I realized that I was not using a useful piece of information in my statistical analysis -- the time sequence of the scores. This makes a significant difference, because the scores are highly correlated by week.
If we calculate the sequence of JDG minus benchmark scores for each week, we get: -1 -1 -4 -2 -2 which has an average of -2, SSD=1.22, and SSD/sqrt(N) = 0.55 and sqrt(N)*AVG/SSD = -3.65 Using t-statistics, this gives a probability of 98.9% (assuming 4 degrees of freedom) that JDG's average score is lower than the benchmark's average score. Since the t-statistic for one-tail 0.975 and 4 degrees of freedom is 2.78, we can also say that we are 95% confident that JDG's score trails the benchmarks score by a value between -3.5 and -0.5. If we reverse JDG's "upset special", then JDG's score is almost as high as the benchmark's, although still slightly behind. On Mon, Jan 03, 2005 at 07:01:35AM -0500, Erik Reuter wrote: > > Both JDG and the benchmark went negative for week 17, with JDG again > trailing the benchmark by -2. The benchmark totaled -2 (6-8--2) and JDG > -4 (6-10). > > For the 5 games I tracked this season JDG trailed the benchmark by a > cumulative -10. Benchmark scored +26 (47-21--12) and JDG scored +16 > (48-32). > > >From these results, you might think that JDG's scores are significantly > worse than the benchmark, but statistically there is no significant > difference between the benchmark score and JDG's score after 5 games. > > The benchmark averaged +5.2 with a 95% confidence range of +1.2 to > +9.2, so statistically the benchmark is quite likely to have a positive > average score. JDG has an average of +3.2 with a 95% confidence range > of -1.3 to +7.7, so we cannot say with confidence that JDG's average > is above zero. > > Since the 95% confidence ranges of benchmark and JDG overlap, we > also cannot say with confidence that JDG's average is worse than the > benchmark's (perhaps if we tracked the scores for an entire season, but > I'm not interested enough to do that...) > > week 17: > -2 benchmark 6-8--2 > -4 JDG 6-10 > > cumulative week 13-17: > +26 benchmark 47-21--12 > +16 JDG 48-32 (* 1-4 *) > > Recap AVG SD SD/sqrt(N) > Benchmark: +7 +9 +4 +8 -2 5.2 4.44 1.99 > JDG: +6 +8 +0 +6 -4 3.2 5.02 2.24 > > *** > > Week 17 Benchmark favorites: > + Arizona+3 (Tampa Bay) > + Baltimore+11 (Miami) > - Buffalo+9 (Pittsburgh) > - Carolina+7.5 (New Orleans) > - Chicago+3 (Green Bay) > + Cincinnati+3 (Philadelphia) > + Denver+8.5 (Indianapolis) > - Detroit+3 (Tennessee) > - Houston+10 (Cleveland) > - Kansas City+3 (San Diego) > - Minnesota+4 (Washington) > + New England+13.5 (San Francisco) > - NY Jets+3.5 (St Louis) > + Seattle+5.5 (Atlanta) > > Week 17 Benchmark abstain: > NY Giants+2.5 (Dallas) > Oakland (Jacksonville) > > ------------------------------ > > > JDG picks week 17: > - Tampa Bay (Arizona) > + Baltimore (Miami) > - Buffalo (Pittsburgh) > - Carolina (New Orleans) > - Chicago (Green Bay) > - Philadelphia (Cincinnati) > - Indianapolis* (Denver) > + Tennessee (Detroit) > - Houston (Cleveland) > - Kansas City (San Diego) > - Minnesota (Washington) > + New England (San Francisco) > + St. Louis (NY Jets) > + Seattle (Atlanta) > - Dallas (NY Giants) > + Jacksonville (Oakland) > > > _______________________________________________ > http://www.mccmedia.com/mailman/listinfo/brin-l -- Erik Reuter http://www.erikreuter.net/ _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
