• TABLE OF CONTENTS
HIDE
 Front Cover
 Acknowledgement
 Preface
 Table of Contents
 Introduction
 The objectives of grading and the...
 Techniques for measuring the performance...
 Evaluation of four statistical...
 A method of diagnosing grading...
 Potential uses of the index of...
 Literature cited
 Appendices
 Back Cover














Title: Economic & Statistical Evaluation of Grading Cattle
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Table of Contents
    Front Cover
        Page 1
    Acknowledgement
        Page 2
    Preface
        Page 3
    Table of Contents
        Page 4
    Introduction
        Page 5
    The objectives of grading and the means of achieving them
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Techniques for measuring the performance of graders
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
    Evaluation of four statistical measures of grading performance
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
    A method of diagnosing grading performances
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
    Potential uses of the index of precision
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
    Literature cited
        Page 46
    Appendices
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
    Back Cover
        Page 58
Full Text




An Economic & Statistical

:V AT N of GRADING CATTLE



W. K. McPherson, L. V. Dixon
H. L. Chapman, Jr.
Department of Agricultural Economics
and
Everglades Experiment Station












Technical Bulletin 632
September 1961



UNVRT F FL
AGRICLTURL EXERIMET STTIOo
J.R.Bekebah Dreto, aievile Ford












Florida Agricultural Experiment Station
in cooperation with
Marketing Economics Research Division
Agricultural Marketing Service
U. S. Department of Agriculture
















ACKNOWLEDGMENTS

The authors are indebted to the many persons who made some con-
tribution to this study, and especially to the following individuals and
organizations whose counsel and assistance was most useful: Willard Ash,
Department of Agronomy, University of Florida; Gifford Rhodes and his
staff of market reporters, Florida State Marketing Bureau; Gerald Engel-
man and K. J. McCallister, Agricultural Marketing Service; and the Meat
Grading Branch of the Livestock Division, Agricultural Marketing Service.
The authors, of course, accept full responsibility for the analysis and con-
clusions.















Single copies free to Florida residents upon request to
AGRICULTURAL EXPERIMENT STATIONS
GAINESVILLE, FLORIDA







Economic and Statistical Evaluation of Grading Cattle 3






PREFACE
Since the turn of the century, the American people have been
endeavoring to identify an appropriate role for the federal gov-
ernment in the establishment and interpretation of grade stand-
ards for livestock. The fact that some of the firms in at least
1 segment of the industry are not satisfied with the role that
Congress has delegated to the Department of Agriculture in the
establishment and enforcement of a uniform grading system
strongly suggests that more research is needed in this area.
This bulletin constitutes an organized effort to identify some
fundamental reasons why the task of identifying the role of a
government in this type of activity is so difficult. More specifi-
cally, the bulletin consists of:
1. A statement of the economic role of grades and its appli-
cation to livestock and meat.
2. A review of several methods that have been used to evalu-
ate the accuracy of grading livestock.
3. The description of a proposed method for comparing and
diagnosing the abilities of individuals to grade cattle accurately.
4. An illustration of how index of precision scores, mean
error of estimate scores, and standard deviation of error scores
can be used to evaluate the ability of individuals to grade.
A broad and general statement of the problem is combined
with a detailed description and analysis of 1 method of improving
the usefulness of grade standards in an effort to give the reader
an adequate background for formulating public policy with re-
spect to the use of federal grades.













CONTENTS

Page
INTRODUCTION ........---- ......--.......--- .-------- .......------- 5
Statement of the Problem ..................-------......... -- ..-- 5
Scope of the Analysis .......-....-- ........--------- .......---- 6

THE OBJECTIVES OF GRADING AND THE MEANS OF ACHIEVING THEM 6
Nature of Grades ..-.......-..........--------- --. ....-- ...... 6
Purpose of Grading ------.........---------..........----- ... 6
Definition of Grades .-----------................. -------.......---. 7
Issues in the Current Controversy ............ .....----- ......------ 9
An Alternative Course of Action ........--.....-....----- ...--- ...... 12

TECHNIQUES FOR MEASURING THE PERFORMANCE OF GRADERS .-....... 15
Economic Measures ......---......--... ...------. ......--- ...... 15
Statistical Measures --....----..........----- ........ ------.......--- 18

EVALUATION OF FOUR STATISTICAL MEASURES OF GRADING
PERFORMANCE ......----......--............-.. ----........---.... 22
Methods Compared ......-.. -----.... .. ............. ..... ---.... 22
Sources of Data .--......---.......-- ........... ----... ......-- .... 23
Comparison of Individual Scores ......------............ ........----- ...---24

A METHOD OF DIAGNOSING GRADING PERFORMANCES .-----......................--. 29
Components of Index of Precision ..............- ..............---..... 29
Mean Error of Estimate .-.....---.............. ..---.--........- 29
Standard Deviation of Errors of Estimate -.............................. 35

POTENTIAL USES OF THE INDEX OF PRECISION .--...--...- ---.................... 39
Quantitative Evaluations -................. ...-- -------...... ........- 39
Inferential Analysis .--.......----. ................ ........ 44
LITERATURE CITED -----.............-------- ................-... 46

APPENDIX ..--- -- --------..............................-------..---..... 47









AN ECONOMIC AND STATISTICAL

EVALUATION OF GRADING CATTLE

W. K. MCPHERSON, L. V. DIXON and H. L. CHAPMAN, JR.'

INTRODUCTION
The Problem.-The need for adopting a system for classify-
ing and grading cattle was first recognized about the turn of
the century (7).* In 1913 the Secretary of Agriculture placed
the responsibility for developing such a system in the Office of
markets (12) and by 1916 tentative (though yet unpublished)
grade standards were being used as a basis for reporting the
prices of cattle and calves (3).
The lively controversy over the quality of the beef being
sold to consumers that started in 1924 did much to stimulate
the publication of the first Federal grade standards for beef
in 1927 and the establishment of the Federal Meat Grading
Service in 1928 (11). Since then these grades have been revised
periodically, and their use has been voluntary except for the
duration of World War II and the Korean incident.
During and after World War II a controversy developed over
the use of Federal grade standards for beef. In 1946 most of
the national and a number of the independent meat packing
firms wanted to abolish all federal grades. In sharp contrast,
a substantial number of independent wholesalers, independent
retailers and retail chains would have made the use of federal
grading of beef compulsory (13). More recently, the contro-
versy over the desirability of grading other meats has been
questioned, and lamb grading was actually abolished for a short
time in 1960.
Would either the abolishment of federal grades for beef ani-
mals and beef or making the use of these grades compulsory
create a more desirable economic environment within the indus-
try? If not, is there an alternative course of action that is more
desirable, and how could it be implemented?

Figures in parentheses refer to Literature Cited.
1Agricultural Economist, Florida Agricultural Experiment Station,
Gainesville; Agricultural Economist, Marketing Economics Research Di-
vision, Agricultural Marketing Service, United States Department of Agri-
culture; and Associate Animal Nutritionist, Everglades Experiment Station,
Belle Glade, respectively.







6 Florida Agricultural Experiment Stations

Scope of the Analysis.-In section II of this report a state-
ment of the objectives of grading and alternate means of achiev-
ing them is used as a basis for identifying the issues in the cur-
rent controversy and suggesting how they may be resolved. The
techniques that have been used for measuring the ability of in-
dividuals to interpret grade standards are evaluated in section
III, and 4 statistical measures of accuracy of grading cattle are
compared in section IV. Finally, the method of diagnosing the
ability of individuals to grade cattle that is proposed in section
V is outlined in section VI in some detail.

THE OBJECTIVES OF GRADING AND THE MEANS
OF ACHIEVING THEM

Nature of Grades
Grades provide a basis for separating a heterogeneous com-
modity into several more homogeneous products on the basis of
characteristics that buyers and sellers take into consideration
while negotiating the terms of sales. One of the earliest char-
acteristics used for this purpose was weight. Now, such diverse
things as size, color, hardness, texture, odor and taste are used
as a basis for grades. The standards that define grades provide
the basis for establishing the extent to which selected character-
istics must be present in a product to be classified in a particular
grade. Thus grade standards establish the range within which
selected characteristics of a product may vary.

Purpose of Grading
In a highly specialized market economy, the use of grades
provides a means of:
1. Increasing the net returns to sellers by (a) facilitating
sales on the basis of grade rather than inspection, (b) providing
a basis for advertising differences between the physical char-
acteristics of products and (c) enabling sellers to exercise some
control over supply of specific products.
2. Reducing the cost and increasing the utility of the market
information that enables traders to compare prices of relatively
homogeneous products.
3. Establishing a basis for determining the economic value
of products (a) used as collateral for securing loans, (b) pooled







Economic and Statistical Evaluation of Grading Cattle 7

for the purpose of reducing marketing costs or (c) damaged or
destroyed in storage or transit.
4. Reducing the cost of purchasing by (a) enabling buyers
to identify products having the same characteristics at a lower
cost and (b) permitting buyers to purchase products that have
these characteristics without physically inspecting them.

Definition of Grades
The type of organization that assumes the primary responsi-
bility for grading varies from industry to industry, and in many
industries 2 or more types of organizations define grades. In-
dividual firms; trade associations, professional organizations or
private testing laboratories; representatives of consumers and
government agencies define grades when the economic returns
of doing it appear to be sufficiently attractive. The economic
ends each type of organization strives to achieve by defining
grades differ widely.
An individual firm establishes grades in an effort to maxi-
mize its own net returns, i.e., profits. To establish grades, firms
(1) identify and standardize the useful characteristics of the
products, (2) obtain patents on products with new and unique
characteristics and (3) register the trademarks and brands they
use with the appropriate government agency to prevent others
from identifying the same or similar products with the same
label, name or mark.
Firms selling privately graded products under trademarks
or brands are free to (1) alter the characteristics of the product
at any time without obligation to advise prospective buyers of
these changes, (2) decide how many units of a product to offer
for sale or (3) withhold the product from the market altogether.
Thus the establishment of private grades provides individual
firms with a means of maximizing net returns by (1) creating
new or improving old products (research and product improve-
ment), (2) making consumers aware of the availability of prod-
ucts having new and/or uniform characteristics (advertising)
and (3) reducing supply of a product to increase price or with-
holding it from the market in order to stimulate the sale of a
more profitable product (monopoly power).
When all or most of the firms in any segment of an industry
endeavor to maximize their returns by the use of 1 set of grade
standards, they often turn to their trade association, a testing
laboratory or a professional society to define grade standards






8 Florida Agricultural Experiment Stations

and police the use of them. In doing this, individual firms re-
linquish some of their right to establish grades and pay another
organization to do it-either in the form of membership dues
or fees for the service. Many industries use the prestige of
professional organizations and private testing laboratories to
build up the buyer's confidence in the value of the characteristics
of products-characteristics they have chosen to standardize.
Nevertheless, the group of firms that sponsor the use of grades
developed in this manner pass final judgment on whether the
grades used are good or bad when they either pay for or use
them. Consequently, the economic goals that the grades de-
veloped by trade associations, testing laboratories and profes-
sional societies are designed to achieve are largely the economic
goals of 1 segment of the industry rather than the economic
goals of any 1 firm, the entire industry or the consumers of the
product.
Efforts to establish grades for the primary purpose of maxi-
mizing the satisfaction consumers derive from a good are reported
in 2 periodicals primarily dedicated to this purpose. Numerous
other periodicals use 1 or 2 pages of each issue for this purpose.
Consumer reports are based on a physical examination and/or
tests of products currently being sold. Inasmuch as consumers
finance these examinations and tests through the purchase of or
subscription to magazines, the economic interests of buyers are
emphasized and those of sellers largely ignored. Most consumer
reports describe the characteristics of products in narrative
form, and in some instances the standards by which competitive
products are compared are published.
Government agencies assume the responsibility of establish-
ing and policing the use of grades when legislative bodies
endeavor to improve the economic well-being of producers, pro-
cessors, wholesalers, retailers and consumers simultaneously.
Obviously then, government grades are compromises and will
never assist any 1 segment of the industry to achieve its own
economic goals as much as a set of grade standards designed
for that particular purpose. Whether the use of 1 set of federal
grades throughout an industry is more desirable than the use
of numerous grades designed to maximize the profits of some
of the individuals or firms in the industry depends upon (1)
the kind of an economic environment society wants to create
within the industry and (2) how effective grades are in main-
taining such an environment.







