May 31, 2007

Statistical analysis of Scottish shows good correlation

The piping rankings from judges in each grade at the 2007 Scottish Pipe Band Championships show good consistency, with the exception of the Grade 3A event, according to Tim Murphy, a well known snare drummer who teaches statistics at Brock University in Ontario.

As he did for the 2006 World Pipe Band Championships, Murphy assembled scatter-plot graphs for this year’s Scottish, and concluded that “all of the contests appear to be pretty consistent except Grade 3A.”

The graphs of piping judges’ results for each event are available here, in Adobe Acrobat pdf format.

“When there is good agreement between judges you should see a pattern that is linear and slopes up to the right,” Murphy said last year. “This indicates that the two judges are each placing bands in comparable positions. In this case, the correlation will be positive. If one judge had the band ranked high, the other judge also had them ranked high – no necessarily the same, but in the same general range.”

He adds that “Sig” – included in each chart – is “the probability of results happening simply by random chance. The probability of the other contests results being that consistent simply by chance range from essentially 0 (.001, .003, etc, the majority of contests) up through Grade 4A, at .075 and Grade 3A at .233. Less than .05 is considered statistically significant – in other words if the probability of these results simply by chance is less than one in 20. Therefore, the results in Grade 3A would have been that least that scattered about one in four times (.233) if the placings had been drawn from a hat randomly.”

The RSPBA’s system does not allow for judges to confer with one another before handing in their results. The organization tried “consultative judging,” where judges convened to discuss their results and potential amend their scores, in the 1980s and early ’90s, but discontinued the practice.


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