Schedule - Parallel Session 2 - Noise and Imprecision

True and Error Model of Response Variability Theories of decision-making are based on axioms or imply theorems that can be tested empirically. For example, expected utility (EU) theory assumes transitive preferences; if A is preferred to B and B is preferred to C, then A should be preferred to C. However, human behavior shows variability; the same person may make different choice responses when presented the same choice problem. A person may choose A over B on one trial, and B over A on another trial. How do we decide whether a given rate of violation exceeds what would be expected by the inherent variability of response? A standard approach has been to test stochastic properties such as weak stochastic transitivity or the triangle inequality on the binary choice proportions. It will be shown that this method can lead to systematically wrong conclusions regarding transitivity when the data contain random error. Similarly, EU theory also implies independence properties whose violations are known as Allais paradoxes. For example, EU implies R = ($98, .1; $2, .9) is preferred to S = ($47, .2; $2, .8) if and only if R’ = ($98, .9; $2, .1) is preferred to S’ = ($98, .8; $48, .2). But some people switch. Are these reversals due to variability of responses or are they “real”? A standard approach has been to compare the number of cases that switch from R to S’ to the number who switch in the opposite direction using the test of correlated proportions. It will be shown that this statistical test is not diagnostic and easily leads to wrong conclusions. This talk will present a family of true and error (TE) models that can be applied to individual or group data. The TE models require the experimenter to present the same choice problems at least twice to each person in each session. Variability of responses by the same person to the same choice problem in the same session is used to estimate the error variability. The TE models are testable models, and provide special cases representing the properties to be tested. This means that there are at least two statistical tests in any given application: First, one tests the TE model; second, one tests the special case (assuming the formal property such as transitivity or branch independence). TE models are more general than the “tremble” model. They also include the transitive, Thurstone and Luce models as well as certain random preference models as special cases. They are generic, like the Analysis of Variance. Whereas in ANOVA, there is a breakdown of total variance into components representing main effects, interactions, and errors, in TE, response variability is decomposed into probabilities of true response patterns and error rates. This talk will present both hypothetical and real data to illustrate how TE analysis works and to illustrate how it can lead to different theoretical conclusions from commonly applied methods that make unnecessary assumptions.