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NFL Forum
Results (and computation)
Posted By: Colin Caster In Response To: Sure (Colin Caster)
Date: 20 Aug 01, 1:02 pm
Two non-independent correlations can be tested for significance by:
(r12-r13)(SQRT((n-1)(1+r23)/((2((n-1)/(n-3))|R|)+((r12+r13)^2)((1-r23)^3)/4))), where |R| is the determinant of the 3X3 R matrix (i.e., (1-r12^2-r13^2-r23^2)+(2r12r13r23)). It is distributed as t with n-3 df.
We're interested in testing the difference between "expected wins" and actual wins in predicting wins in a subsequent year, so:
Wins in year 2 is x1;
"Expected wins" in year 1 is x2;
Actual wins in year 1 is x3;
r12 is the correlation between expected wins, year 1, and wins, year 2; according to docriver's data from the past 12 years (n=346), this correlation is .408.
r13 is the correlation between wins, year 1, and wins, year 2; its value is .366.
r23 is the correlation between expected wins and actual wins in year 1; its value is .908.So, substituting above: |R| = .146.
t = (.408-.366)(SQRT((345)(1+.908)/((2((345-1)/(345-3)).146)+((.408+.366)^2)((1-.908)^3)/4) = .042(SQRT(658.26/.294)) = 1.99. This value is just barely significant at p<.05, two-tailed.
Conclusion: this is a very small difference between correlations, but they were unlikely to have been drawn from the same population. Docriver's "expected wins" should be considered more useful than actual wins until demonstrated otherwise with additional data.
Nice work, docriver. It is possible that a slightly different exponent will work better, but, generalizing from the baseball research, not much better. Cheers,
CC
- Pythagorean Formula for wins -- docriver -- 16 Aug 01, 12:02 pm
- Pythagorean -- Editor -- 16 Aug 01, 1:33 pm
- tails? -- docriver -- 16 Aug 01, 1:57 pm
- Tails -- Editor -- 16 Aug 01, 3:50 pm
- Starting point -- Colin Caster -- 16 Aug 01, 9:40 pm
- Starting point -- Colin Caster -- 16 Aug 01, 9:40 pm
- Tails -- Editor -- 16 Aug 01, 3:50 pm
- 1988 thru 2000 data -- docriver -- 17 Aug 01, 2:51 pm
- also.. -- docriver -- 17 Aug 01, 3:01 pm
- Nice work! Testing significance of correlation differences -- Colin Caster -- 19 Aug 01, 1:01 pm
- email stats? -- docriver -- 19 Aug 01, 7:18 pm
- Sure -- Colin Caster -- 19 Aug 01, 10:13 pm
- Results (and computation) -- Colin Caster -- 20 Aug 01, 1:02 pm
- Results (and computation) -- Colin Caster -- 20 Aug 01, 1:02 pm
- Sure -- Colin Caster -- 19 Aug 01, 10:13 pm
- Nice work! Testing significance of correlation differences -- Colin Caster -- 19 Aug 01, 1:01 pm
- Re: Bill James -- T. Hopper -- 19 Aug 01, 2:01 pm
- I am told that the exponent for college football is 1.68 (nt) -- Colin Caster -- 19 Aug 01, 10:16 pm
- tails? -- docriver -- 16 Aug 01, 1:57 pm
- Pythagorean -- Editor -- 16 Aug 01, 1:33 pm
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