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> Note: In all of the following plots, the white line is the mean and the shaded blue area is the 95% confidence interval [for the mean of moves-per-game] Is c
by jcrites 12y ago
> Note: In all of the following plots, the white line is the mean and the shaded blue area is the 95% confidence interval [for the mean of moves-per-game]
Is confidence interval the right statistical concept to use when characterizing this data set? It seems like it would be more meaningful to examine how various percentiles of "moves per game" change over time rather than plotting a confidence interval around the mean.
In particular, the mean moves-per-game that he displayed is (I assume) the actual mean of his data set. It's not an estimate of the mean of some larger population of games, if I'm understanding the article correctly. So what does it mean to display a confidence interval for a parameter that's known rather than been estimated?
It seems more interesting to treat the data set as the population and analyze how it changes over time. For example, I'd be interested to see a graph of 5th, 50th, and 95th percentile of match length. I notice that the confidence interval is shrinking around his mean -- is that really reflecting that percentiles are converging on the mean because of changes in play style? Or have I misunderstood and the data set is being treated as a random sample of some larger population of chess games? (In that case, since there are more games in his data set in later years, it is unsurprising for the confidence interval to shrink. Whereas if the percentiles of match length are converging on the mean, then I think that's pretty interesting.)
- rhiever 12y ago>In particular, the mean moves-per-game that he displayed it is simply the actual mean of the data set. It's not an estimate of that mean, if I'm understanding the article correctly. So what does it mean to display a confidence interval for a parameter that's known rather than been estimated? Technically, I don't have the "true" mean because this data set isn't a set of all games ever. As such, I'm treating the games I have as a sample of all games ever, and providing an estimate of how confident I am in the mean I'm reporting. >I notice that the confidence interval is shrinking around his mean -- is that because there are more recorded games Exactly! Law of large numbers.
- deleted 12y ago[deleted]
- jsweojtj 12y agoI have to admit that I (also?) was expecting the shaded region to give something like the standard deviation about the mean, not the confidence in the mean.