Economic and Statistical Evaluation of Grading Cattle 9

Issues in the Current Controversy
At the present time no efforts are being made to establish
beef and beef animal grades for the singular purpose of maxi-
mizing the economic position of any single major segment of
the industry, e.g., producers, processors, wholesalers, retailers
or consumers.
Instead the current controversy is simply a controversy over
whether or not a uniform system of federal grading should be
made available to the industry. The economic consequences of
abolishing the federal grading system, compared with those
that would result from the use of a federal grading system that
is generally acceptable to the industry as a whole, can be sum-
marized as follows:2
la. The availability of Federal grades gives sellers in the
industry an opportunity to reduce selling costs by reducing or
eliminating the cost of physically inspecting the products; where-
as the use of private grades enables only the firms that establish
them to do so.
lb. Firms that use private grades have more opportunities
to increase their net returns by advertising differences between
their product and the products offered by their competitors than
the firms using federal grades. To the extent that the use of
private grades stimulates the development of new products that
many firms can produce and sell either now or in the foreseeable
future, they benefit the entire industry. Since the firms that
operate on a regional or national basis can generally benefit more
from advertising their own grades than firms that operate in a
relatively small geographic area, the abolition of federal grades
would enhance their economic position.
Ic. The use of private grades enables the firms that establish
them to control supply of the products (grades) for which they
register trademarks; whereas no firm can establish a legal right
to control the supply of a product that meets the standards for
a federal grade. The ability of firms to control the supply of
privately graded and branded products enables them to exercise
some influence on price and in this way earn monopolistic profits.
When private firms use this monopolistic power to increase the
price of products that are no more useful to consumers than
federally graded products, no one gains but the firms that pro-

SNumbers refer to points made in outline of purposes of grading. See
page 6.







10 Florida Agricultural Experiment Stations

duce them. On the other hand, when monopolistic power gained
in this manner provides a means of financing the development
of new improvement of old products, the entire industry may
benefit.
2. The exclusive use of the large number of private brands
(grades) of beef and beef animals that now exist in the industry
would make the task of reporting market news much more diffi-
cult and expensive than when some federally graded animals and
beef products are traded. Since both beef animals and beef
move so freely in interstate trade, buyers and sellers find the
task of discovering the true market price both difficult and ex-
pensive. To the extent that the abolition of federal grades would
increase the difficulty and cost of discovering prices, firms that
operate over large areas-i.e., national and regional packers and
chain stores-would gain a competitive advantage, due to the
fact that they would be in a position to use their own employees
and communications system to discover price at a relatively low
cost and without disclosing the knowledge they accumulate to
others.
3a. Federal grades enable any firm wishing to use warehouse
stocks as collateral loans to establish their market value. In
many instances, lenders make the certification by a federal grader
that a particular lot of a product meets the standards for a
particular federal grade-a requisite for using that lot as col-
lateral. In this way, both the borrower and lender use the judg-
ment of a third party-a party not financially interested in the
transaction-as a basis for establishing the value of the product.
Without federal grades, it would be difficult and sometimes im-
possible for small firms not having established brands to borrow
any appreciable proportion of the market value of their ware-
house stocks.
3b. When the products of many buyers or sellers are pooled
to obtain the economies of scale, federal grades provide a means
of determining the value of the products each member con-
tributes. The added cost of defining private grades for every
pool would reduce and sometimes offset any reduction in buying
or selling costs that might accrue from pooling.
3c. Federal grade standards provide a basis for determining
the economic value of products damaged or destroyed in transit
or in storage. Again the report of the federal grader constitutes
an evaluation of a third party not financially interested in the
transaction. Private grade standards cannot be used for this







Economic and Statistical Evaluation of Grading Cattle 11

purpose because they are not generally known and accepted in
the industry.
3d. Both federal and private grades enable buyers to identify
products with the same or nearly the same characteristics. The
principal difference lies in the fact that private grades enable
buyers to identify only products that have the same character-
istics that are produced by 1 firm; whereas federal grades enable
buyers to identify products having the same characteristics but
made by several firms.
4a. The use of 1 set of Federal grades throughout the indus-
try would result in a lower cost of buying than the use of
numerous private grades. The reason for this lies in the fact
that it is easier for buyers to become familiar with 1 set of
grade standards than with many different grade standards. In
the beef industry, the number of consumers that know the
characteristics of Federal grades is small but is still much larger
than the number that know the characteristics of privately
graded beef. However, practically everyone who buys beef and
beef animals as a means of earning a living-i.e., the processors,
wholesalers and retailers-are sufficiently familiar with the
Federal grade standards to use them to minimize cost of trading.
4b. Firms that establish private grades tend to standardize
only those characteristics of a product that will maximize profit;
whereas the Federal grades are based on characteristics that
buyers and sellers consider. However, characteristics that are
standardized by the government and private firms do not vary
greatly, since both must take the consumer into consideration,
even though for quite different reasons.
From the foregoing analysis 3 conclusions can be drawn.
First, the availability of Federal standards and a Federal
grading service to the firms that buy and sell beef animals and
beef (1) stimulates price competition within the industry and
(2) enables buyers and sellers to trade at a lower cost than would
prevail without some kind of a uniform grading system. A com-
petitive economic environment in which goods and services will
be traded freely at a minimum cost has always been 1 of the
nation's economic goals.
Second, the use of private grades enable firms that have the
resources to take the initiative to establish them with a means
of influencing prices by controlling the supply of products that
meet unpublished specifications that can be changed without







12 Florida Agricultural Experiment Stations

notice. To the extent that returns earned in this manner are
used to finance research, product development and advertising
based on product differentiation 3 the use of private grades can
benefit the entire industry. The maintenance of an economic
environment in which there are incentives for producers to
develop new and improve old products is also an economic goal
that Americans strive to achieve.
Finally, it is clear that the abolition of Federal grades would
enhance economic power and hence the profits of the firms hav-
ing the initiative and resources to establish private grades,
especially firms now operating on a regional or national basis.
The numerous laws designed to curb monopolies and establish
rules for fair trading and the efforts that are made to enforce
them seem to justify the assumption that the public will hesi-
tate to abolish the use of Federal grades at least until an alterna-
tive method of stimulating competition and defining a basis of
trading has been developed.

An Alternative Course of Action
What, if any, are the alternatives to the present proposal of
abolishing the Federal grades and grading services for beef ani-
mals and beef ? To achieve 2 of the nation's most highly valued
economic objectives simultaneously-i.e., an economic environ-
ment in which there is a high degree of price competition and
yet an attractive reward for technological innovation 4-it will
be necessary to define Federal grades broadly enough to give the
firms that want to use them an opportunity to sell new and im-
proved products at a premium. This premium should be suffi-
ciently large to constitute an incentive for firms to finance
research and the advertising of products that have been differ-
entiated on the basis of physical attributes, but not large enough
to destroy all price competition and enable firms to earn monopo-
listic profits by differentiating the demand, i.e., selling the same
product under different brand names.

S In this context, the phrase "product differentiation" implies there are
physical differences between products having the same general charater-
is'ics but sold under different brand names or grades. The practice of
selling identical products under different trade or brand names is more
appropriately called demand differentiation. Ruby Turner Norris, The
Theory of Consumer Demand (New Haven: Yale University Press, 1952).
In his article, "Uniform Grades and Standards, Product Differentiation
and Product Development," Paul L. Farris (Journal of Farm Economics,
Nov. 1960, p. 854) discusses the possibility that uniform grading and product
differentiation may be compatible from a theoretical standpoint. The
authors were not aware of Farris's work when this bulletin was prepared.








Economic and Statistical Evaluation of Grading Cattle 13

It may be well that the current controversy over Federal
grades reflects general dissatisfaction with the quality of the
Federal standards now being used rather than an effort of 1
group of firms to enhance their economic position. The common
practice of packers of appealing the first decision of meat graders
on all border line cases (liners) and the numerous differences
in the manner individual graders interpret the standards indicate
this is true. If this is correct, every effort should be made to
determine (a) the extent to which the grade standards them-
selves can be improved and (b) the degree of precision with which
graders (both Federal and private) can use them to classify beef
and beef animals into homogeneous products.
The task of improving the grade standards for beef animals
and beef is particularly difficult because (a) the attributes that
it is appropriate to standardize are, for the most part, highly
subjective and (b) natural commodities are more heterogeneous
than manufactured commodities. Numerous USDA and Agri-
cultural Experiment Station research projects are designed to
identify the attributes of beef animals and beef that might be
standardized and to develop techniques for measuring them ob-
jectively.5 An analysis of the work that is being done in this
area is not within the scope of this report. Nevertheless, the
USDA is now studying the feasibility of making important re-
visions of the meat grading system. A "dual" system could be
established that would identify 2 separate and independent. at-
tributes of value. The meat quality attribute could be identified
with the present grade names, whereas the yield of high value
retail cuts attribute might be identified by a system of numbers.

"Results of some of this research are reported by:
R. H. Alsmeyer, A. Z. Palmer, M. Koger and W. G. Kirk, "The Relative
Significance of Factors Influencing and/or Associated with Beef Tender-
ness," Proceedings of 11th Research Conference of America Meat Institute
Foundation, p. 85. 1959.
O. D. Butler, M. J. Garber and R. L. Smith, "Beef Carcass Composition
and Yield of Wholesale Cuts as Estimated from Left and Right Sides,"
Journal Animal Science, 15:891. 1956.
O. D. Butler, B. L. Warwick and T. C. Cartwright, "Slaughter and
Carcass Characteristics of Shortfed Yearling, Hereford and Brahman x
Hereford Steers," Journal Animal Science, 15:93. 1956.
R. R. Woodward, J. R. Quesenberry, R. T. Clark, E. E. Shelby and O. G.
Hankins. Relationships Between Pre-Slaughter and Post-Slaughter Evalu-
ations of Beef Cattle. U. S. Department of Agriculture Circular 945.
Washington: Government Printing Office. 1954.
H. Farris, Jr., E. N. Hoffman, W. A. Sawyer, R. Bogart and A. W.
Oliver. Brahman x Hereford with Hereford, A Comparison. Oregon Agri-
cultural Experiment Station Bulletin 549. 1955.







14 Florida Agricultural Experiment Stations

In evaluating the work of those who conduct the research
and prepare the grade standards, it must be remembered that
animals and meat are produced by natural processes. Commodi-
ties produced by natural processes tend to be more heterogeneous
than manufactured products, primarily because it is impossible
to control the physical attributes of the finished product with
sufficient precision to produce a high degree of homogeneity-
the kind of precision manufacturing firms use to produce highly
homogeneous products.
It is the continuity of the attributes of agricultural products
over a wide range that makes it so difficult to separate into
products with acceptable degrees of homogeneity. For example,
the characteristics of beef vary from lean dark red meat to meat
that is well-marbled and covered with fat. Between these 2
extremes, the characteristics of beef carcasses and cuts do not
fall into any specific number of well defined homogeneous prod-
ucts. In sharp contrast to agricultural products, the character-
istics of manufactured products generally can be controlled
within narrow limits and hence are much easier to group into
homogeneous products (5). For example, it is possible to con-
struct a machine that will produce nails of any specific length
within a tolerance of one-thirty-second (1/32) of an inch or less.
Thus, it is possible to produce 2 kinds of nails that differ only
in length, yet the nails of each length are homogeneous and
easily distinguishable from nails of other lengths.
When the lots or units of commodities having attributes that
differ very small amounts-i.e., constitute a continuous function
-are classified by any standard into products comprised of units
of more homogeneous attributes, differences between the units
that lie near the boundary line between grades will be difficult
to recognize and hence a source of error and confusion. Scien-
tists can minimize these errors by developing objective measures
of such attributes of beef that are associated with texture, flavor
and juiciness but cannot be expected to classify animals and
meat into products that are as distinguishable as the different
lengths of nails.
The precision with which any given set of grade standards
can be used is a function of the person who interprets them, i.e.,
a grader. Some graders can interpret grade standards more
accurately than others.
Errors in separating homogeneous commodities into grades
is always a source of confusion and dissatisfaction among traders.







Economic and Statistical Evaluation of Grading Cattle 15

In the case of nails, errors in grading are not tolerated and sellers
quickly replace or exchange nails incorrectly classified. Errors
in grading nails are not tolerated because (1) the grade standards
are based on the attributes that can be measured objectively
and (2) errors in interpreting the standards are easily recognized.
In sharp contrast, the precision with which the standards
currently used to grade beef animals are applied by different
individuals at the same time or the same individual at different
times may vary widely. Alleged errors in grading beef are
sometimes a source of considerable controversy. What is the
magnitude of these errors? To what extent can they be mini-
mized without altering the standards? The remainder of this
bulletin is devoted to the presentation of a method evaluating
the ability of individuals to interpret grade standards.

