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--- On Wed, 10/22/08, Truman Prevatt <tprevatt@xxxxxxxxxxxxxx> wrote:

> From: Truman Prevatt <tprevatt@xxxxxxxxxxxxxx>
> Subject: Re: [RC] Completion rate by Wt division
> To: "Michael Maul" <mmaul@xxxxxxxxx>, "ridecamp" <ridecamp@xxxxxxxxxxxxx>
> Date: Wednesday, October 22, 2008, 9:23 AM
> While these "numbers look close" there is a
> significant statistical 
> difference between HW and the other weight divisions. One
> might suspect 
> this since the difference between MW and HW (2.4%) is 8
> times greater 
> than that between the other categories (.3%).
>
> The Strong Law of Large Numbers is a wonderful property -
> it allows one 
> to make mathematically valid decisions from statistics that
> appear 
> "close" when the sample sizes become large which
> is the case here. When 
> you calculate the standard errors for the four categories
> and then 
> compare the number of "sigmas" apart the
> completion probabilities you 
> find for the three categories, FW, LW and MW the maximum
> simgage (FW to 
> MW) is 1.2 which is well within expected statistical
> variation at 
> random. However, when you compare the simage of HW to MW it
> is on the 
> order of 4.5 sigma - which equates to a probability of less
> than .001 
> for the sample mean for HW actually coming from the MW
> category.
>
> These data show to a confidence of greater than 99% that
> the pull rate 
> for the population of horses carrying heavyweight riders is
> higher than 
> that for any other weight division.  These data also show
> that the 
> difference between the pull rates between MW, FW and LW are
>
> statistically insignificant based on these sample sizes. In
> order to see 
> if the statistics of the pull are statistically different
> for MW, LW and 
> FW - more data would be needed. To conclude to a 99%
> confidence that say 
> the pull rate of FW was greater (or less) than  a sample
> size of over 
> 116000 for each would be required.
>
> Truman
>
> Michael Maul wrote:
> > There was a recent post - either on the member's
> forum or RC - that 
> > commented on the completion rate
> > by wt. division at the NC.
> >
> > It showed some differences by wt division so I decided
> to see if that 
> > was true for a whole season's
> > rides.
> >
> > In 2006
> >
> > Div         starts  completions     % Comp
> > FW  4720    4104    86.9%
> > LW  6558    5677    86.6%
> > MW  4747    4096    86.3%
> > HW  3087    2589    83.9%
> > Jr  815     715     87.7%
> >
> >
> >
> > There's a slight drop in completion rate for HW
> and a slight increase 
> > for Juniors but
> > overall - it looks pretty close.  The average that
> year for all riders 
> > was
> >
> > Mike
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>
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> one spends most of 
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