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In most econometric analyses the data are uniquely defined except for a choice of units (e.g., physical quantities or value flows) and/or a location parameter (e.g., time). In some cases the cardinality of the data is less clear. For instance, building inspectors may rate various aspects of dwellings and neighborhoods on a one to five scale, the resulting indices being used in regressions explaining housing prices [Kain and Quigley (1970), King and Mieszkowski (1973)]. Battalio et al. (1973) recently pointed out that the sign of the correlation coefficient may not be invariant with respect to order preserving transformations of the ordinal variable and presented a numerical example. The exact conditions under which the sign of the sample correlation between a cardinal variable and an ordinal variable is ‘identified’ are given in section 2. The case of two ordinal variables is dealt with in section 3.

Measures of partial association of any order are defined for ordinal measures using the notions of variation and covariation of ordinal measures. They are equivalent to partial correlation and regression coefficients computed on signed differences of pairs of observations. Kendall's and first-order partial and Somers's d and first-order partial d are special cases of the proposed measures.

This paper suggests a new way of applying “Proportional-Reductions-in-Error” related measures (i.e., Gamma, dyx, dxy, and Kendall's Tau's) to link logical forms of hypotheses types of ordinal measures of association. First, the basic form of associations for ordinal data are examined. Second, the analytical properties of “P-R-E” related measures are investigated. Finally, it is proposed that “P-R-E” related measures be used in testing the logical form of the relationship between variables implied in a hypothesis.

Medical researchers are often faced with the need for performing an agecorrection procedure on measurements of a variable. When the form of the underlying regression function is not known, it is customary to approximate this function by a polynomial. In this paper, a method of age-correction is proposed which eliminates the need for many of the parametric assumptions that are required in procedures employing polynomial approximations of regression functions. The Ordac Method estimates the regression function by a sequence of line segments, and leads to the assignment of n ordinal scores, each of which is assigned to 1 n of the subjects being scored. The ordinal age-corrected scores are termed ‘Ordacs’, where the ‘ord’ represents ‘ordinal’, and the ‘ac’ represents ‘age-corrected’. The proposed method is applied to data from a blood pressure study, and the statistical techniques needed to analyze the adjusted data are derived and discussed.

Under appropriate conditions, data merely about the ordering of objects—or of the separations between objects—is sometimes sufficient to fix the positions of those objects on an essentially numerical scale. This paper uses both mathematical and “Monte Carlo” results to establish and clarify the possibility of thus extracting metric information from purely ordinal data for two multidimensional cases: (a) analysis of proximities, in which one is given a single rank order of all n(n−1) 2 pairs of n objects with respect to psychological similarity or “proximity”; and (b) nonmetric factor analysis, in which one is given a different rank order of n individual objects with respect to each of m psychological attributes. As n (and m) increase, the ordinal data are found to determine a spatial representation of the objects more and more nearly to within a general similarity transformation, in the case of analysis of proximities, or an affine transformation, in the case of nonmetric factor analysis. Extensions of these results to other cases are also considered.

In summarizing ordinal data with many tied rankings, generally pre- sented in the form of a cross-tabulation, there are many considerations that enter into the selection of a statistic summarizing the degree of association. When more than two variables are analyzed simultaneously the situation is even more complex. This paper considers, for the joint distribution of three ordinal variables, the interpretation of a set of summary statistics having product-moment characteristics. This interpretation sheds some light on general problems of analysis of causal relations and relates these summary statistics to other procedures for analyzing attribute data. They are illustrated by re-analyzing some data used by Siege1 to illustrate a similar procedure.

An ordinal number is, by definition, a special kind of well ordered set; we proceed to examine its special properties.

The menu of statistics used in the analysis of bivariate tables of nominal and ordinal data is substantial, including among others C, y, D, dyx.dxy, Vp, K, ka, Xb, k, Q, T, two kinds of Ta and Tb, Tc and V, not to mention x2 and other significance tests. This bewildering array is more satisfactory to those who invent statistics than to those who use them, either as analysts or as consumers of political analysis. In choosing a measure of relationship between two attributes, it is necessary to consider more than their mathematical or statistical qualities. The level of measurement of the variables, the number of categories, the substantive meaning of the data, the analyst's purpose, whether testing significance in a sample or measuring association in a population, the proposition being investigated (whether it implies necessary or sufficient consequences or both), and the usefulness of statistics as communication devices (particularly whether they are familiar and understandable to the readership), are among the criteria for selecting measures.

Since the introduction of techniques of path analysis to sociologists less than a decade ago (Blalock, 1964; Duncan, 1966), a number of important elaborations in the use of these techniques have been offered. Among them are recent statements applying the path-analysis framework to the study of item reliability (see Werts and Linn, 1970), the incorporation of techniques for estimating models containing nonrecursive or

Techniques of multivariate analysis currently in use are rarely appropriate to an ordinal level of measurement; they are designed either for interval measurement or for nominal categories. It is possible to construct a hypothetical example in which the neglect of the ordered nature of a control variable leads to erroneous conclusions when three ordered variables are jointly cross-classified. This result suggests that, in addition to traditional methods, an additional criterion, based on the logic of partial rank correlation, should be considered in summarizing such data.

The prevalence of autism in Indonesia continues to increase. Children with autism have limited choices of food that may be consumed. This limitation can affect the low or excess intake of nutrients needed by children with autism. Various factors can affect the nutritional status of children with autism. One of them is the pattern of consumption of foods that do not diet GFCF. This study aims to determine the factors that affect nutritional status in children with autism in the School of Special Needs, Kediri. The design used was cross sectional analytic. The population in this study were all children with autism in the School of Special Needs, Kediri, as many as 31 children. The sampling technique used was simple random sampling, with a sample size of 29 children with autism. The result of ordinal regression test to analyze the influence of knowledge on nutritional status was obtained p = 0,038