TECHNIQUES FOR MEASURING THE PERFORMANCE
OF GRADERS
The techniques that have been used to measure the accuracy
with which individuals separate the parts of a heterogeneous
commodity into more homogeneous products or grades fall into
2 general classifications-economic and statistical.

Economic Measures 6
Price is the most commonly accepted measure of economic

SDefinitions of grading error and related terms.
Grading Error.-The difference between a grade of a live animal and
the Federal meat grade of the carcass produced from the same animal.
A live animal slaughter grade is assumed to be correct if it corresponds to
the Federal meat grade of the carcass produced from that animal. The
authors recognize that some statisticians prefer to restrict the word "error"
to its usage in statistics, where it refers to the element of chance occur-
rence. However, most people understand "error" simply as a failure to
attain perfection, regardless of the reason for its occurrence. It is in this
latter context that the term "error" is used in this bulletin.
Federal Meat Grade or Meat Grade.-The final grade assigned to a
carcass or a wholesale cut of beef by a Federal meat grader.
Federal Meat Grader.-An individual who decides into which U. S.
grade the quality characteristics of beef carcasses or wholesale cuts fall on
the basis of U. S. standards for beef, and who is authorized to place on the
meat an official stamp indicating the grade. Federal meat graders are
employees of the United States Department of Agriculture.
Live Animal Slaughter Grade.-The grade of a live animal is an estimate
of the grade of the carcass it will yield.
Live Animal Grader.-An individual who estimates the grades of live
animals.
Grading Performance.-A grading performance is comprised of the
estimates an individual grader makes of the grades of animals or carcasses
in 1 lot. A lot may be any finite number of animals or carcasses.







16 Florida Agricultural Experiment Stations

value. To the extent that grades provide an effective means of
differentiating either products or the demand for any 1 product,
each grade has a unique demand function (9). Since (1) price
is determined by the relationship between the supply of and
demand for a product in a competitive economic environment
and (2) the characteristics of supply and demand functions of
products differ, it must be concluded that the relationship be-
tween the price of different grades (regardless of whether the
differences are real or illusionary) will vary over time. For
example, the spread between the prices of such things as chicken,
pork, U. S. Good beef and U. S. Choice beef will change in re-
sponse to a change in per capital income of consumers, the price
of chicken or, for that matter, any change that will affect de-
mand for any 1 of the products. Likewise anything that alters
the supply function of a product will change the relationship
between the supply of and demand for competing products.
The following examples illustrate the magnitude and vari-
ation of the economic value of grading errors of 5 live-animal
graders in 2 different economic situations. The price spreads
between 4 grades of beef carcasses at 2 points in time are shown
in Table 1. In situation A, a buyer who paid for U. S. Good
grade cattle on the basis of this estimate of the grade made an
error of 51/2 cents per pound of carcass on every animal that
actually produced U. S. Standard grade carcasses. On a thou-
sand pound animal yielding 55 percent, this error had a value
of $30.25. On the other hand, the same grading error in price
situation B would have an economic value of only $11.00. The
difference between these errors at the 2 points in time was due
entirely to changes in the relationship between the supply of
and demand for these products. The values of the grading

TABLE 1.-ACTUAL PRICES PAID PER POUND, F.O.B., PLANT, FOR FULL
GRADES OF SLAUGHTER STEER CARCASSES, ON Two SEPARATE OCCASIONS.
Official Situation A Situation B
Grade Price E Spread Between Price Spread Between
Paid Full Grades Paid Full Grades

Choice ......... .34 .46
.01 .03
Good --........... .33 .43
.055 .02
Standard ...... .275 .41
.02 .02
Utility ............ .255 .39








Economic and Statistical Evaluation of Grading Cattle 17

errors of 5 individuals on 1 lot of cattle under price situations
A and B are shown in Table 2.

TABLE 2.-POUNDS OF CARCASSES FROM A SELECTED LOT OF STEERS AND
THEIR TOTAL GROSS VALUE BASED ON PRICES IN TABLE 1, BY FOUR U. S.
GRADES, GROUPED AS TO THE OFFICIAL MEAT GRADE AND THE ESTIMATES
OF FIVE LIVE-ANIMAL GRADERS.

SUSDA Live-Grader
Official Meat
Grade Grader 1A 2A 3A 4A 5A

Pounds of Warm Carcass, Less 2% Shrink

Utility ............. 2,771 1,774 4,961 3,636 6,828 9,719

Standard .......... 29,870 44,295 31,411 38,394 45,161 28,369
Good .................. 39,769 29,648 37,251 33,677 25,740 31,023
Choice ................ 6,646 3,339 5,433 3,349 1,327 9.945

Total ...........- 79,056 79,056 79,056 79,056 79,056 79,056


Gross Value of I
Lot Price
Situation A ...... $24,304 $23,552 $24,043 $24,012 $23,105 $23,898
Value of
Grading Error* ........... $ 752 $ 261 $ 292 $ 1,199 $ 406
Gross Value of
Lot Price
Situation B ..-... $33,485 $33,137 $33,330 $33,181 $32,857 $33,336
Value of
Grading Error* .......... $ 348 $ 155 $ 304 $ 628 $ 149

The gross value of the lot was calculated for each individual, using his estimates of
grade. For each of the 4 full grades the carcass weights of all animals were summed, then
multiplied by the appropriate price. For instance, the total weight of the carcasses from all
the animals Grader 1A estimated to be U. S. Utility was 1,774 pounds. At a price of 251
cents per pound, 1,774 pounds has a gross value of $452. The gross value of the carcasses
in each of the 4 grades was added to obtain the lot total. The difference between the lot
total based on the final official grades and the lot total based on a live-grader's estimated
grades constitutes the error.

The fact that both the range and magnitude of the price of
beef are constantly changing makes it impossible to determine
economic value of grading errors any individual may make at
any time in the future. On the other hand, it is possible to
measure the average value of a grading error of any specified
size over any period of time in the past, using past records of







18 Florida Agricultural Experiment Stations

prices and price spreads. Furthermore, it is possible to use
historical data to establish arbitrary monetary value for any
given grading error. This value can then be used to measure
the magnitude of grading errors on any lot of cattle and even
to predict the monetary value of the grading errors that will
be made in the future. Whether such predictions hold true will
of course depend on whether the historical relationships between
prices continue to prevail.
It is also important to recognize that when cattle are graded
in lots, the value of grading errors calculated by different
methods varies widely. For example, on the lot of cattle graded
by Live-Animal Grader 1A (Table 2) the value of the grading
error calculated by summing the weights of each carcass in its
estimated grade was $752. Had this error been expressed as
an average on the basis of the difference between the average
meat grade of the lot (8.81) and Grader 1A's estimate of the
grade of the lot (8.05), it would have been 0.77 thirds of a grade,
or 0.256 of a whole grade. Assuming price to be a straight-line
function of the characteristics within the grade, this grading
error based on a $0.055 price spread between U. S. Standard
and U. S. Good grades would have an economic value of ($0.055)
x (0.256) x (79,056), about $1,113. This is $361 more than when
estimated on an individual animal basis. The same grading
error would have an economic value of zero if the seller received
no price differential for within-grade differences in the character-
istics of the carcass. On the other hand, a grading error of
the same size (.256 of a whole grade) on a lot of cattle actually
grading 9.156 (Low U. S. Good), but estimated to grade 8.900
(High U. S. Standard), would have an economic value of 0.055
cents per pound or $4348 on 79,056 pounds.
Since the price spread between product differential by grades
varies in both time and space, the difference in price of 2 grades
is not a reliable measure of the errors graders make in classify-
ing a heterogeneous commodity with grades. Hence, it is neces-
sary to seek more stable measures of grading errors.

Statistical Measures
Grading performances can also be evaluated in terms of how
accurately individuals can estimate the grades of carcasses pro-
duced from a particular lot of live animals, regardless of the
economic value of the animals or carcasses. Quantitative meas-







Economic and Statistical Evaluation of Grading Cattle 19

ures of the performances of live-animal graders have their
origin in records of (1) estimates of the grades of carcasses
expected from particular animals (live-animal grades) and (2)
the official grades of the carcasses actually produced from the
same animals.
To obtain data of this kind it is necessary to identify each
live animal with a code designation, record its live-grade esti-
mate with this code designation, physically transfer the code
designation from the animal to the carcass just prior to skin-
ning, and record the carcass grade with the code designation.
This is a time-consuming operation, one that commercial packers
consider too expensive to use extensively, even when the sales
are based on carcass grades and weights. In many cases of
carcass grade and weight sales, all of the animals purchased
from 1 seller are kept together by marking the first and last
animal slaughtered and identifying these 2 carcasses on the
rail. The lack of a simple and inexpensive method of identifying
the carcass produced from every animal makes it difficult to
train new graders and check on the accuracy of experienced
live-animal graders. Nevertheless, arrangements can be made
to obtain records of the grades of carcasses produced from
identified animals.
Previous Research.-Early investigations of the accuracy
with which individuals estimate the grades of live animals de-
scribe the performances of single graders in terms of (a) scatter
diagrams of the relationships between live-animal and carcass
grades and (b) statistical measures such as the average or
mean differences between live-animal and carcass grades and
the variance of these differences around actual and arbitrary
means (2), (4). The mean error and the standard deviation of
errors are mathematical measures of the magnitude and disper-
sion of the errors in estimating actual dressing yields and carcass
grades.7 Frequency distributions of the type used in statistical
analyses are also used for this purpose. The percentage of
correct estimates and the percentage of estimates that fall within
a range of one-third of a grade below to one-third of a grade
above the official carcass grade are other measures of a grader's
performance (10), (1), (8). The analysis of variance in a linear
regression of the carcass grades on the estimated grades is still

SA. A. Dowell et.al., op. cit. These researchers used the mean error and
standard deviation of errors to measure the performance of one grader on
several classes of animals, but not to compare the performance of different
graders.







20 Florida Agricultural Experiment Stations

another technique that has been used (6). In this approach
the differences between mean errors and between regression
coefficients are tested for indications of randomness.
Evaluation of Conventional Techniques.-Practically all of
the early investigators used some variation of regression or
correlation analysis to evaluate the performance of graders.
Regression.-The relationship between perfectly accurate
live-animal grade estimates and carcass grades can be described
graphically by an unbiased linear regression line Y = X. Like-
wise, the relationship between an individual's live-animal grade
estimates and the carcass grades can be described by a biased
linear regression line Y = a + bX. A biased regression line
lying above the unbiased line indicates the grader's average
estimate of the grade of animals in each of the several carcass
grades was above the carcass grade (Fig. 1-A). Conversely, a
biased regression line lying below the unbiased line indicates that
the grader underestimated the carcass grade on the average
(Fig. 1-B). A biased line crossing the unbiased line indicates
that the grader overestimated some grades of cattle and under-
estimated others. In each instance, however, it must be remem-
bered that a linear regression line assumes a linear relationship
between the variables. However, there is no compelling reason
to believe that the relationship should be linear between a
grader's estimates of several grades of animals and their official
carcass grades.8
Scatter diagrams or frequency charts describe the relation-
ship between the estimates of several grades of animals and
their official carcass grades in more detail than the regression
equation or line. These graphic measures have the advantage
of being independent of the assumption of linearity, but do not
summarize a grader's ability quantitatively.
Correlation.-A correlation coefficient simply measures the
ability of a live-animal grader to rank the animals in the same
order as the meat grader regardless of the accuracy of either
the live-animal or carcass grades. In other words, a high cor-
relation indicates that the live-animal grader was, so to speak,

8 Postulating a linear relationship between estimate grades Y and
carcass grades X strains the implicit assumption of homoscedasticity, or
homogeneous variance about the true regression line. Because the range
of existing meat grades is restricted to 8 whole grades. It is impossible
to overestimate high prime and underestimate low canner. For any meat
grade the estimates cannot diverge beyond these 2 extremes. However,
the problem does not become acute until inferential analysis is attempted.







