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This article presents a discussion on "segregation indices" which deals with issues like the way to define the amount of Negro segregation in a city. It is to define measures of association for a contingency table with only two columns, that is, where one of the attributes, like Negro and non-Negro, is dichotomous. Instead of a minority and dominant group, one may, for instance, compare men and women, an experimental and control group, and so forth. Likewise, the manifold attribute need not be location. If there is anything special about the residential segregation problem, it is that there are a large number of census tracts roughly equal in population, that is, that the row totals of the contingency table are approximate. To convert chi square for a table with two columns into an index with the range o to 1, one merely divide it by the total population. The quotient is called the mean square contingency, or phi square. Two of the proposed indices are nothing but special applications of phi, in one case for a particular fourfold table, in the other by k table. Furthermore, the familiar approach by k table is more easily generalized.

The Mean Cost Rating (MCR) measures the differentiation ability of those variables or groups of variables used in constructing parole prediction or base expectancy tables. The literature of the past two decades suggests that it represents perhaps the most satisfactory statistical index of predictive selectivity. Its use has been limited, however, by its complex method of computation. The MCR is explained and a simplified procedure for computing it is offered. In addition; the MCR is compared with Chi-square, the J-value, and the Index of Predictive Selectivity, which have also been used to determine the selective ability of factors in the construction of prediction tables. [ABSTRACT FROM AUTHOR]

This article present an approach to measure association such that a single basic logic is used regardless of the measurement level of the variables being associated. As data progress from nominal to ordinal to equal interval in mathematical character, association measures should simply incorporate the added properties into the format used at the lower levels. The logic is adapted to the types of measurement present in the independent and dependent variables so that a complete range of association measures is available. The approach requires little new at the interval-measurement level (dependent variable) and only modest modification of existing procedures for ordinal dependent variables. The two basic approaches to association measures appear to be assessing departure from randomness and determining extent of predictive accuracy. Departure from randomness is characteristic of the chi-squared based measures, which typically suffer from normalizing procedures that admit no easy operational interpretation.

The article presents a study on 238 first-grade children's perceptions of interactions, as reported by questionnaire-interviews; and actual teacher-student interaction, and measured by a Reading Observation Record, to determine whether teachers discriminated against boys. Obtained data were treated by use of chi-square and analysis of variance procedures. In addition, reading achievement scores of boys and girls were compared. Results indicated that children perceived that teachers discriminated against boys and favored girls in the situation of reading instruction. On the other hand, an analysis of observations of actual teacher-pupil interaction revealed no differential treatment. Boys' and girls' achievement did not differ significantly.

This discussion of the hypothesis, evidence, and inference presented in an American Educational Research Journal article has attempted to highlight the strengths and weaknesses of the material presented. The purpose here is not to question the competency of the principal investigator, for undoubtedly many of the questions raised herein could be answered by referring to the detailed report of the study that was submitted to the U. S. Office of Education. This discussion is presented to call the attention of the readers to strengths and weaknesses of the study, to encourage their consideration of them in reaching conclusions, and to encourage others to engage in the process of critical evaluation of publisbed research articles. [ABSTRACT FROM AUTHOR]

A response by Enrico T. Federighi to a letter to the editor about his article "The Use of Chi-Square in Small Samples" in the December 1950 issue is presented.