Generality of likelihood ratio decisions.

A basic assumption of Signal Detection Theory - a special case of Bayesian Decision Theory - is that decisions are based on likelihood ratios (the likelihood ratio hypothesis). In a preceding paper, Glanzer et al. (2009) tested this assumption in recognition memory tasks. The tests consisted of formal proofs and computational demonstrations that decisions based on likelihood ratios produce three regularities (1. the Mirror Effect, 2. the Variance Effect, and 3. the z-ROC Length Effect). Glanzer et al. found that the three implied regularities do indeed hold for a wide range of item recognition memory studies taken from the literature. We now claim that the likelihood ratio regularities hold for decisions generally: decisions about sensory events, reasoning, weather forecasting, etc. An examination of past decision studies supports the generalization. We also report new experimental studies of decisions in two additional areas, semantic memory and mental rotation, further supporting the generalization. The results highlight the optimal characteristics of decision making in contrast to the current emphasis on its inefficiencies.

One mirror effect: The regularities of recognition memory.

The mirror effect is a pattern of results generally found in two-condition recognition memory experiments that is consistent with normative signal detection theory as a model of recognition. However, the claim has been made that there is a distinct mirror effect, the "strength mirror effect," that differs from the normative one. This claim is based on experiments on recognition memory in which repetition or study time is varied to produce differences in accuracy, where typically the ordinary mirror effect pattern is absent. If this claim is correct, it has major implications for theories of recognition memory. Therefore, a full examination of the data that support the claim was called for. To do that, we replicated the basic demonstration of the no-mirror-effect data and analyzed it further in a series of experiments. The analysis showed the following: (1) Whether or not the mirror effect occurs is determined by whether the experimenter furnishes effective discriminanda that distinguish the weak and strong conditions for the participant. (2) Once Finding 1 is taken into account, no adjustments of or additions to the normative signal detection theory explanations are necessary. (3) There is only one mirror effect, and no separate "strength mirror effect."

Three regularities of recognition memory: the role of bias.

A basic assumption of Signal Detection Theory is that decisions are made on the basis of likelihood ratios. In a preceding paper, Glanzer, Hilford, and Maloney (Psychonomic Bulletin & Review, 16, 431-455, 2009) showed that the likelihood ratio assumption implies that three regularities will occur in recognition memory: (1) the Mirror Effect, (2) the Variance Effect, (3) the normalized Receiver Operating Characteristic (z-ROC) Length Effect. The paper offered formal proofs and computational demonstrations that decisions based on likelihood ratios produce the three regularities. A survey of data based on group ROCs from 36 studies validated the likelihood ratio assumption by showing that its three implied regularities are ubiquitous. The study noted, however, that bias, another basic factor in Signal Detection Theory, can obscure the Mirror Effect. In this paper we examine how bias affects the regularities at the theoretical level. The theoretical analysis shows: (1) how bias obscures the Mirror Effect, not the other two regularities, and (2) four ways to counter that obscuring. We then report the results of five experiments that support the theoretical analysis. The analyses and the experimental results also demonstrate: (1) that the three regularities govern individual, as well as group, performance, (2) alternative explanations of the regularities are ruled out, and (3) that Signal Detection Theory, correctly applied, gives a simple and unified explanation of recognition memory data.

Likelihood ratio decisions in memory: three implied regularities.

We analyze four general signal detection models for recognition memory that differ in their distributional assumptions. Our analyses show that a basic assumption of signal detection theory, the likelihood ratio decision axis, implies three regularities in recognition memory: (1) the mirror effect, (2) the variance effect, and (3) the z-ROC length effect. For each model, we present the equations that produce the three regularities and show, in computed examples, how they do so. We then show that the regularities appear in data from a range of recognition studies. The analyses and data in our study support the following generalization: Individuals make efficient recognition decisions on the basis of likelihood ratios.