Economic and Statistical Evaluation of Grading Cattle 21

BIASED REGRESSION
"Y LINE DOMINATED BY
OVERESTIMATE
U V

1-A


I- /
SUBASED REGRESSION LINE
OF CORRECT ESTIMATES
S,4
450

CARCASS GRADE

Y
UNBIASED REGRESSION/
W LINE OF CORRECT
ESTIMATES 1
1-B







BIASED REGRESSION
45. LINE DOMINATED BY
OVERESTIMATES

CARCASS GRADE
Fig. 1.-Two hypothetical lines of linear regression of estimated grade (Y)
on official grade (X).







22 Florida Agricultural Experiment Stations

"in gear" with the meat grader, but does not show whether
they were on the same road.
In more technical language, a coefficient of perfect correlation
(one) indicates a degree of correspondence between the carcass
grades and a live-animal grader's estimates that is represented
on a graph by a straight line passing through all the points.
However, this straight line would indicate a perfect grading
performance only if it were identical with the unbiased regres-
sion line, thus passing through the origin and having a slope
of 45 degrees (Fig. 1). If all the estimates lay along a biased
line the correlation would be perfect, but it would not indicate
a perfect grading performance. Thus it is apparent that meas-
uring grading performances in terms of correlation coefficients
can be misleading.
Since neither conventional regression nor correlation provides
a very satisfactory technique for measuring the accuracy of
graders, the usefulness of these techniques that have been used
for these purposes and 1 new application of a recognized statisti-
cal technique are compared in the following section.

EVALUATION OF FOUR STATISTICAL MEASURES
OF GRADING PERFORMANCE
Measures Compared
The 4 statistical measures of grading performance compared
are:
1. Percentage of Correct Estimates.9
2. Percentage of Estimates Falling within a Range of One-
Third of a Grade Below to One-Third of a Grade Above the
Official Carcass Grade.10

Number of Correct Estimates Percent Correct
x 100 Estimates
Total Number of Estimates Estimates
1o Number of Estimates Within
One-Third Grade Above and
Below the Official Carcass Grade Percentage of Estimates
x 100 = Within One-Third of
Total Number of Estimates Official Carcass Grade
In terms of errors this measure is also the percentage of errors of
estimate within a range of plus and minus one-third grade. In most of the
published studies on grading accuracy a grade unit of one-third federal
grade was used.







Economic and Statistical Evaluation of Grading Cattle 23

3. Mean Absolute Error." The average of the absolute dif-
ferences between the live grade estimates and their correspond-
ing official carcass grades.
4. Index of Precision in Grading.12 The square root of the
average of the squared differences between the live-grade esti-
mates and their corresponding official carcass grades.

Source of Data
Three lots of animals were used. Lots A and B consisted of
steers selected for experiments designed to study the response
of different breeds of cattle to different rations. Lot C was
made up of animals offered for sale on a single day in 1 stock-
yard.13 The number of animals and the number of individuals
estimating the grades of the animals in each lot are shown in
Table 3. Of the 26 grading performances 14 recorded on the 3
lots, 18 were recorded by individuals grading 1 lot of animals
and 8 were recorded by four individuals grading both lots
A and B.

This measure is similar to the conventional mean deviation or average
deviation in which all deviations are entered as positive quantities. Alge-
braically this is:
n
i ij 1 Yij X
n
where
d = the mean absolute error calculated for the i'" grader,
Yij = the live grade estimate of the jt animal by the ith grader,
Xj = the official carcass grade of the jth animal and
n = number of animals on which live grade estimates were made by
the ith grader.
This measure is computed as a standard error of estimate, or a standard
deviation about the line Y = X. The calculation differs from the Mean
Absolute Error only in that the differences are squared before summing
and then the square root is taken. Algebraically this is:

S (Yij X )
Ip= =
n
where Ip is the index of precision, and the other symbols are defined in
footnote.
"3A description of the 3 lots of animals and how they were graded
appears in Appendix 1.
A grading performance is comprised of the estimates 1 individual
makes of the grades of animals or carcasses in 1 lot.







24 Florida Agricultural Experiment Stations

TABLE 3.-NUMBER OF ANIMALS, AND NUMBER OF INDIVIDUAL GRADING
PERFORMANCES, BY THREE SELECTED LOTS OF CATTLE.

Lot Number of Animals Number of Grading
Performances
A 128 5
B 119 11
C 236 10

Total 483 26


Because the data examined in this study were not, in a prob-
ability sense, representative of specified populations, they can-
not be used to draw statistical inferences-inferences about the
validity of conclusions regarding the differences among the
abilities of individuals to estimate the grades of cattle. On the
other hand, these data are quite adequate to (a) illustrate the
application of alternative techniques evaluating the performance
of graders and (b) provide information that will aid the design
of experiments from which statistical inferences can be made
about the performances of graders.

Comparison of Individual Scores
Data describing the 26 performances were first summarized
in the form of frequency distributions (Appendix 2), and the
5 performances on Lot A animals were summarized also in the
form of scattergrams (Appendices 3, 4, 5, 6, 7). As pointed
out earlier, these graphic summaries provide detailed insight
into the nature of performances but do not provide a basis for
comparing them quantitatively. Nevertheless, they are of some
value in interpreting the methods presented herein.
Four scores representing percentage of correct estimates,
percentage of estimates within a third of a grade of the carcass
grade, mean absolute error and index of live grading precision
were calculated for each of the 26 performances (Table 4). The
performances were then arrayed in order of rank according to
index of precision scores, and these ranks were compared with
ranks according to scores by the 3 other measures (Table 5).
The rankings according to scores based on percentage of correct
estimates and percentage of estimates within plus or minus
one-third of a Federal grade of the carcass grade differ from







Economic and Statistical Evaluation of Grading Cattle 25

each other and from the rankings by mean absolute error and
index of grading precision scores. The differences between
ranking by the percentage of correct estimates and percentage
of estimates within a third of a grade of the Federal grade origi-
nate largely from the number of estimates considered correct
in calculating the percentages. For example, grading perform-
ance 5A had the highest score based on percentage of correct
estimates, but ranked fourth when scored on the percentage
of estimates within plus or minus a third of a grade of the carcass
grade, since graders 1A, 3A, and 4C were able to place a larger
proportion of their estimates within the broader limits (Table 4).

TABLE 4.-ARRAY OF SCORES BY PERCENTAGE OF CORRECT ESTIMATES, PER-
CENTAGE OF ESTIMATES WITHIN ONE-THIRD OF A FEDERAL GRADE OF THE
CARCASS GRADE, MEAN ABSOLUTE ERROR AND INDEX OF LIVE GRADING
PRECISION, FOR 26 GRADING PERFORMANCES.
Percent-
age of
SCorrect
Percent- Esti- Mean Index
age of Per- mates Per- Abso- Per- of Per-
Correct form- Within form- lute form- Pre- form-
Esti- ance + or ance Error ance cision ance
mates % of a
Federal
Grade

33.6 5A 77.3 3A 1.03 1A 1.38 1A
31.4 8C 76.6 1A 1.05 3A 1.39 3A
29.7 1A 71.6 4C 1.06 5A 1.44 5A
29.2 6C 70.3 5A 1.11 8C 1.47 2A
28.8 9C 69.5 8C 1.12 2A 1.49 4C
28.8 1C 69.5 2A 1.13 4C 1.50 8C
28.1 2A 67.8 1C 1.16 1C 1.53 1C
27.5 7C 65.7 9C 1.24 4A 1.62 4A
27.1 4C 64.4 6C 1.25 6C 1.68 20
26.6 4A 64.1 4A 1.28 9C 1.69 6C
26.6 3A 63.9 5C 1.30 5C 1.70 5C
25.8 5C 62.7 10C 1.32 2C 1.73 9C
25.4 10C 61.4 2C 1.34 10C 1.76 10C
25.2 7B 61.0 | 7C 1.38 3C 1.77 3C
22.7 10B 60.6 | 3C 1.39 7C 1.86 7C
22.5 2C 49.6 10B 1 1.59 7B 2.01 7B
22.1 6B 48.7 7B 1.62 10B 2.04 10B
21.8 2B 44.5 1B 1.70 4B 2.09 4B
21.0 4B 43.7 4B 1.74 1B 2.14 1B
20.3 3C 42.9 11B 1.73 2B 2.15 2B
20.2 8B 42.9 2B 1.76 8B 2.17 8B
20.2 1B 42.0 8B 1.82 6B 2.21 6B
19.3 9B 38.7 5B 1.87 5B 2.25 5B
17.6 5B 36.97 9B 1.91 11B 2.33 11B
16.8 11B 36.97 3B 1.99 3B 2.39 3B
16.0 3B 36.8 6B 2.08 9B 2.56 9B
-- I. _ I I I I







26 Florida Agricultural Experiment Stations

Similarly, grading performance 3A had the highest score based
on percentage of estimates within a third of a Federal grade of
the carcass grade but ranked tenth on percentage of correct
estimates because of a failure to estimate the correct grades
of more animals.

TABLE 5.-TWENTY-SIX GRADING PERFORMANCES ARRAYED IN ORDER OF
RANK ACCORDING TO INDEX OF PRECISION SCORES, AND COMPARISON OF
RANKS ACCORDING TO SCORES BY MEAN ABSOLUTE ERROR, PERCENTAGE OF
CORRECT ESTIMATES, AND PERCENTAGE OF ESTIMATES WITHIN + OR -
ONE-THIRD OF A FEDERAL GRADE.

Rank on Basis of
I Percentage of
Perform- Index Mean Percentage Estimates Within
ance of Absolute of Correct + or -
Precision Error Estimates One-third of a
S_ Federal Grade

1A 1 1 3 2
3A 2 2 10.5 [ 1
5A 3 3 1 I 4
2A 4 5 7 5
4C 5 6 9 3
8C 6 4 2 6
1C 7 7 5.5 7
4A 8 8 10.5 10
2C 9 12 16 13
6C 10 9 4 9
5C 11 11 12 11
9C 12 10 5.5 8
10C 13 13 13 12
3C 14 14 20 15
7C 15 15 8 14
7B 16 16 14 I 17
10B 17 17 15 16
4B 18 18 19 19
1B 19 20 21.5 18
2B 20 19 18 21
8B 21 21 21.5 22
6B 22 22 17 26
5B 23 23 24 23
11B 24 24 25 20
3B 25 25 26 25
9B 26 26 23 24


Since neither of these percentage scores fully evaluates the
accuracy of all the estimates in a grader's performance, it is quite
obvious that all estimates falling within two-thirds of a federal
grade of the carcass grade would produce still a different rank-
ing. Thus, it appears that any score calculated on a portion
rather than all of a grader's estimates is unnecessarily arbitrary
and fails to adequately describe the performance. Consequently,







Economic and Statistical Evaluation of Grading Cattle 27

the 2 methods of scoring that evaluate all rather than part of
a grading performance are examined.
The mean absolute error and the index of live animal grading
precision both evaluate all of the estimates in a performance
and differ from each other only in their weighting of errors of
different magnitudes. The mean absolute error gives the same
weight to all errors of estimation (see definition p. 23) while
the index of precision, due to the fact that the errors are squared,
places more weight on large errors than on small errors. Be-
cause of this difference in weighting, the index of grading pre-
cision scores are somewhat larger than the mean absolute error
scores (Table 4), but the rankings are almost identical (Table 5).
This tends to support a prior logic that a score evaluating all
the estimates in a grading performance is more informative and
reliable than one using only a portion of the estimates.
The difference between the index of precision and the mean
absolute error is best illustrated empirically by grading per-
formances 2C and 6C (Fig. 2 and Table 5). On the basis of the
index of precision performance 2C ranks ninth, whereas on the
basis of the mean absolute error it ranks twelfth. Performance
6C ranks tenth on the basis of the index and ninth on the basis
of mean absolute error. Performance 2C contained a narrower
range of errors (3 below to 5 above the correct grade) than
performance 6C (4 below to 6 above), but a higher percentage
of the error in performance 6C were small (64 percent within
one-third of a federal grade of the carcass grade in performance
6C compared to 61 percent in performance 2C). In calculating
the mean absolute error, the errors of each magnitude are
weighted by their frequency or total number. While perform-
ance 2C had a narrower range of errors, performance 6C had a
greater frequency of errors in the smaller magnitudes; there-
fore, the mean absolute error ranked performance 6C three
places above performance 2C. In contrast, by placing more
weight on the magnitude of larger errors, the index of precision
ranked performance 6C one place below 2C. Thus, there is some
evidence to support a hypothesis that the index of grading pre-
cision provides a better measure of a grader's over-all ability
than does the mean absolute error. However, the validity of
this hypothesis rests squarely on the value judgment that a
larger number of small errors is more desirable than a smaller
number of larger errors.







