**A Better "Weigh"
for Horses: Equine Weight Estimation**

** **

Through
the analysis of data gathered on 224 horses over a two year period, three
statistical equine weight estimation models were developed utilizing multiple
regression analysis. Girth, height,
length, age, breed, and gender were recorded for each horse in the research
sample. Additionally, a visual estimate
of each horse’s weight was made prior to obtaining its actual weight on a
digital scale.

Weight
estimates for each horse were also calculated using three commercially
available girth weight tapes. These
were the Purina, Nutrena, and Sure Measure weight tapes. Additionally a weight estimate was
calculated using the Carroll/Huntington formula** ^{1}**. This
information was obtained to test the comparative accuracy of these estimation
methods against the statistical models
developed through this research project.

Comparisons
were made between the equine weight estimates using the girth weight tapes,
visual estimates, the Carroll / Huntington formula, and the new regression
models developed.

Overall
accuracy comparisons were made by comparing the adjusted R squared statistics
for each estimation technique/model.
The three estimation models built during the project included girth,
height and length as independent variables and actual weight as the dependent
variable.

The
models constructed through this research project reflect higher adjusted
R-squared numbers than any of the other existing equine weight estimation
models.

__INTRODUCTION__**:**

** **

The
importance of accurate equine weight estimates is unquestionable. Veterinarians, equine management facilities,
stables, and individual horse owners rely on accurate weight information to
determine proper medication dosage, feed and nutrition considerations, racing
performance, and transportation requirements** ^{2}**.

The
problem is that horse weigh scales are not available in most situations to get
an accurate weight on a horse.

There are currently three primary
methods available for estimating equine weight when access to scales is not
possible: 1) Visual Estimation, 2)
Girth Weight Tapes, and 3) Weight estimation formulae, with the most frequently
used and most accurate formula to date being the Carroll/Huntington Formula** ^{3}**.

It
was anticipated that improvements upon the accuracy of the existing methods
could be made to develop “A Better *‘Weigh’
*For Horses”. Therefore, it was
hypothesized that a more accurate equine weight estimation model could be
developed through statistical analysis.

__MATERIALS AND METHODS__**:**

** **

The
most difficult and time-consuming portion of this research project has been
gathering data on a sufficient number of horses. The very problem that generated the interest in this project also
created a problem with the data gathering phase—That was finding a facility
with an equine scale that could be utilized.

In
order to develop a more accurate equine weight estimation model, during phase
one of this project data was gathered on 59 Oklahoma State University equine
research horses, including girth, length, height, age, breed, gender, an estimated
weight by visual estimation, and an actual weight on a scale.

This year, permission was obtained from the Board of the Oklahoma State Fair to measure and weigh horses during the various breed shows at the State Fair. A formal presentation of the project was given to this group and permission was given to proceed with the data gathering process. State Fair officials were extremely helpful in arranging stall space for research efforts, passes for entry into the Fair, etc. At the State Fair data similar to that recorded in 1999 was gathered on 165 additional horses.

For
phase one of this project three different commercial horse weight tapes were
obtained. These tapes are used by
taking a girth measurement and reading an estimated weight off of the tape. Each horse in the research sample database
was measured and weighed with a regular measuring tape in inches. Measurements of girth, height, and length
were recorded. Before each horse was
weighed on the scale, a visual estimate of the horse’s weight was made. Each horse’s actual weight in pounds was
recorded before returning them to their stalls.

The
girth weight tape results were extrapolated by later laying the girth weight
estimation tapes on the ground, taping the ends so that they wouldn’t slide. The inch measurements were then converted
into the weight indication on each girth weight tape and the data was
recorded. These same procedures were
also utilized in this year’s data gathering efforts.

Data
entry was a substantial task because of all the information gathered on each of
224 horses. Data was entered into SPSS
Statistical Software for analysis and model building.

Initially, the correIation coefficients of each variable to actual weight were analyzed and the results were compared using the Pearson Correlation Coefficient. Girth was the most highly correlated to actual weight with a coefficient of .9520, followed by height at .8886, length at .8578, gender at -.4385, breed at .4191, and age at .2632.

Initially it was hypothesized that age, breed, and gender would be more highly correlated with actual weight than they were. This result caused further investigation into how the variables were coded. It was determined that binary variables should be used on gender and breed and age to improve the correlation.

Recoding the variables made no significant difference in the correlation of these variables to actual weight. Also, when age, breed, and gender were utilized in regression equations, they were consistently rejected from the models by the parameters established. Therefore, efforts were focused on model building with girth, height, and length as the variables in the multiple regression analysis models.

Through Multiple Regression
Analysis (MRA), and using the variables girth, height and length, a new
multiplicative model was developed by
using the natural logarithm of actual weight as the dependent variable, and the
natural logarithms of girth, height, and length as independent variables in a
linear regression equation. When
converted, this produced model one with an adjusted R Square of .97559.^{}

Using the same regression technique, a model was also built
using volume and height. The volume
variable was created by using girth as the circumference of the base of a
cylinder and converting girth into a radius number so volume could be
calculated. The length of the horse was used as the height of the cylinder in
the volume calculation.

Model two was built in phase one of the
project, using Girth^{2} x Length x Height in a power curve
formula. Each of the three models
exceed all existing weight estimation models in accuracy using the sample of
224 horses, as measured by the Adjusted R Square statistic.

