Toward an ecological analysis of Bayesian inferences: How task characteristics influence responses

In research on Bayesian inferences, the specific tasks, with their narratives and characteristics, are typically seen as exchangeable vehicles that merely transport the structure of the problem to research participants. In the present paper, we explore whether, and possibly how, task characteristics that are usually ignored influence participants' responses in these tasks. We focus on both quantitative dimensions of the tasks, such as their base rates, hit rates, and false-alarm rates, as well as qualitative characteristics, such as whether the task involves a norm violation or not, whether the stakes are high or low, and whether the focus is on the individual case or on the numbers. Using a data set of 19 different tasks presented to 500 different participants who provided a total of 1,773 responses, we analyze these responses in two ways: first, on the level of the numerical estimates themselves, and second, on the level of various response strategies, Bayesian and non-Bayesian, that might have produced the estimates. We identified various contingencies, and most of the task characteristics had an influence on participants' responses. Typically, this influence has been stronger when the numerical information in the tasks was presented in terms of probabilities or percentages, compared to natural frequencies - and this effect cannot be fully explained by a higher proportion of Bayesian responses when natural frequencies were used. One characteristic that did not seem to influence participants' response strategy was the numerical value of the Bayesian solution itself. Our exploratory study is a first step toward an ecological analysis of Bayesian inferences, and highlights new avenues for future research

Natural frequencies facilitate diagnostic inferences of managers

In Bayesian inference tasks, information about base rates as well as hit rate and false-alarm rate needs to be integrated according to Bayes' rule after the result of a diagnostic test became known. Numerous studies have found that presenting information in a Bayesian inference task in terms of natural frequencies leads to better performance compared to variants with information presented in terms of probabilities or percentages. Natural frequencies are the tallies in a natural sample in which hit rate and false-alarm rate are not normalized with respect to base rates. The present research replicates the beneficial effect of natural frequencies with four tasks from the domain of management, and with management students as well as experienced executives as participants. The percentage of Bayesian responses was almost twice as high when information was presented in natural frequencies compared to a presentation in terms of percentages. In contrast to most tasks previously studied, the majority of numerical responses were lower than the Bayesian solutions. Having heard of Bayes' rule prior to the study did not affect Bayesian performance. An implication of our work is that textbooks explaining Bayes' rule should teach how to represent information in terms of natural frequencies instead of how to plug probabilities or percentages into a formula

The Transmission Game: Testing behavioral interventions in a pandemic-like simulation

During pandemics, effective nonpharmaceutical interventions encourage people to adjust their behavior in fast-changing environments in which exponential dynamics aggravate the conflict between the individual benefits of risk-taking and its social costs. Policy-makers need to know which interventions are most likely to promote socially advantageous behaviors. We designed a tool for initial evaluations of the effectiveness of large-scale interventions, the transmission game framework, which integrates simulations of outbreak dynamics into large-group experiments with monetary stakes. In two studies (n = 700), we found substantial differences in the effectiveness of five behavioral interventions. A simple injunctive-norms message proved most effective, followed by two interventions boosting participants’ ability to anticipate the consequences of risky behavior. Interventions featuring descriptive norms or concurrent risk information failed to reduce risk-taking

From reading numbers to seeing ratios: a benefit of icons for risk comprehension

Promoting a better understanding of statistical data is becoming increasingly important for improving risk comprehension and decision-making. In this regard, previous studies on Bayesian problem solving have shown that iconic representations help infer frequencies in sets and subsets. Nevertheless, the mechanisms by which icons enhance performance remain unclear. Here, we tested the hypothesis that the benefit offered by icon arrays lies in a better alignment between presented and requested relationships, which should facilitate the comprehension of the requested ratio beyond the represented quantities. To this end, we analyzed individual risk estimates based on data presented either in standard verbal presentations (percentages and natural frequency formats) or as icon arrays. Compared to the other formats, icons led to estimates that were more accurate, and importantly, promoted the use of equivalent expressions for the requested probability. Furthermore, whereas the accuracy of the estimates based on verbal formats depended on their alignment with the text, all the estimates based on icons were equally accurate. Therefore, these results support the proposal that icons enhance the comprehension of the ratio and its mapping onto the requested probability and point to relational misalignment as potential interference for text-based Bayesian reasoning. The present findings also argue against an intrinsic difficulty with understanding single-event probabilities

A creative destruction approach to replication: implicit work and sex morality across cultures