28 Florida Agricultural Experiment Stations

Actually, the differences in ranking of graders on the basis
of mean absolute error and index of precision scores are too
small to provide basis for choosing one over the other. From a
practical standpoint the mean absolute error is easier to cal-
culate. On the other hand, the index of precision can be broken
down into 2 components, each of which reveals useful information
about the nature of the errors. For this reason, the index ap-
pears to be the more useful measure.



29.2 PERCENTAGE CORRECT ESTIMATES 22.5
64.5 PERCENTAGE ESTIMATES CORRECT 61.4
WITHIN ONE-THIRD GRADE
1.25 MEAN ABSOLUTE ERROR 1.32
1.67 INDEX OF PRECISION 1.68


80

70
_J
< 60
z
< 50

o 40

w 30

S20-
z
10F


-4 -3-2-1 0 +1+2+3+4*56 -3-2-1 0 +1 +2+34 +5
ERRORS IN. LIVE GRADE ESTIMATE
BY THIRDS OF GRADES

Fig. 2.-Frequency Distributions of Errors of Estimate, and the Scores by
Four Measures of Grading Performance, for Two Live-Graders.








Economic and Statistical Evaluation of Grading Cattle 29

A METHOD OF DIAGNOSING GRADING PERFORMANCES

Components of Index of Precision

The 2 components of the index of precision that describe the
nature of grading errors are the mean error and the standard
deviation of errors 15. The mean error is simply a measure of
the average difference between a grader's estimates and the
grades of the carcasses. In contrast, the standard deviation of
errors around this mean is a measure of how consistently a grader
arrives at this mean error. Several methods of using these
components of the index to diagnose grading performance are
suggested below.
Mean Error of Estimate.-A zero mean error score (d) indi-
cates that, on the average, the individual recording such a score
estimated the average grade of the carcass produced from a lot
of animals exactly. A perfect or zero mean error score (d)
might be achieved by estimating the grade of each animal cor-
rectly. A zero mean error score achieved in this way can be
15

Z (Yij X)2 2 2
Ip j1i s di
where n
= the sample mean or average error of estimates or the differ-
ence between the mean of a live-grader's estimates and the
mean of the official carcass grades on a lot of animals.
2 = a sample variance of errors of estimate around the sample
s di mean error.
Si = the standard deviation of errors of estimate around the mean
error.
2
A distinction should be made between the variance s di com-
puted for use as a scoring formula, and the variance required in making
tests of significance. The variance computed as a scoring formula is the
sample variance in which the divisor is n:

2 (dij di)
a di j =
n
The same sample variance used as an estimate of a population variance
requires a divisor of n-1:
n -2
2 E (dij di)
a di J = 1
n 1








30 Florida Agricultural Experiment Stations

illustrated graphically (Fig. 3, Grading Performance L). How-
ever, a perfect mean error score might also have been achieved
by estimating half of the animals two-third of a grade low, and
the other half of the animals two-thirds of a grade high (Fig. 3,
Grading Performance M).

GRADING PERFORMANCE L
w I
0 125 I
I I

100
U)

2 75- &
d=
z

u. 50
0

W 25


Z 0 ,
-2 -1 0 +1 +2 +3
SIZE OF THE ERROR IN
THIRDS OF A GRADE.

GRADING PERFORMANCE M GRADING PERFORMANCE N
C 125-
0

100- I

d=o d =4
75 I 2 sd0 0
z I
50 -
0


oI
25-
z 3

Z 0 ,
-2 -1 0 +1 +2 -2 -I 0 +1 +2 +3 +4
SIZE OF THE ERROR IN THIRDS OF A GRADE.
Fig. 3.-Hypothetical Distribution of Errors in Live-Grade Estimates, by
Thirds of a Grade.








Economic and Statistical Evaluation of Grading Cattle 31

Since errors of over and under estimation offset each other
in the calculation, the mean error score measures only the ability
of an individual to estimate the average grade of a lot of cattle
correctly. It does not evaluate the accuracy with which the
grade of any individual animal is estimated. The mean error
score is an estimate of bias, that is, the average difference be-
tween an individual's interpretation of the standards for the
several grades of meat and the interpretation the author of the
standards intended. Mean error scores do not measure how
consistently graders can recognize animals with similar grade
characteristics.
Mean error scores of the 26 grading performances on the
cattle in the 3 lots included in this study ranged from -1.06 to
1.83 thirds of a federal grade, indicating that it is possible for
the average grade estimates of individuals to differ almost 1
full federal grade (Table 6). The economic significance of a
range of errors of 1 full grade between individuals is the differ-

TABLE 6.-MEAN ERROR SCORES AND RANK OF 26 GRADING PERFORMANCES
ON THREE LOTS OF CATTLE.

Rank Perform- Mean
ance Error*

1 10C .13
2 4C .16
3 1C .20
4 6C .26
5 2C .30
6 5C .34
7 8C .36
8 9C .43
9 7C .44
10 2A .47
11 3C .48 Range Within Lots
12 3A .49
13 5A .50 A .............. .47 to -1.06 .59
14 1A .77 B ---. ......- 1.29 to 1.83 .54
15 4A -1.06 C ............. .13 to .48 .35
16 10B 1.29
17 2B 1.43 All Lots .... -1.06 to 1.83 2.91
18 8B 1.445
19 7B 1.454
20 11B 1.54
21 4B 1.55
22 1B 1.57
23 6B 1.72
24 5B 1.74
25 3B 1.81
26 9B 1.83

Thirds of a federal grade.







32 Florida Agricultural Experiment Stations

ence that exists between the prices of the grades of cattle at the
time the performance of graders are recorded-sometimes as
much as $4.00 per hundredweight. The possibility of using these
mean error scores to diagnose the performance of graders is
illustrated in the following analysis of scores made by several
individuals on cattle (a) in different lots, (b) fed different rations,
(c) of different breeds and (d) of different grades.
Lots.-The substantially smaller range of the mean error
scores made on each of the 3 lots (less than 0.59) suggests that
the size and composition of a lot of animals and/or the conditions
under which they are graded may affect the mean error scores
of graders appreciably.16 A rather large sample of records of
the performances of graders on lots of animals that differed with
respect to composition and conditions under which they were
graded would be needed to establish source and magnitude of
the individual biases.
Ration.-The magnitude of the mean error scores on animals
fed different rations varied widely within both Group A and B
(Table 7). For animals on full feed in the dry lot, the mean
error scores were relatively small (positive and negative) ; where-
as the scores on animals fed limited rations in the drylot were
generally high (positive or negative).
The range of scores among the graders on animals in any 1
lot and fed any particular ration also varied widely (Table 7).
Again, on animals on full feed in the drylot, the mean error
scores covered a narrower range than on animals fed other
rations, with 1 exception in Lot A, that is, the animals fed
limited rations on pasture.
Breed.-The average mean error scores on animals of the
same breed were considerably smaller than the average mean
error scores on animals fed the same rations (Table 8). In both
groups of graders the best scores, that is, the low mean errors,
were made on Brahman cattle, with the average mean error
score on the Hereford-Brahman cross in Group A almost as low.
On the other hand, the highest mean error scores were made
on Hereford and Angus cattle. Had these data had their origin
in experiments designed for the purpose, they might have pro-

"1 The significance of the differences of mean error scores between lots
was not evaluated because the 3 lots of animals were not deliberately
drawn as random samples of definitive populations. Tests of significance
can provide evidence of similarities or differences among grading perform-
ances. See L. V. Dixon, "Pricing Efficiency in Marketing Beef Cattle in
South Florida," (Ph.D. dissertation, Dept. of Agricultural Economics, Uni-
versity of Florida, 1959), (Microfilm).








Economic and Statistical Evaluation of Grading Cattle 33


TABLE 7.-RANGE OF MEAN ERROR SCORES, FOR Two GROUPS OF GRADERS
ON TWO LOTS OF CATTLE, BY RATION.

Group A (5 Graders) Group B (11 Graders)

Ration Mean Error Score Mean Error Score
SNo. I No. I
SAni- [ Low High Range I Ani- Low High Range
mals I mals_

Pasture, I
No Feed ...... 0 ..... ...... 16 1.12 2.00 ] 0.88
Pasture,
Limited Feed 32 0.25 -0.44 0.69 24 1.62 2.58 0.96
Pasture,
Full Feed .... 32 0.12 -1.25 1.37 32 1.06 2.38 1.32

Dry Lot,
Limited Feed 32 0.72 -1.84 1.12 23 1.26 2.35 1.09

Dry Lot,
Full Feed .... 32 0.09 -0.91 1.00 24 0.50 1 1.08 0.58



TABLE 8.-RANGE OF MEAN ERROR SCORES, FOR Two GROUPS OF GRADERS
ON TWO LOTS OF CATTLE, BY BREED.

Group A (5 Graders) I Group B (11 Graders)

Breed I Mean Error Score I Mean Error Score
No. No. I I
SAni- I Low High | Range Ani- Low I High I Range
__mals _I mals ___I

Brahman ...--... 16 -0.06 1 -0.50 0.44 28 0.82 1.57 0.75
Charbray ........ 16 -0.12 -0.88 0.76 28 0.68 1.86 1.18
Santa Gertrudis 16 -0.31 -1.12 0.81 28 1.07 2.00 0.93
Angus ............. 0 ... .... 28 1.68 2.32 0.64
Hereford ...... 48 -0.67 -1.48 0.81
Hereford x
Brahman .... 16 -0.37 +0.50 0.87
Brahman x
Angus .... 16 -0.75 -1.56 0.81
_ _ I I _ ._ _ _







34 Florida Agricultural Experiment Stations

vided a basis for concluding that the graders were not able to
recognize the characteristics identified and described in the grade
standards as well in British breed animals as in the Brahman
or Charlaise breeds or in crosses between these with British
breeds. This, in turn might have been due to the fact that in
the area where this experiment was conducted Oriental, French
and cross-bred cattle are produced in considerable volume.
The range of mean error scores among performances also
was smaller within each lot of animals of the same breed than
on animals fed the same rations.
Grades.-Differences in the magnitude of the mean error
scores on animals of 2 groups producing 9 grades of carcasses
(Table 9) suggest, but are not sufficient to prove, that the graders
were able to estimate the grades of animals producing carcasses
ranging from Low Standard to Mid Good better than those pro-
ducing Cutter, Utility and High Good, and are likely to under-
grade the Cutter, Utility and Choice animals.

TABLE 9.-RANGE OF MEAN ERROR SCORES, FOR Two GROUPS OF GRADERS
ON TWO LOTS OF CATTLE BY CARCASS GRADE.

Group A (5 Graders) Group B (11 Graders)

Carcass Mean Error Score Mean Error Score
Grade No. No.
Ani- Low IHigh Range Ani- Low High Range
mals mals _
Cutter ............. 0 ...... ...... ...... 13 2.23 3.23 1.00
Utility ........... 6 0.17 0.83 0.66 27 1.11 1.96 0.85
Low Standard 11 -0.09 0.54 0.63 18 1.72 2.33 0.61
Mid Standard .. 20 -0.10 -1.00 0.90 21 1.33 2.29 0.96
High Standard 21 0.00 -0.86 0.86 11 0.73 2.09 1.36
Low Good ....... 14 -0.79 -1.50 0.71 11 1.00 2.09 1.09
Mid Good ........ 30 -0.43 -1.43 1.00 8 0.62 1.12 0.50
l |
High Good ...... 16 +0.06 -1.25 1.31 *......
Low Choice .... 8 -0.62 -2.00 1.38 ..

Fewer than 6 animals in each grade unit.