__RESULTS__**:**

Summary
Statistics, Model One

Weight = .003584 x Girth ^{1.630634}
x Height ^{.954088} x Length ^{.399860}

Multiple R .98788

R Square .97591

Adjusted R Square .97559

Standard Error .06387

__Step
MultR Rsq F (Eqn) SigF Var. BetaIn__

1
.9771 .9547 4679.440
.000 In: LNGIRTH
.9771

2 .9850
.9702 3593.580 .000
In: LNHEIGHT .3269

3
.9879 .9759 2971.388
.000 In: LNLENGTH
.1567

Summary
Statistics, Model Two

Weight = .018534 x Volume ^{.629388}
x Height ^{1.087000}

** **

Multiple R .98668

R Square .97353

Adjusted R Square .97329

Standard Error .06680

** **

__Step
MultR Rsq F (Eqn) SigF Var. BetaIn__

1
.9766 .9537 4573.049
.000 In: LNVOL .9766

2
.9867 .9735 4064.203
.000 In: LNHEIGHT
.3507

** **

** **

Summary
Statistics, Model Three

Weight = .004209 x (Girth^{2} x
Height x Length) ^{.733855}

** **

Multiple R .98561

R Square .97142

Adjusted R Square .97129

Standard Error .06926

** **

__Variable B
SE B Beta T Sig T__

G2HTLGTH .733855
.008448 .985606 86.864 .0000

(Constant)
.004209 .000601 6.997 .0000

**
**

As demonstrated in the summary statistics above on the two models constructed this year, and the 1999 model, all are more accurate than any other estimation method or formula currently available as measured by the Adjusted R Square against the sample of 224 horses collected to date.

It should also be noted that the three girth weight tapes were not able to estimate a substantial number of horses in the database because the girths of many horses exceeded the maximum number reflected on the tape. In calculating the Adjusted R Square for the weight tape estimates, these weight tape samples which could not produce an estimate of weight were excluded. Thus the true accuracy difference between the models created during this research project and those of the weight tapes is actually larger when it is considered that there were 21 horses for which the weight tapes could not calculate a weight estimate.

__CONCLUSIONS / RECOMMENDATIONS__**:**

** **

The research hypothesis that a more accurate equine weight estimation model could be developed through statistical analysis was proven. Not only was the phase one model proven to be more accurate than all other equine weight estimation methods tested with the increased sample size, but the two new models created this year in phase two of the project further improved accuracy levels beyond those of last year.

Through Multiple Regression Analysis (MRA), and using the
variables girth, height and length, a new multiplicative model was developed by
using the natural logarithm of actual weight as the dependent variable, and the
natural logarithms of girth, height, and length as independent variables in a linear
regression equation. When converted,
this produced the following model:

**Weight = .003584 x Girth ^{1.630634}
x Height^{ .954088} x Length^{ .399860}**

This model produced an adjusted R Square of .97559, compared to .95349 for the next most accurate model, that of the Australian Equine Veterinarians Carroll / Huntington (The first research model built last year produced an adjusted R Square of .97129 on the new sample, and the volume and height power model resulted in an adjusted R Square of .97329). Through further data collection and analysis, these models will be refined.

The practical implications of this research are enormous. An equine weight estimation software program has already been created as a result of this research project, which allows a user to type a girth, height, and length measurement into the appropriate boxes, press <Enter>, and instantly have an accurate weight estimate appear on the screen. This same concept will eventually be incorporated into an equine weight estimation calculator that can be utilized in the field, producing an immediate weight estimate without the necessity of a personal computer or laptop.

This will simplify the use of the mathematical formulae
developed through this research project, and give the average horse owner a
more accurate option for estimating the weight of their horses than anything
currently available.

At the present time, patents are being sought for the new
formulae, and grants for funding necessary equipment (portable equine scale)
are being pursued so this research can be continued over the next several
years.

**Acknowledgments**

** **

**PHASE II ASSISTANCE, FALL 2000:**

** **

Oklahoma State Fair
Board, with special thanks to D.J. Walker

Pat Rush, State Fair
Horse Show Secretary

Oklahoma City Mounted
Police, with special thanks to Danny Booth

Glenda Bales,
Oklahoma Apaloosa Club President

State Fair Horse Show
Participants who volunteered their time and allowed their 165 horses to be
weighed and measured.

My parents, Kris and
Joe Hapgood for their untiring support

**PHASE I ASSISTANCE, FALL 1999:**

** **

Dr. David Freeman, Professor of Animal Science, State Equine Specialist, Oklahoma State University

Dr. MacAllister,
Professor, Department of Veterinary Clinical Services, Oklahoma State
University

Clay Dalluge, Herd
Manager, Equine Research Herd, Oklahoma State University

The following
Oklahoma State University Animal Science Graduate Students: Britton, Matt, Tammy, Wes and Amber

Carl Gedon, Herd
Manager, Oklahoma State University

Dr. Mark Bianchi,
D.V.M.

Dr. Jennifer Bianchi,
D.V.M.

Dr. Bob Curley,
Professor of Mathematics, University of Central Oklahoma

**References**

**[1]** **Carroll
C.L. , and Huntington P.J., (1988), Body Condition Scoring and Weight
Estimation of Horses, Equine Veterinary
Journal 20 (1), 21-45.**

** **

**[2] Lewis Lon
D.,(1982), Feeding and Care of the Horse. Publisher: Lea & Febiger.**

** **

**[3] Reavell,
D.G., (1999), Measuring and Estimating the Weight of Horses With Tapes,
Formulae, and by Visual Assessment, Equine
Veterinary Education/AE, December 1999, 188-193.**

** **

**[4] Marcenac,
L.N. and Aublet, H. (1964) Encyclopedie
du Cheval, Maloine, Paris.**

** **

**[5] Ensminger,
M.E. (1977) Horses and Horsemanship,
5^{th} ed.**

** **

**[6] Jones, R.S.,
Lawrence, T.L.J., Veevers, A., Cleave, N. and Hall, J. (1989) Accuracy of
prediction of the liveweight of horses and body measurements. Vet.
Rec. 125, 549-553.**