How can we maximize what is learned from a replication study? In the creative destruction approach to replication, the original hypothesis is compared not only to the null hypothesis, but also to predictions derived from multiple alternative theoretical accounts of the phenomenon. To this end, new populations and measures are included in the design in addition to the original ones, to help determine which theory best accounts for the results across multiple key outcomes and contexts. The present pre-registered empirical project compared the Implicit Puritanism account of intuitive work and sex morality to theories positing regional, religious, and social class differences; explicit rather than implicit cultural differences in values; self-expression vs. survival values as a key cultural fault line; the general moralization of work; and false positive effects. Contradicting Implicit Puritanism's core theoretical claim of a distinct American work morality, a number of targeted findings replicated across multiple comparison cultures, whereas several failed to replicate in all samples and were identified as likely false positives. No support emerged for theories predicting regional variability and specific individual-differences moderators (religious affiliation, religiosity, and education level). Overall, the results provide evidence that work is intuitively moralized across cultures

Examining the generalizability of research findings from archival data

This initiative examined systematically the extent to which a large set of archival research findings generalizes across contexts. We repeated the key analyses for 29 original strategic management effects in the same context (direct reproduction) as well as in 52 novel time periods and geographies; 45% of the reproductions returned results matching the original reports together with 55% of tests in different spans of years and 40% of tests in novel geographies. Some original findings were associated with multiple new tests. Reproducibility was the best predictor of generalizability—for the findings that proved directly reproducible, 84% emerged in other available time periods and 57% emerged in other geographies. Overall, only limited empirical evidence emerged for context sensitivity. In a forecasting survey, independent scientists were able to anticipate which effects would find support in tests in new samples

Crowdsourcing hypothesis tests: Making transparent how design choices shape research results

To what extent are research results influenced by subjective decisions that scientists make as they design studies? Fifteen research teams independently designed studies to answer fiveoriginal research questions related to moral judgments, negotiations, and implicit cognition. Participants from two separate large samples (total N > 15,000) were then randomly assigned to complete one version of each study. Effect sizes varied dramatically across different sets of materials designed to test the same hypothesis: materials from different teams renderedstatistically significant effects in opposite directions for four out of five hypotheses, with the narrowest range in estimates being d = -0.37 to +0.26. Meta-analysis and a Bayesian perspective on the results revealed overall support for two hypotheses, and a lack of support for three hypotheses. Overall, practically none of the variability in effect sizes was attributable to the skill of the research team in designing materials, while considerable variability was attributable to the hypothesis being tested. In a forecasting survey, predictions of other scientists were significantly correlated with study results, both across and within hypotheses. Crowdsourced testing of research hypotheses helps reveal the true consistency of empirical support for a scientific claim.</div

Competition and moral behavior: A meta-analysis of forty-five crowd-sourced experimental designs

Significance Using experiments involves leeway in choosing one out of many possible experimental designs. This choice constitutes a source of uncertainty in estimating the underlying effect size which is not incorporated into common research practices. This study presents the results of a crowd-sourced project in which 45 independent teams implemented research designs to address the same research question: Does competition affect moral behavior? We find a small adverse effect of competition on moral behavior in a meta-analysis involving 18,123 experimental participants. Importantly, however, the variation in effect size estimates across the 45 designs is substantially larger than the variation expected due to sampling errors. This “design heterogeneity” highlights that the generalizability and informativeness of individual experimental designs are limited. Abstract Does competition affect moral behavior? This fundamental question has been debated among leading scholars for centuries, and more recently, it has been tested in experimental studies yielding a body of rather inconclusive empirical evidence. A potential source of ambivalent empirical results on the same hypothesis is design heterogeneity—variation in true effect sizes across various reasonable experimental research protocols. To provide further evidence on whether competition affects moral behavior and to examine whether the generalizability of a single experimental study is jeopardized by design heterogeneity, we invited independent research teams to contribute experimental designs to a crowd-sourced project. In a large-scale online data collection, 18,123 experimental participants were randomly allocated to 45 randomly selected experimental designs out of 95 submitted designs. We find a small adverse effect of competition on moral behavior in a meta-analysis of the pooled data. The crowd-sourced design of our study allows for a clean identification and estimation of the variation in effect sizes above and beyond what could be expected due to sampling variance. We find substantial design heterogeneity—estimated to be about 1.6 times as large as the average standard error of effect size estimates of the 45 research designs—indicating that the informativeness and generalizability of results based on a single experimental design are limited. Drawing strong conclusions about the underlying hypotheses in the presence of substantive design heterogeneity requires moving toward much larger data collections on various experimental designs testing the same hypothesis