Economic and Statistical Evaluation of Grading Cattle 35

Standard Deviation of Errors of Estimate
The standard deviation of error score (Sd) is simply an
evaluation of a grader's ability to place animals with the same
characteristics into the same grade, that is, an evaluation of
the consistency of his performance. A grader who is able to
place all animals with the same characteristics into the same
grade would achieve a standard deviation of errors score (sd)
of zero regardless of how accurately he is able to estimate the
correct grade of the entire lot of animals, that is, regardless of
his mean error score (d). For example, it is theoretically pos-
sible for an individual to achieve a perfect or zero standard
deviation of error score (Sd) to gether with a perfect or zero mean
error score (d) by estimating the grade of every animal correctly
(Fig. 3, Grading Performance L). It is also possible to achieve
a zero standard deviation of error score (Sd) and a mean error
score (d) of four-thirds of a federal grade (Fig. 3, Grading Per-
formance N). On the other hand, a perfect mean error score
(d) might be achieved by a grader who estimated half of the
cattle two-thirds of a grade low and half two-thirds of a grade
high and did not estimate the grade of a single animal correctly,
thus achieving a standard deviation of error score (sd) of 2
(Fig. 3, Grading Performance M).
In addition to its obvious use as a measure for quantitatively
evaluating the consistency of a grader's performance, the stand-
ard deviation of error score (sd) also establishes the range within
which 68 percent of the errors fall on either side of what the
grader considered to be an average or mean grade of the lot.
For example, Grader 8B scored a mean error (d) of 1.45
thirds of a grade above the average official grade (Table 6).
This mean error score is an average of over-estimates and under-
estimates, some of which were larger than 1.45 thirds and some
of which were smaller. These errors of over and under esti-
mation in this mean error score (d) resulted in a standard
deviation of error score (Sd) of 1.62 thirds of a grade (Table 10).
This means that approximately 68 percent of these errors in
estimating the average grade of the lot lie within plus or minus
1.62 thirds of a grade on either side of this grader's estimate of
the average grade of the lot. The grader's estimate of the
average grade is the average official grade of the carcasses
adjusted (plus or minus) for the grader's mean error score (d).
In this case grader 8B's estimates for the lot averaged 1.45
thirds of a grade above the average official grade of the carcasses







36 Florida Agricultural Experiment Stations

produced. By adding 1.62 to 1.45, (+3.07), and subtracting
1.62 from 1.45, (-0.17), the range within which 68 percent of
the errors lie is established as being from -0.17 thirds of a grade
below the estimated average grade of the carcasses to +3.07
above, or a range of 3.24, (2 x 1.62), thirds of a grade. This
is shown graphically in the following manner.
Mean Error -1.62 Mean Error Mean Error +1.62
-0.17 1.45 3.07
Range Within Which 68 Percent of Grading
Errors Fall
A small standard deviation of errors score (sa) shows that a
grader is consistent in his judging regardless of the size of the
mean error recorded. A grader who records a low standard
deviation of error score (sd), that is, whose errors are tightly
clustered about the mean error, will probably find it easier to
learn how to interpret the grade standards more accurately
(that is, reduce the mean error) than a grader whose errors
vary widely (recording a high standard deviation of errors score).
The standard deviation of errors in the 26 grading perform-
ances ranged from 1.15 to 1.81 thirds of a federal grade (Table
10). Just as in the case of mean error scores, standard deviation
of error scores can be used to diagnose the performance of
graders. This is illustrated by the following analysis of the
performance of graders on (a) animals in different lots, (b)
animals fed different rations in Lots A and B and (c) animals
of different breeds comprising Lots A and B.
Lots.-The standard deviation of error scores on the animals
in Lot A were generally lowest, while the scores in Lot C were
highest, suggesting that the graders were able to recognize ani-
mals with similar characteristics in Lot A more accurately than
Lot C (Table 10). This is in sharp contrast to the mean error
scores, in which the Group C performances were best and Group
B the poorest.
For the individuals recording 2 performances, the differences
in the standard deviation of error scores were small, much smaller
than the corresponding differences between their mean error
scores. Thus, in moving from Lot A to B, the 4 live graders
maintained approximately the same degree of consistency in
interpreting grade standards even though their ability to inter-
pret the grade standards, that is, their bias, had shifted in the
direction of overestimation (Appendix 8).








TABLE 10.-STANDARD DEVIATION OF ERROR SCORES AND RANK COMPARED
WITH MEAN ERROR RANK ON THREE LOTS OF CATTLE.
SRank on Rank
Per- Standard Basis of on
form- Deviation Standard Mean
ance of Errors Deviation Error
Score* of Errors Score

1A 1.15 1 14
4A 1.23 2 15
3A 1.30 3 12
5A 1.35 4 13
7B 1.394 5 19
6B 1.3970 6 23
2A 1.3972 7 10
4B 1.40 8 21 Range of Standard Deviation of
5B 1.43 9 24 Error Scores Within Lots
1B 1.45 10 22
8C 1.46 11 7 A ........... 1.15 to 1.3972 .24
4C 1.49 12 2 B ............ 1.394 to 1.78 .39
1C 1.52 13 3 C ............ 1.46 to 1.81 .35
3B 1.57 14 25
10B 1.58 15 16 All Lots.. 1.15 to 1.81 .66
2B 1.61 16 17
8B 1.62 17 18
2C 1.66 18 5
5C 1.671 19 6
6C 1.672 20 4
9C 1.68 21 8
3C 1.71 22 11
10C 1.76 23 1
11B 1.777 24 20
9B 1.78 25 26
7C 1.81 26 9
Thirds of a federal grade.


TABLE 11.-RANGE OF STANDARD DEVIATION OF ERROR SCORES FOR TWO
GROUPS OF GRADERS ON TWO LOTS OF CATTLE, BY RATION.

Group A (5 Graders) Group B (11 Graders)
Standard Deviation Standard Deviation
Ration of Error Score of Error Score
No. No. I
Ani- Low I High Range Ani- Low High Range
mals ) mals __

Pasture,
No Feed ...... 0 ...... ...... 16 1.42 2.57 1.15

Pasture,
Limited Feed 1 32 1.03 1.58 0.55 24 1.06 1.56 0.50

Pasture,
Full Feed .... 32 1.00 1.41 0.41 32 1.16 1.39 0.23

Dry Lot,
Limited Feed 32 0.94 1.12 0.18 23 0.92 1.59 0.67

Dry Lot,
Full Feed .... 32 1.01 1.34 0.33 24 1.21 1.82 0.61







38 Florida Agricultural Experiment Stations

Rations Compared with Lots.-The standard deviation of
error scores varied over a much narrower range than did the
mean error scores (Table 11). Whereas the grade of animals
on full feed in the drylot were estimated relatively accurately
on the basis of mean error scores, the magnitude of the standard
deviation of error scores was relatively high. Conversely, the
lowest standard deviation of error scores were recorded on ani-
mals on limited feed in the drylot, the same animals upon which
the graders made the highest mean error scores.
Breed and Grade.-The range of standard deviation of error
scores of the grading performances on Lot A was similar for
each breed. On Lot B the ranges among breeds were somewhat
wider (Table 12). Grading scores sampled in well designed ex-
periments would be needed to demonstrate whether or not the
consistency with which graders estimate the grades of different
breeds is significantly different. Just as in the case of the
standard deviation of error scores by ration, for the 4 individuals
recording 2 performances, the standard deviation of error scores
by breed were generally higher on Lot B animals than on Lot A
animals (Appendix 8).

TABLE 12.-RANGE OF STANDARD DEVIATION OF ERROR SCORES FOR TWO
GROUPS OF GRADERS ON TWO LOTS OF CATTLE, BY BREED.

Group A (5 Graders) Group B (11 Graders)
Standard Deviation Standard Deviation
Breed o. of Error Score N of Error Score
No. No. 1
Ani- Low High Range Ani- Low High Range
mals ___mals Ig
Brahman .....- 16 0.97 1.37 0.40 28 1.11 1.86 0.75
Charbray ........ 16 0.93 1.32 0.39 28 1.37 1.95 0.58
Santa Gertrudis 16 0.93 1.44 0.51 28 1.16 2.11 0.95
Angus .............. 0 ..... ...... ..... 28 1.19 1.56 0.37
Hereford ........ 48 1.03 1.37 0.34
Hereford x
Brahman .... 16 1.01 1.37 0.36
Brahman x
Angus ....--. 16 1.22 1.55 0.33
I







Economic and Statistical Evaluation of Grading Cattle 39

The standard deviation of error scores do not indicate that
the consistency with which graders recognize animals having
the characteristics associated with the grade of the carcass pro-
duced from them varies much between grades (Table 13).
The impact of mean error and standard deviation of error
scores of different magnitudes on the index of precision scores
is shown in Table 14. Inasmuch as variance rather than the
standard deviation of errors is used in testing the significance
of the mean error, it will probably be desirable to record the
squared values of I,, d and sd as well as the roots (again see
Table 14).

POTENTIAL USES OF THE INDEX OF PRECISION

Quantitative Evaluations
The index of precision and its 2 components may be used in
several ways.
1. Mean error and standard deviation of error scores provide
a means of evaluating 2 sources of grading errors. As demon-
strated earlier, the scores achieved by individuals on a given
lot of cattle provide a basis for ranking the individuals accord-
ing to their ability to (a) estimate the average grade of a lot
correctly and (b) consistently classify animals with similar
characteristics into the same group. Furthermore, the range in
the magnitude of the mean error and standard deviation of error
scores reported here provide crude scales upon which the grading
abilities of other graders can be evaluated.
For example, under conditions similar to those that prevailed
at the time the scores were recorded, it may be possible to esti-
mate the mean grade of a lot of cattle within one-sixth of a
federal grade. Similarly, the standard deviation of error scores
suggest that under the same conditions, it may be possible to
recognize animals of similar characteristics with consistency
sufficient to predict that about 68 percent of an individual's
errors of estimates of live grade would fall within 1.5 thirds of
a federal grade on either side of the individual's average or mean
error of estimate.
The fact that several individuals did achieve these or better
scores is only an indication of the magnitude of the maximum
scores (minimum quality of performance) that an individual
would have to attain before being judged competent to report
livestock market news. When a larger number of scores have








40 Florida Agricultural Experiment Stations

TABLE 13.-RANGE OF STANDARD DEVIATION OF ERROR SCORES FOR Two
GROUPS OF GRADERS ON TWO LOTS OF CATTLE, BY CARCASS GRADE.

Group A (5 Graders) Group B (11 Graders)

Carcass Standard Deviation Standard Deviation
Grade of Error Score of Error Score
No. [ I I No. I
Ani- Low High Range Ani- Low High I Range
mals I I I mals

Cutter .........-- 0 ..... ...... - 13 1.08 1.71 0.63
Utility .............. 6 0.37 1.21 0.84 27 1.22 1.94 0.72
Low Standard 11 0.43 0.98 0.55 18 0.83 1.41 0.58
Mid Standard 20 0.86 1.58 0.72 21 0.79 1.75 0.96
High Standard 21 0.93 1.58 0.65 11 0.78 1.74 0.96
Low Good ........ 14 0.67 1.62 0.95 11 0.77 1.44 0.67
Mid Good ........ 30 1.23 1.48 0.25 8 1.05 1.73 0.68
High Good ...... 16 0.99 1.20 0.21 .....
Low Choice.... 8 0.99 1.50 0.51 *....

Fewer than 6 animals in each grade unit.

TABLE 14.-COMPARISONS OF SCORES AND RANKS BY INDEX OF PRECISION,
MEAN ERROR AND STANDARD DEVIATION OF ERROR, FOR 26 GRADING PER-
FORMANCES.

Per- Rank Scores Square of Scores
formance I* Sd 2 S2
formance d I d IpI* d sd d sd

1A 1 14 1 1.38 .77 1.15 1.91 .59 1.32
3A 2 12 3 1.39 .49 1.30 1.93 .24 1.69
5A 3 13 4 1.44 .50 1.35 2.07 .25 1.82
2A 4 10 7 1.47 .47 1.40 2.18 .22 1.96
4C 5 2 12 1.49 .16 1.49 2.25 .03 2.22
8C 6 7 11 1.50 .36 1.46 2.26 .13 2.13
1C 7 3 13 1.53 .20 1.52 2.35 .04 2.31
4A 8 15 2 1.62 -1.06 1.23 2.63 1.12 1.51
2C 9 5 18 1.68 .30 1.66 2.85 .09 2.76
6C 10 4 20 1.69 .26 1.67 2.86 .07 2.79
5C 11 6 19 1.70 .34 1.67 2.91 .12 2.79
9C 12 8 21 1.73 .43 1.68 3.00 .18 2.82
10C 13 1 23 1.76 .13 1.76 3.12 .02 3.10
3C 14 11 22 1.77 .48 1.71 3.15 .23 2.92
7C 15 9 26 1.86 .44 1.81 3.47 .19 3.28
7B 16 19 5 2.01 1.45 1.40 4.06 2.10 1.96
10B 17 16 15 2.04 1.29 1.58 4.16 1.66 2.50
4B 18 21 8 2.09 1.55 1.40 4.36 2.40 1.96
1B 19 22 10 2.14 1.57 1.45 4.57 2.47 2.10
2B 20 17 16 2.15 1.43 1.61 4.63 2.04 2.59
8B 21 18 17 2.17 1.44 1.62 4.69 2.07 2.62
6B 22 23 6 2.21 1.72 1.40 4.92 2.96 1.96
5B 23 24 9 2.25 1.74 1.43 5.07 3.03 2.04
11B 24 20 24 2.33 1.54 1.78 5.54 2.37 3.17
3B 25 25 14 2.39 1.81 1.57 5.74 3.28 2.46
9B 26 26 25 2.56 1.83 1.78 6.52 3.35 3.17

Because of differences due to rounding, the IP will not always be precisely equal to
V I2P in the second decimal place.







