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Re: [RC] Completion rate by Wt division - Michael Maul

I noticed the difference too and decided that Truman would let me know if I was 
wrong.  He did and I was off a little on how long that would take... :-)

Truman is certainly correct.

I considered looking at the 12 years of data and whether distances like 100 
miles vs LD made a difference but given my present "job", I don't have the time.

Doing simple averages as I did is OK when the results are close but real 
statistical analysis is needed when they are not.

What it means - I'm not sure other than it went from lightest - Juniors to 
heaviest - in completion rates.

Mike


--- On Wed, 10/22/08, Michael Maul <mmaul@xxxxxxxxx> wrote:

From: Michael Maul <mmaul@xxxxxxxxx>
Subject: Re: [RC] Completion rate by Wt division
To: "ridecamp" <ridecamp@xxxxxxxxxxxxx>, "Truman Prevatt" 
<tprevatt@xxxxxxxxxxxxxx>
Date: Wednesday, October 22, 2008, 10:50 AM
--- 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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