Biomedical subjects
Publications and source records attributed to U Hoffrage.
Most people, experts included, have difficulties understanding and combining statistical information effectively. Hoffrage et al. demonstrate that these difficulties can be considerably reduced by communicating the information in terms of natural frequencies rather than in terms of probabilities. Several applications in medicine, legal decision-making, and education are discussed.
With the benefit of feedback about the outcome of an event, people's recalled judgments are typically closer to the outcome of the event than their original judgments were. It has been suggested that this hindsight bias may be due to a reconstruction process of the prior judgment. A model of such a process is proposed that assumes that knowledge is updated after feedback and that reconstruction is based on the updated knowledge. Consistent with the model's predictions, the results of 2 studies show that knowledge after feedback is systematically shifted toward feedback, and that assisting retrieval of the knowledge prior to feedback reduces hindsight bias. In addition, the model accounts for about 75% of cases in which either hindsight bias or reversed hindsight bias occurred. The authors conclude that hindsight bias can be understood as a by-product of an adaptive process, namely the updating of knowledge after feedback.
Interpreting medical test results demands statistical reasoning on the part of doctors: How great is the probability of falsely diagnosing an illness based on a positive test result? This probability can be determined with the assistance of Bayes's Rule. Several studies show, however, that doctors often experience problems with these kinds of Bayesian inferences. We demonstrate that doctors' judgments can be considerably improved when numerical information is presented in a form easily accessible to the ways humans process information. This is not the case with the utilization of applied probabilities that has become customary, but is the case when the problem is presented in terms of "natural frequencies" that result from the counting of observed isolated cases in a natural environment. In a series of studies, we varied the representation format of the relevant statistical information. If the information was not presented in the form of probabilities or percentages but simply in natural frequencies, medical experts, as well as laymen, were able to improve their judgments significantly. And dealing with probabilities and percentages can also be easily learned: Two training programs, which showed how probabilities can be translated into natural frequencies, placed the participants in the position of being able to obtain very good results when solving these tasks. Finally, we discuss the impact of a comprehensible risk and utility communication on the doctor-patient relationship.
This study addresses the counselling of heterosexual men with low-risk behaviour who, voluntarily or involuntarily, take an HIV test. If such a man tests positive, the chance that he is infected can be as low as 50%. We study what information counsellors communicate to clients concerning the meaning of a positive test and whether they communicate this information in a way the client can understand. To get realistic data, one of us visited as a client 20 public health centres in Germany to take 20 counselling sessions and HIV tests. A majority of the counsellors explained that false positives do not occur, and half of the counsellors told the client that if he tests positive, it is 100% certain that he is infected with the virus. Counsellors communicated numerical information in terms of probabilities rather than absolute frequencies, became confused and were inconsistent. Based on experimental evidence, we propose a simple method that counsellors can learn to communicate risks in a more effective way.
PURPOSE: To test whether physician's diagnostic inferences can be improved by communicating information using natural frequencies instead of probabilities. Whereas probabilities and relative frequencies are normalized with respect to disease base rates, natural frequencies are not normalized. METHOD: The authors asked 48 physicians in Munich and Düsseldorf to determine the positive predictive values (PPVs) of four diagnostic tests. Information presented in the four problems appeared either as probabilities (the traditional way) or as natural frequencies. RESULTS: When the information was presented as probabilities, the physicians correctly estimated the PPVs in only 10% of cases. When the same information was presented as natural frequencies, that percentage increased to 46%. CONCLUSION: Representing information in natural frequencies is a fast and effective way of facilitating diagnosis insight, which in turn helps physicians to better communicate risks to patients, and patients to better understand these risks.
Research on people's confidence in their general knowledge has to date produced two fairly stable effects, many inconsistent results, and no comprehensive theory. We propose such a comprehensive framework, the theory of probabilistic mental models (PMM theory). The theory (a) explains both the overconfidence effect (mean confidence is higher than percentage of answers correct) and the hard-easy effect (overconfidence increases with item difficulty) reported in the literature and (b) predicts conditions under which both effects appear, disappear, or invert. In addition, (c) it predicts a new phenomenon, the confidence-frequency effect, a systematic difference between a judgment of confidence in a single event (i.e., that any given answer is correct) and a judgment of the frequency of correct answers in the long run. Two experiments are reported that support PMM theory by confirming these predictions, and several apparent anomalies reported in the literature are explained and integrated into the present framework.