Economic and Statistical Evaluation of Grading Cattle 41

been recorded on lots of animals constituting statistically valid
representations of definitive populations, thus permitting reliable
estimates of some of the recognized variabilities, it will be
possible to establish minimum standards of performance for
each attribute of a grader's ability.
2. The index of precision score provides an over-all measure
of ability of individuals to grade the animals in a given lot or
stratum of a lot. These scores make it possible to rank individ-
uals on the basis of their over-all grading ability and to establish
minimum standards of achievement in over-all ability.
Just as the mean error and standard deviation of error scores
can be used to rank individuals on the basis of their ability to
(a) estimate the average grade of the lot and (b) estimate the
grade of animals with similar characteristics consistently, the
index of precision can be used to rank the same individuals on
their over-all ability to grade an entire lot of animals or any
stratum within the lot.
The limited data analyzed in this study suggest that under
the grading conditions that prevailed at the time the scores were
recorded, it is entirely possible for graders to achieve an index
of precision score of 2.0 thirds of a grade. In fact, 6 graders
recorded index of precision scores of 1.50 or less. Here it is
interesting to note that if the individual who scored the sixth
lowest standard deviation of error score (1.40) had scored the
same mean error as the individual who scored the sixth lowest
mean error (.34), he would have achieved an index of precision
score of 1.44 thirds of a grade, the third lowest index of pre-
cision score of 26 graders examined.
When the results of more comprehensive studies are avail-
able, it will be possible to establish a maximum value of the
index of precision score that cannot be exceeded by individuals
seeking certification as graders. Thus, the index of precision
score provides those responsible for training graders with a
practical tool for determining on a quantitative basis when an
individual achieves sufficient proficiency to be certified as a grader.
3. Quantitative measures of grading performances achieved
by the same individuals on a specific lot of cattle provide tools
for evaluating the usefulness of alternative grade standards.
Two of the objectives of preparing and adopting grade stand-
ards for beef cattle are (a) to facilitate the estimation of grade
of the carcass that can be produced from an animal and (b)
provide a uniform basis of relating prices paid for animals to







42 Florida Agricultural Experiment Stations

the price of the carcasses produced from them. Of the several
possible criteria for estimating the carcass grade an animal will
produce, the best criterion is the one that will enable individuals
to estimate the carcass grade most accurately, that is, score
minimum mean errors, standard deviations of error and indices
of precision. Hence, by holding the lot of cattle constant and
recording the estimates of the same individuals using alternative
standards, that is, having the same individuals estimate the
grade of the same animals by the use of different criteria, it is
possible to evaluate quantitatively how effectively each standard
will facilitate the estimate of carcass grades.
4. Quantitative measures of grading performance can be
used to evaluate the performance of meat graders.
Inasmuch as the grade a federal meat grader places on a
carcass is final, except in the relatively few instances in which
they are appealed, it is most important the first grade placed
on a carcass be as nearly correct as possible. Until objective
methods of distinguishing between the grades of carcasses are
developed, the accuracy of the meat grade will necessarily in-
clude some degree of human judgment.
The same measures used to evaluate the performance of live-
animal graders can be used to (1) establish a standard of per-
formance of meat graders and (2) measure the consistency with
which meat graders can recognize carcasses and cuts with similar
characteristics. Since the carcass grade is to a large extent
subjective, the standards must be established by a group of
people whose ability to identify carcasses with homogeneous
characteristics is recognized. This can be done by choosing as
a board of judges at grading schools perhaps 3, 4 or 5 individuals
whose long and successful experience in identifying federal meat
grades has demonstrated a recognized ability to interpret the
federal grade standards. For a representative lot of carcasses
or wholesale cuts each of these individuals would record his own
estimate of the meat grades independently and secretly. The
means of the grades of the board of judges would then be used
as the correct grades in calculating the mean errors and standard
deviations of errors of the members of the board. Of course,
all of the mean errors and standard deviations of error scores
made by members of the board would qualify them as graders
by virtue of the fact that they were selected as members.
Once the statistics were available describing the performance
of the board on a particular lot of carcasses or cuts, they would







Economic and Statistical Evaluation of Grading Cattle 43

constitute criteria by which the performance of individuals
seeking certification as meat graders could be evaluated. Ex-
perience might show that on a specific lot of animals, it would
be possible to train meat graders to achieve an average grade
that did not differ significantly from the average grade of the
board. In other words, the difference between the mean error
score of a successful candidate and that of the board would fall
within limits of acceptable probability. Likewise, it might be
possible for successful candidates to achieve standard deviation
of error scores that differed from the board by magnitudes within
limits of acceptable probability.
When the variance of the ability of qualified meat graders
to grade carcasses consistently has been estimated, it will be
possible to estimate more accurately the mean error and standard
deviation of error of the performance of live-animal graders. As

TABLE 15.-ADJUSTED INDEX OF PRECISION, RANK AND COMPARISON WITH
NON-ADJUSTED INDEX OF PRECISION, AND RANK FOR 26 GRADING PER-
FORMANCES ON THREE LOTS OF CATTLE.

Perform- Adjusted Rank by Unadjusted Rank by
ance Index of Adjusted Index of Unadjusted
Precision* Index Precision Index

1A 1.38 i 1 1.38 1
3A 1.40 2 1.40 2
5A 1.44 3 1.44 3
7B 1.46 4 2.00 16
2A 1.47 5 1.47 4
4C 1.498 6 1.498 5
8C 1.50 7 1.50 6
4B 1.50 8 2.08 18
1C 1.53 9 1.53 7
1B 1.56 10 2.14 19
6B 1.57 11 2.22 22
10B 1.60 12 2.04 17
5B 1.61 13 2.25 23
4A 1.62 14 1.62 8
2B 1.66 15 2.15 20
8B 1.68 16 2.17 21
2C 1.687 17 1.687 9
6C 1.69 18 1.69 10
5C 1.70 19 1.70 11
9C 1.73 20 1.73 12
10C 1.76 21 1.76 13
3B 1.76 22 2.39 25
3C 1.78 23 1.78 14
70 1.86 24 1.86 15
11B 1.86 25 2.35 24
9B 1.96 26 2.55 26

The indices of precision of Lot B graders have been reduced one-third of a grade,
while no adjustments have been made on the indices of precision of Lot A and Lot C.







44 Florida Agricultural Experiment Stations

pointed out earlier, the mean error and standard deviation of
error as calculated in this report include mean error and standard
deviation of the meat grader's errors. The importance of know-
ing the potential mean error of meat graders is demonstrated
in the following example. Assuming the individuals who graded
the carcasses produced from the animals in Lot B had graded
them an average of one-third of a grade low, the ranks of the
live-graders on the basis of indices of precision would have been
altered to some extent (Table 15).
Inferential Analysis
The usefulness of quantitative measures of grading perform-
ance will be greatly enhanced when these measures can be based
upon statistically reliable data. Reliable data will permit an
analysis from which probability statements can be made about
the significance of the differences between scores, confidence
limits, etc. Collecting the necessary data can be aided by con-
structing a model that takes the several components of grading
errors into account. A general model might take the form of
the following equation:
E = f(W, X, Y)
E = the differences between estimates of grades of live animals
and the final grades assigned to the carcasses produced
from them.
W = interpretation of the attributes of the grade standards for
live animals, that is, age of animal, degree of conforma-
tion, finish, bone structure and other attributes evaluated
in estimating the grade of live animals.
X = characteristics of external attributes of animals-attributes
that are not now in the standards and generally are not
evaluated in estimating the grade of live animals. These
variables include such things as color, breed, ration fed
and distance hauled.
Y = characteristics of the environment in which the live grade
is estimated such as length of time available for examin-
ing the animal, time of day animals are graded, char-
acteristics of light, temperature and the angle of vision
of the grader.
The results of the research reported in this bulletin suggest
the desirability of designing an experiment to quantify the co-
efficients of the variables in the above equation if it is not pos-
sible to measure the accuracy and variance of meat graders.







Economic and Statistical Evaluation of Grading Cattle 45

In the event it becomes permissible to measure the accuracy and
variance of meat graders, the equation would be modified as
follows, and the resulting E would represent a relaxation of the
assumption of 100 percent accurate meat grading.
E = f(W, X, Y, Z)
Z = interpretation of the attributes of the grade standards for
meat, that is, degree of marbling, cover, etc.
The components in the equations may be estimated as either
inclusive or individual variables, depending upon the resources
available for experimental work. A series of carefully designed
experiments are needed to determine how much of a grader's
performance can be explained by the identifiable characteristics
of W, X, Y and Z, and how much remains in the uncontrolled
terms, that is, the unexplainable causes of grading errors. When
estimates of the parameters of these unexplainable terms are
established, it will be possible to analyze the variance of any
grader's performance and make probability statements regard-
ing the range within which his grading errors will fall. This,
in turn, will make it possible to establish confidence limits on
all aspects of a grader's performance-limits that can be used
to define the minimum performance an individual must achieve
to be certified as a grader.
As reported in this bulletin, the magnitude and the variation
in the estimates based on the external characteristics of animals
provide some insight into the magnitude of the parameters of
the X factors. Similarly, the magnitude of the differences in
the scores recorded by the 4 individuals reporting 2 perform-
ances suggests the possible magnitude of the Y facors (Appendix
8). A comparison of the magnitude of the differences due to X
and Y factors in this study suggests that environmental factors
may have more influence on grading performance scores than
the external characteristics of the animals (Tables 8 and 12 and
Appendix 8).
The experimental data needed to quantify either of these
equations can be obtained by sampling defined populations and/or
by designing experiments that will produce coefficients for pre-
determined variables. Both techniques should be tried, but care-
fully designed experiments will probably produce the data that
will be most useful in the training and selection of graders and
hence, in improving the efficiency of the pricing mechanism.
More comprehensive studies based on data collected from
carefully designed experiments or adequate samples of specified







46 Florida Agricultural Experiment Stations

populations are needed (a) to make statistically valid statements
about the accuracy with which it is possible to estimate the grade
and hence, the price of cattle, (b) to establish standards for the
certification of livestock and meat graders and (c) to measure
the accuracy with which individuals can recognize the character-
istics that are used in both proprietary and public grade stand-
ards. It is neither feasible nor desirable to conduct the research
needed to achieve these broad objectives at any one time, at any
one place or by any 1 group of investigators.


LITERATURE CITED
1. E. S. Clifton. Pricing Accuracy of Slaughter Cattle, Veal Calves and
Lambs. Indiana Agricultural Experiment Station Bulletin 611,
North Central Regional Publication 53. Lafayette: Purdue Uni-
versity, 1954.
2. A. A. Dowell, Gerald Engelman, E. F. Ferrin and P. A. Anderson.
Marketing Slaughter Cattle by Carcass Weight and Grade. Minne-
sota Agricultural Experiment Station Technical Bulletin 181. Minne-
apolis: University of Minnesota, 1949.
3. A. R. Dowell and K. Bjorka. Livestock Marketing. New York: 1941.
4. Gerald Engelman, Austin A. Dowell and Robert Olson. Relative
Accuracy of Pricing Butcher Hogs on Foot and by Carcass Grade
and Weight. Minnesota Agricultural Experiment Station Technical
Bulletin 208. Minneapolis: University of Minnesota. 1953.
5. H. E. Erdman. Problems in Establishing Grades for Farm Products.
Journal of Farm Economics 32: (1)15-29. February 1950.
6. E. H. Jebe and E. S. Clifton. Estimating Yields and Grades of Slaugh-
ter Steers and Heifers. Journal of Farm Economics, pp. 584-96.
May 1956.
7. W. H. Mumford. Market Classes and Grades of Cattle with Sugges-
tions for Interpreting Market Quotations. Illinois Agricultural
Experiment Station Bulletin 78. Urbana: 1902.
8. J. J. Naive et.al. Accuracy of Estimating Live Grades and Dressing
Percentages of Slaughter Hogs. Indiana Agricultural Experiment
Station Bulletin 650. Lafayette: Purdue University, 1957.
9. Ruby Turner Norris. The Theory of Consumer Demand. New Haven:
Yale University Press, 1952.
10. C. D. Phillips and James L. Pearson. Accuracy of the Present Methods
in Pricing Veal Calves, Slaughter Cows, and Lambs. Kentucky
Agricultural Experiment Station Bulletins 610, 611, 612. Lexing-
ton: University of Kentucky, 1954.
11. James Rhodes. How the Marking of Beef Grades Was Obtained.
Journal of Farm Economics 42: 133, 149. February 1960.
12. Henry C. and Anne Dewees Taylor. The Story of Agricultural Eco-
nomics. Ames, Iowa: Iowa State College Press, 1952.
13. Willard F. Williams, E. K. Bowen and F. C. Genevese. Economics
Effects of U. S. Grades for Beef. U. S. Department of Agriculture,
Marketing Research Report 298, p. 160. 1959.








