happen?
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