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Analysis of ordinal data by David K. Hildebrand, James D. Laing, Howard Rosenthal

By David K. Hildebrand, James D. Laing, Howard Rosenthal

Ordinal facts will be rank ordered yet now not assumed to have equivalent distances among different types. utilizing help by means of judges for civil rights measures and bussing because the basic instance, this paper exhibits how such facts can most sensible be analyzed.

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Social scientists, however, frequently impose an order, viewing Independent as the middle categorypresumably because party affiliation is an index of preferences on the liberal-conservative dimension. 625, Republican 0. Typically social scientists don't go this far; although they operate as if the categories were ordered, social scientists are generally unwilling to assert that they can measure numerically the amounts of the variable represented by these categories. In fact, the Aberbach and Rockman research illustrates the typical approach; they used party affiliation as an ordinal independent (predictor) variable in the analysis of support for social services as a dependent (predicted) variable.

There are at least two related reasons which suggest that ordinal variables will long remain at the core of social science. First, ordinality appears to be important in many social phenomena. The ranking of people (in terms of their performance or seniority, for example) is often the primary criterion used to allocate rewards such as raises in pay and promotion to positions of higher responsibility, whether in professional baseball, Congress, business firms, or other institutions. Second, recent research in human cognition (Newell and Simon, 1972) suggests that it is useful to assume that people have limited information processing, hence quantifying, capacity.

Consequently, knowledge of the X state cannot benefit any prediction about Y. This implies that all Ñ values for such a distribution, whatever the specification of the error cells and weights, ought to be zero. j = Pi. for this special case, it follows that every Pij = Pi. j and "observed" errors equal "expected" errors, hence Ñ = 0. When Pij = Pi. j holds for all i and j, the variables are said to be statistically independent. The "expected" error rate then equals the rate that would occur in a population that exhibited statistical independence and had marginal probabilities identical to those of the population under analysis.

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