An information theory analysis of grades and grading with an application to beef cattle
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Information theory is used for the quantitative evaluation of beef grading schemes. This study assumes that the primary purpose of a grading scheme is to provide information about the quantities of selected quality characteristics contained in graded lots of a commodity;The entropy function is interpreted as a measure of the amount of uncertainty that exists about the quantities of quality characteristics per unit of commodity prior to receipt of a quality report. An information channel is used to represent a grading scheme, with the quantities of the quality characteristics per unit of commodity interpreted as inputs to the channel and grade messages as outputs. Mutual information between grades and quality characteristics is interpreted as the average amount of information that a set of grade messages provides about the quantities of the characteristics;Equivocation is interpreted as the amount of uncertainty remaining about the quantities of the characteristics given receipt of a grade message. In certain situations, information theory provides a definite rule for locating grade class boundaries once the number of grade classes is specified. A cascaded channel is used to represent the grade definition process when the grading scheme is based on measurements of surrogate characteristics or characteristics measured with error;Information theory techniques are developed for both discrete and continuous distributions of characteristics. It is shown that mutual information is directly related to the R('2) of regression analysis and to Anderson's likelihood ratio criterion for testing the null hypothesis that two sets of variables are independent and that equivocation is directly related to the standard error of estimate of regression analysis;Information theory is used in grade determining and quality predictive analyses of beef characteristics and five sets of beef grades in use prior to 1975 (feeder calf, slaughter steer quality, slaughter steer yield, carcass quality and carcass yield). In grade determining analyses it was possible to identify all of the characteristics that determine slaughter steer yield and carcass yield grades, but not all of the characteristics that determine feeder calf, slaughter steer quality and carcass quality grades. Aggregation of measurements on grade determining characteristics into grades results in a loss of information for all grades. The ability to predict a characteristic is greater at later stages of the market channel than at ealier stages.