... it would be very likely that the ... conspirators' votes would be the extremes that would be discarded, as the culprits tried to inflate one skater's marks and low-ball another's.
Seat nine judges, no random draw, then trim the mean by discarding the bottom two and the top two for each line.
nylynnr said:As always with IJS, though, the trouble is it is rather complicated and most folks don't want to sit and hear (or read!) a half-hour explanation.
Nowadays, it's far harder for judges to sit there and calculate precisely where the GOEs and PCS scores they enter will put skaters in the order.
The bottom line for determining the precision of the results is how many sets of marks are in the calculation -- and under the new panel size there are five sets of marks in the calculation. It doesn't matter how you get down to the five sets of marks. What drives the mathematical "quality" of the scores is the number 5.
I think throwing out the high and low scores muddles that a little.
Actually, I was thinking of the extreme case. Suppose you sat 9 judges, "counted" all nine, then took the median. This reduces the magic number from 5 all the way down to 1.
I don't agree. All nine marks are being used to determine the median in your example.
And in all cases, the median (for PCs) could differ from the mean of the distribution by up to 0.25 points while the standard deviation of the mean for marks is typically 0.13 points.
In other words, I would expect the trimmed mean of random samples of size 7 to behave more like the untrimmed mean of samples of size 7 than like the untrimmed mean of samples of size 5.
Hm!The most important is the assumption that there is an objective quantifiable thing, external to and independent of our methods of measurement, that is "out there" waiting to be measured.
In contrast, the branch of statistics that looks at means, standard deviations, etc., rests on a number of assumptions that I do not think are satisfied in the case of figure skating judging. The most important is the assumption that there is an objective quantifiable thing, external to and independent of our methods of measurement, that is "out there" waiting to be measured.
gsrossano said:Further, in staking out that position you are saying that there is no point in discussing the mathematics of the scores since a skating program cannot be measured;...
Ordinals are quite mathematical enough and express more honestly what is really going on in the "second mark" than do add-up-the-points methods. Under ordinal judging we can still do plenty of mathematical analyzes. I do not agree that because something cannot be measured therefore it cannot be judged, or that the judging cannot be subjected to mathematical scrutiny.
gsrossana said:Even ordinals are a measurement -- a relative measurement but still a measurement -- and have a mean, a median, a standard deviation and an an associated uncertainty in the final results.