As originally proposed by Kenneth Deffenbacher, the optimality hypothesis states that the likelihood of obtaining statistically reliable positive correlations of witness confidence and accuracy varies directly with the degree of optimality of information-processing conditions present for the witness at stimulus encoding, during memory storage (retention interval), and at memory test. The more nearly ideal the processing conditions are for witnesses, the more they should be able to track accurately the adequacy of their memory performance in overtly expressed confidence ratings. The context in which the optimality hypothesis was proposed is discussed next.

By the end of the first decade of the modern resurgence of interest in conducting research concerned with the psychology of testimony, several dozen studies had accumulated wherein both witness accuracy and confidence in their identification decisions was measured. The commonsense intuition of laypersons, jurists, and researchers alike was that witness confidence should accurately track witness accuracy. In addition, signal detection theory, perhaps the most widely accepted theory of human judgment, made the same prediction. That is, the expectation was that when the accuracy of an identification decision made by each of a number of witnesses was correlated with a measure of their confidence in their decisions, the correlation coefficient expressing the predictability of accuracy from expressed confidence should be positive and relatively strong. The problem was that the empirical findings in this regard were decidedly mixed. Approximately half these initial studies reported positive correlation coefficients, ranging from +.20 to +.95, and the other half reported either correlation coefficients not statistically different from 0 or reversed (negative) correlations of witness accuracy and certainty.

At least on the surface, there would appear to be equal arguments both for and against the prior expectation that witness confidence should track witness accuracy with reasonable fidelity. In an effort to resolve this apparent contradiction of expectation and to account for the very large range of obtained correlation coefficients, a close examination of the studies in question revealed that there was substantial statistical support for the optimality hypothesis. Studies were first classified as having provided either high optimal or low optimal information processing conditions for witnesses. High optimal studies were defined as those wherein overall accuracy was at least 70% and that possessed at least three of the following information-processing conditions: warning of an impending memory test, stress levels low enough to permit adequate monitoring of the environment, ample opportunity to observe the target person, a brief retention interval, high familiarity with the target, similar condition of the target at encoding and memory test, low similarity of the target to foils (an innocent person in a police lineup) at test, unbiased memory test instructions, and additional consistent information presented during the retention interval. Then, both the number of significant positive accuracy-confidence correlation coefficients and the number of not significant or reversed accuracy-confidence correlations were determined for each category of study, those possessing of high and those possessing low optimal processing conditions. Fully 77% of studies had either high optimal processing conditions and a significant positive accuracy-confidence correlation or low optimal conditions and a not significant or reversed correlation coefficient. This proportion of cases is significantly greater than the proportion (.23) of cases wherein high optimal conditions resulted in not significant or reversed correlation coefficients or low optimal conditions produced significant positive correlations. Further analysis showed that this strong support for the optimality hypothesis was not related to whether the information-processing conditions in a study were of greater or lesser forensic relevance.

Since the proposal of the optimality hypothesis, publication of substantially greater numbers of investigations in which accuracy-confidence correlations were computed has occurred, and at least two meta-analyses (assessments of the average effect size, for the accuracy-confidence correlation in this case) have been conducted. As a result, two conclusions may be drawn. First, the average effect size has been estimated to be in the range of +.25 to +.35. That is, only 6% to 12% of the variation in accuracy judgments can be explained by variations in witness confidence. This result can be contrasted with the finding in one study that variations in juror perceptions of witness confidence accounted for as much as 50% of the variance in juror judgments as to witness accuracy. Second, additional empirical support for the optimality hypothesis has been obtained. In one published meta-analysis, clear evidence was found of longer target exposures being associated with a higher accuracy-confidence correlation (+.31) than shorter target face exposures (+.19). Other separate empirical investigations have found moderately strong positive correlations between target face distinctiveness and the size of the accuracy-confidence correlation. Still other studies have obtained markedly higher accuracy-confidence correlations in no-disguise conditions versus disguise conditions and in conditions with lower stress than in conditions with higher witness stress.

Finally, a theoretical analysis has been conducted in which the optimality hypothesis has been derived within the framework provided by signal detection theory. This analysis has resulted in the prediction of the average size of the accuracy-confidence correlation at six different levels of accuracy ranging from zero to very high levels. An example illustrates the utility of this analysis. Within the range of accuracy levels typically obtained in field experiments, a midrange predicted value of the accuracy-confidence correlation coefficient would be +.256, quite close to the estimated population value of +.252 obtained in a published meta-analysis.

### References:

- Bothwell, R. K., Deffenbacher, K. A., & Brigham, J. C. (1987). Correlation of eyewitness accuracy and confidence: Optimality hypothesis revisited. Journal of Applied Psychology, 72, 691-695.
- Deffenbacher, K. A. (1980). Eyewitness accuracy and confidence: Can we infer anything about their relationship? Law and Human Behavior, 4, 243-260.
- Deffenbacher, K. A. (1996). Updating the scientific validity of three key estimator variables in eyewitness testimony. In D. Herrmann, C. McEvoy, C. Herzog, P. Hertel, & M. K. Johnson (Eds.), Basic and applied memory research: Vol. 1. Theory in context (pp. 421-138). Mahwah, NJ: Lawrence Erlbaum.

### See also:

- Confidence in Identifications
- Confidence in Identifications Malleability
- Expert Psychological Testimony on Eyewitness Identification