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/

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