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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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