Economic and Statistical Evaluation of Grading Cattle 47


APPENDIX 1

Groups A and B.-The 5 individuals in Group A estimated
the live animal slaughter grades of 128 steers in Lot A that had
been fed 120 days in a split-split plot design using several anti-
biotics and feed combinations. The 11 individuals in Group B
live-graded 119 steers in Lot B that had been treated similarly
to those in Lot A. The breeds in each lot were:

Lot A Lot B
No. No.
Braford ............ ----------..........-- 16 Braford ........-----........ ............ 30
Charbray --..........-.......- --......- ...... 16 Charbray ..........-----...... ..........------ 30
Santa Gertrudis .......--...........-...... 16 Santa Gertrudis ....----...........- ...- --- 30
Brahman x Angus .--....-.......-..-- 16 Angus ....-... --......-- --.... -.......... 29
Brahm an .--.......--...... ..... .... .......... 16
Hereford ...................................----- 48
Total ....................................... 128 Total .......---....---.....--- .... ..----- 119

The graders made independent estimates of the live animal
grade on each animal individually as it moved about in a large
penned area. Each animal was observed for a longer time than
occurs in an auction ring. The weight of each animal was not
given to the graders.
All the men in Group A and B had previous experience in
live grading, and several had at some time in the past followed
animals through to slaughter where they compared their esti-
mates with the carcass grades.
Group C.-The 10 individuals in Group C live graded 236 ani-
mals in Lot C. Information as to breed is not available. The
classes in Lot C were:

Heifers ...----------.................. ........... 86
Calves .......----....... ........-- ...... -82
Cows ........ .....---- ..---- --... .- ...... 45
Steers ...---..--.............- ........--- .... 23
Total ...----.... --.....-- .......... .-- 236

The graders made independent estimates of the live animal grade
after observing each animal independently, in a pen, for a longer
time than occurs in an auction ring. All men had previously
attended a brief grading school. Experience in grading varied;
all men had at least some experience in comparing live and car-
cass weights and grades.








48 Florida Agricultural Experiment Stations






APPENDIX 2


Frequency Distributions of Errors for Twenty-Six Grading
Performances, and Five Quantitative Measures of Each Distribu-
tion.


hi1 I, Index of Precision 'd Mean Error s,, Standard Deviation of Error
"" = Percentage Correct Estimates d= Mean Absolute Error


50' GRADER IA GRADER 2A GRADER 3A GRADER 4A

40
Z I, = 1.38 I, =1.47 I, 1.40 Ir =1.62
S 30 d .7 = -.47 d -.49 = 1.06
s 1.15 sa = 1.40 s1 =1.30 s, 1.23
d 1.03 d =1.12 d 1.05 d 1.24
z 20-

10 |
0

"4321012 4321 _0123 432 10123 432101
MAGNITUDE OF ERRORS IN LIVE -RADE ESTIMATE
LE BY THIRDS OF GRADE
50 GRADER 5A GRADER IB GRADER 2B GRADER 3B

40
""I, =1.44 I, = 2.14 I = 2.15 I 2.39
S= -.50 = 1.57 d 1.43 d 1.81
30 19o
sS 1.35 s =1.45 s 1.61 s 1.57
Z 30 d=1.06 =1.74 d 1.73 d 1.99

20

Sto
10


4321012 321012345 321012345 321 0(123456
MAGNITUDE OF ERRORS IN LIVE GRADE ESTIMATE
"u. BY THIRDS OF GRADE









Economic and Statistical Evaluation of Grading Cattle 49





APPENDIX 2-Cont.



50 GRADER 4B GRADER 5B GRADER 6B


40


S5 I, =2,08 I, =2.25 I= 2.22
d = .55 [ 1.74 d =1.72
s=1.40 s- = 1.43 _t = 1.40
S2- d =1.70 d = 1.87 =1.82


S10-I-
5 0 - .. . . --

S 321 0123456 21012345 321012345
-+4 -+4.
MAGNITUDE OF ERRORS IN LIVE GRADE ESTIMATE
Z BY THIRDS OF GRADE
50 GRADER 7B GRADER 8B GRADER 98

o 40

S30


0 I, =2.00 I 2i.17 = 2.55.
20 1.1
20= 1.1.45 1 .4 1.s
I) s., =1.9 =1.62 2.0
w 1 0, 1.59 .76

0-
z 321012345 3210123456 3210123456
-+ -+ -+
S MAGNITUDE OF ERRORS IN LIVE GRADE ESTIMATE
o BY THIRDS OF GRADE
50 GRADER IOB GRADER 11B
>
2 40

w 30 1 .- 2.35
=1.29 sl= 1.78,
20 1.580 = 1.91
0
" 350 I* I 2.35








5432101234 43210 123456
MAGNITUDE OF ERRORS IN LIVE GRADE ESTIMATE
BY THIRDS OF GRADE








50 Florida Agricultural Experiment Stations

APPENDIX 2-Cont.

80 GRADER IC GRADER 2C

70

60
I-

S50-
S, 1.53 I, = 1.68
|1, 1.53
40 d=.20 =
S=1.52 = 1.66
S- d =1.16 .32
w 30

-20

" 10


4321.0,12345 3210 ,12345
0 MAGNITUDE OF ERRORS IN LIVE GRADE
ESTIMATE BY THIRDS OF GRADE

s 80 GRADER 3C GRADER 4C
w
S70
o
z
K 60

50
0
SI, = 1.78 I = 1.49
"' 40 d = .48 d = .16
S=1.66 d = 1.40
Sd = 1.38 d = 1.13
": 30

20 ~

10

0 '
54321012345 4321012345
-4 -+
MAGNITUDE OF ERRORS IN LIVE GRADE
ESTIMATE BY THIRDS OF GRADE








Economic and Statistical Evaluation of Grading Cattle 51




APPENDIX 2-Cont.



80 GRADER 5C GRADER 6C GRADER 7C

70

60

so
t: 50
z I, = 1.70 I, =1.69 I = 1.8c
d .34 d = .26 d .4
- 40 s =1.67 -- sa = 1.66 s,= 1.81
d = 1.30 d = 1.25 d_ = 1.39

"I 30

"20





4321012345 43210123456 543210123456
-4 ---
MAGNITUDE OF ERRORS IN LIVE GRADE ESTIMATE
u. BY THIRDS OF GRADE
o
80- GRADER 8C GRADER 9C GRADER IOC

w 70


z 60 I, =1.50 1,=1.73 1, =1.76
d .36 = .43 d = .13
S .4 = 1.68 s 1.76
0 50 d 1.12 d =1.28 d 1.34












0- -
o 40
w
S30


10

0


32101234 4321012345 54321012345
-4- -4- -4
MAGNITUDE OF ERRORS IN LIVE GRADE ESTIMATE
BY THIRDS OF GRADE







52 Florida Agricultural Experiment Stations



APPENDIX 3


Scatter Frequency Diagram of Live Animal Estimates and
Corresponding Official U. S. Carcass Grades for 128
Steers, by Live-Grader 1A.*




"w H 14
o
o M 13
o
L 12 2 2
w
H H4 2 4 I
Lr 0
0
S0 M 10 1 4 9
L 9 4I 2
W a
SH 8 3 7 4 6 1 2

2 M 7 I 8 9 4 5

4 5/9/7 4 2
SH 5. / I/ 2
I--
"M 4
c-



"3 4 5 6 7 8 9 10 I 12 13 14
L M H L M H L M H L M H
UTILITY STANDARD GOOD CHOICE

OFFICIAL CARCASS GRADE

Frequencies appearing between the parallel lines are correct estimates.







Economic and Statistical Evaluation of Grading Cattle 53





APPENDIX 4


Scatter Frequency Diagram of Live Animal Estimates and
Corresponding Official U. S. Carcass Grades for 128
Steers, by Live-Grader 2A.




"' H 14

0 M 13
L 12 I 32
w -
0 HII 4/5
"0 o
SM 10 I 2 8 4 3

SL 9 3 6 3 8 4
I a
S H 8 1 2 474 7 I
2 M M 7 I 2/26 I

-n u" L 6 5 2 5 1
SH 5 4 2 5
I-
3 M 4
I-
L 3


3 4 5 6 7 8 9 10 11 12 13 14
L M H L M H L M H L M H
UTILITY STANDARD GOOD CHOICE

OFFICIAL CARCASS GRADE







54 Florida Agricultural Experiment Stations





APPENDIX 5

Scatter Frequency Diagram of Live Animal Estimates and
Corresponding Official U. S. Carcass Grades for 128
Steers, by Live-Grader 3A.




H 14
SM 13 I
0
L 12 I I I
w
o H II I 4 /33 I
o
0 M 10 4 7 /

L9 1 4/5/13 3
S H 8 I I 4 1 7 5 I 2

Sz M 7 6/65 2 2

S L 6 2 2/ 6 I
H 5 3/2 3


I-
SM 4
I-


T-I I .
3 4 5 6 7 8 9 10 II 12 13 14
L M H L M H L M HL
UTILITY STANDARD GOOD CHOICE

OFFICIAL CARCASS GRADE







Economic and Statistical Evaluation of Grading Cattle 55





APPENDIX 6


Scatter Frequency Diagram of Live Animal Estimates and
Corresponding Official U. S. Carcass Grades for 128
Steers, by Live-Grader 4A.




SH 14
SM 13
L 12

0 H 11 2 5 4

n oM 10 I 5 6 I

o L 9 2 8 2
- H 8 1/7 7 10 2 2

Sz M 7 5 6 4 3 I

c a L 6 4 5 8 3 2
w
>. H 5 /5/2 8
I-
3j M 4
I--
SL 3


3 4 5 6 7 8 9 10 11 12 13 14
L M H L M H L M H L M H
UTILITY STANDARD GOOD CHOICE

OFFICIAL CARCASS GRADE







56 Florida Agricultural Experiment Stations





APPENDIX 7


Scatter Frequency Diagram of Live Animal Estimates and
Corresponding Official U. S. Carcass Grades for 128
Steers, by Live-Grader 5A.




gI H 14

o M 13 I /
3:
"L 12 2 7 1
w
H II 1 6 6 2
C: 0
S 0 M 10 I I I1 I 2

S L 9 6 4 4 I
Woa
H H 8 4 4 2 2 I
S M7 2/3/13 5

S L 6 1 /65 6 2

SH 5 5 3 8 3

M 4
I,-
S L 3


3 4 5 6 7 8 9 10 11 12 13 14
L M H L M H L M H L M H
UTILITY STANDARD GOOD CHOICE

OFFICIAL CARCASS GRADE








Economic and Statistical Evaluation of Grading Cattle 57




APPENDIX 8


COMPARISON OF MEASURES OF GRADING ACCURACY FOR FOUR
GRADERS EACH RECORDING TWO GRADING PERFORMANCES.

Standard
Grading Mean Error Deviation Index of
Performance of Error Precision

5A .50 1.35 1.44
1B 1.57 1.45 2.14

4A -1.06 1.23 1.62
2B 1.43 1.61 2.15
2A .47 1.40 1.47
3B 1.81 1.57 2.39
3A .49 1.30 1.39
4B 1.55 1.40 2.09













CENTENNIAL

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