Stability and agreement criteria for the termination of Delphi studies

This paper addresses the question of the methodology of testing for stability between successive Delphi rounds and the necessity of doing so prior to the analysis of the level or type of consensus. Following a discussion of a hierarchical set of a criteria for determining the termination of such studies, the paper reviews some of the more common treatments of the subject in the literature. It is finally proposed that a χ² test be used to test the stability of responses between rounds. The method is demonstrated by a numerical example.     

A note on the extension of tables for the Friedman statistic

Abstract  The tables for the Friedman rank-test arc extended using a sampling method. A table is given for the traditional significance levels .01, .025, .05 and .10 for number of blocks equal to 7 and 8 and for treatments of size 6 and 7. A brief discussion of available tables is also included along with an example of an application.     

Exceptional Convergence of the Sample Variance

The case is investigated when Hoeffding's one sample U–statistic theorem for the sample variance S² is not applicable. It is shown that this occurs only when the parent distribution is the two–point distribution with jumps of equal magnitude. For this exceptional case the standardised S² is shown to converge in distribution to (1 – V )√2, where V has chi–square distribution with one degree of freedom.     

Testing equality of variances in the analysis of repeated measurements

The problem of comparing the precisions of two instruments using repeated measurements can be cast as an extension of the Pitman-Morgan problem of testing equality of variances of a bivariate normal distribution. Hawkins (1981) decomposes the hypothesis of equal variances in this model into two subhypotheses for which simple tests exist. For the overall hypothesis he proposes to combine the tests of the subhypotheses using Fisher's method and empirically compares the component tests and their combination with the likelihood ratio test. In this paper an attempt is made to resolve some discrepancies and puzzling conclusions in Hawkins's study and to propose simple modifications.
The new tests are compared to the tests discussed by Hawkins and to each other both in terms of the finite sample power (estimated by Monte Carlo simulation) and theoretically in terms of asymptotic relative efficiencies.     

Ratings and confirmation

We present a formalism which makes explicit and precise the confirming effect of multiple observers and repeated trials on composite ratings, considering the relevant subjective inputs.     

Analysis of arrest rates for trends in criminality

During the 1960s, the United States experienced a substantial increase in crime with the rates of reported crime more than doubling. It has been postulated that the increase in the proportion of young adults in the population which also occurred during the Sixties is a primary factor in the increase in crime. In this paper, we attempt to explore this question by partitioning the recent increases in rates between an increasing crime-committing propensity for various demographic groups on one hand, and a changing demographic mix to the other. We do this by analyzing arrest rates by demographic group over time. However, since arrest rates are a complex function of both criminality and police activity, a model is developed which attempts to distinguish between these phenomena. The model is estimated using data on age, race, and sex-specific arrest rates for Pittsburgh residents over the period 1967–1972. The results of the analysis suggest that there has been no significant increase in criminality for men in the Pittsburgh population, while there is some evidence of increased criminality for women. However, this increase may reflect an increased willingness of the police to arrest women. We hesitate to generalize our conclusions too widely from the experience of a single urban center. Additional analysis, using the model developed here, of arrest rates from other cities or regions would do much to illuminate this very significant issue.     

Dynamic effects of externalities,optimal saving and economic growth

Conclusion Recognizing the fact that provision of mixed public goods can result in both consumption externalities of the Samuelsonian variety as well as production externalities we set out to extend the earlier results of Rao and Kalpagam (1977) on the effect of public goods on economic growth. In so doing, we considered three standard specifications of production externalities and enlarged the concept of consumption displacement. Our basic conclusion is that the results of our earlier paper remain valid under the more general conditions set out in this paper.