Sidney Siegel

A Nonparametric Sum of Ranks Procedure for Relative Spread in Unpaired Samples

Abstract A nonparametric procedure is presented to test the null hypothesis that two independent samples come from the same population against the alternative hypothesis that the samples come from populations differing in variability or “spread.” Extensive tables of critical values are included for n 1≤n 2≤20. Large sample procedures are presented which include a correction for tied observations. The test is entirely distribution-free under the usual randomization procedures against the null hypothesis that the two distributions are identical. The absence of any normality assumption is a particularly important feature of the test, because its parametric alternative, the F test for variance differences, is quite sensitive to departures from normality. The test has the additional advantage of being directly applicable to non-numerical ordinal data.

Theoretical models of choice and strategy behavior: Stable state behavior in the two-choice uncertain outcome situation

A theoretical approach to the understanding of human behavior in uncertain outcome situations is suggested, an approach which draws upon utility theory, decision-making theory, and statistical association theory. Experimental evidence supporting this approach as opposed to alternative approaches is summarized. Three different formalizations are presented, and a variety of experimental tests is suggested.

DECISION MAKING AND LEARNING UNDER VARYING CONDITIONS OF REINFORCEMENT

From the work of philosophers, mathematicians, economists, and psychologists, a theory of rational choice has emerged that considers the nature of rational behavior in human decision-making.’-’O According to this approach, when a person can specify a set of alternative outcomes such that for any strategy p , he knows the probability distribution of outcomes, that person is LLrational” if he chooses a strategy that will enable maximization of expected utility. Most decision-making theorists take “probability” to mean subjective probability, and “utility” to mean subjective value. Thus a strategy p , is admissible if there is no other strategy p , such that

A method for obtaining an ordered metric scale

A method is presented for collecting data which will yield a scale on which the entities are ranked in preference (ordinality), the distances between the entities on the scale are ranked (ordered metric), and all combinations of the distances are ranked (higher-ordered metric). The sources drawn upon are von Neumann and Morgenstern (9), and lattice theory. An empirical example is given in which a higher-ordered metric scale is derived.