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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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