Salience Versus Proportional Reasoning: Rethinking the Mechanism Behind Graphical Display Effects

Two experiments examined predictions from two separate explanations for previously observed display effects for communicating low‐probability risks: foreground:background salience and proportional reasoning. According to foreground:background salience, people's risk perceptions are based on the relative salience of the foreground (number of people harmed) versus the background (number of people at risk), such that calling attention to the background makes the risk seem smaller. Conversely, the proportional reasoning explanation states that what matters is whether the respondent attends to the proportion, which conveys how small the risk is. In Experiment 1, we made the background more salient via color and bolding; in contrast to the foreground:background salience prediction, this manipulation did not influence participants' risk aversion. In Experiment 2, we separately manipulated whether the foreground and the background were displayed graphically or numerically. In keeping with the proportional reasoning hypothesis, there was an interaction whereby participants given formats that displayed the foreground and background in the same modality (graphs or numbers, thereby making the proportion easier to form) saw the probability as smaller and were less risk averse than participants given the information in different modalities. There was also a main effect of displaying the background graphically, providing some support for foreground:background salience. In total, this work suggests that the proportional reasoning account provides a good explanation of many display effects related to communicating low‐probability risks, although there is some role for foreground:background salience as well. Copyright © 2018 John Wiley & Sons, Ltd.     

用不同外部表征方式集中呈现信息条件下的因果力判断

在分别用文字陈述、表格和图形三种外部表征方式集中呈现因果信息的条件下,用直接估计因果力大小的实验范式考察单一因果关系因果力估计的特点,检验概率对比模型,效力PC理论和pCI规则。让287名大学生被试估计不同化学药物影响动物基因变异的能力。结果发现,对单一因果关系因果力估计具有以下4个特点：⑴不对称性：在预防原因条件下的因果力估计较多符合效力PC理论,而在产生原因条件下的因果力估计一般符合概率对比模型;⑵文字陈述、表格和图形三种信息外部表征方式,不影响产生原因条件下的因果力估计,但影响预防原因条件下的因果力估计。在预防原因条件下,与文字陈述和表格表征相比,图形表征会促使更多被试按效力PC理论来做因果力估计;⑶没有被试使用pCI规则;⑷被试估计因果力所使用的规则存在明显的个体差异。     

Beyond inference by eye: Statistical and graphing practices in JEAB, 1992‐2017

Debates about the utility of p values and correct ways to analyze data have inspired new guidelines on statistical inference by the American Psychological Association (APA) and changes in the way results are reported in other scientific journals, but their impact on the Journal of the Experimental Analysis of Behavior (JEAB) has not previously been evaluated. A content analysis of empirical articles published in JEAB between 1992 and 2017 investigated whether statistical and graphing practices changed during that time period. The likelihood that a JEAB article reported a null hypothesis significance test, included a confidence interval, or depicted at least one figure with error bars has increased over time. Features of graphs in JEAB, including the proportion depicting single‐subject data, have not changed systematically during the same period. Statistics and graphing trends in JEAB largely paralleled those in mainstream psychology journals, but there was no evidence that changes to APA style had any direct impact on JEAB. In the future, the onus will continue to be on authors, reviewers and editors to ensure that statistical and graphing practices in JEAB continue to evolve without interfering with characteristics that set the journal apart from other scientific journals.     

Non‐ignorable missingness item response theory models for choice effects in examinee‐selected items

Examinee‐selected item (ESI) design, in which examinees are required to respond to a fixed number of items in a given set, always yields incomplete data (i.e., when only the selected items are answered, data are missing for the others) that are likely non‐ignorable in likelihood inference. Standard item response theory (IRT) models become infeasible when ESI data are missing not at random (MNAR). To solve this problem, the authors propose a two‐dimensional IRT model that posits one unidimensional IRT model for observed data and another for nominal selection patterns. The two latent variables are assumed to follow a bivariate normal distribution. In this study, the mirt freeware package was adopted to estimate parameters. The authors conduct an experiment to demonstrate that ESI data are often non‐ignorable and to determine how to apply the new model to the data collected. Two follow‐up simulation studies are conducted to assess the parameter recovery of the new model and the consequences for parameter estimation of ignoring MNAR data. The results of the two simulation studies indicate good parameter recovery of the new model and poor parameter recovery when non‐ignorable missing data were mistakenly treated as ignorable.     

How probability theory explains the conjunction fallacy

The conjunction fallacy occurs when people judge a conjunctive statement B‐and‐A to be more probable than a constituent B, in contrast to the law of probability that P(B ∧ A) cannot exceed P(B) or P(A). Researchers see this fallacy as demonstrating that people do not follow probability theory when judging conjunctive probability. This paper shows that the conjunction fallacy can be explained by the standard probability theory equation for conjunction if we assume random variation in the constituent probabilities used in that equation. The mathematical structure of this equation is such that random variation will be most likely to produce the fallacy when one constituent has high probability and the other low, when there is positive conditional support between the constituents, when there are two rather than three constituents, and when people rank probabilities rather than give numerical estimates. The conjunction fallacy has been found to occur most frequently in exactly these situations. Copyright © 2008 John Wiley & Sons, Ltd.     

Identifying Variables Responsible for Data not Missing at Random

When data are not missing at random (NMAR), maximum likelihood (ML) procedure will not generate consistent parameter estimates unless the missing data mechanism is correctly modeled. Understanding NMAR mechanism in a data set would allow one to better use the ML methodology. A survey or questionnaire may contain many items; certain items may be responsible for NMAR values in other items. The paper develops statistical procedures to identify the responsible items. By comparing ML estimates (MLE), statistics are developed to test whether the MLEs are changed when excluding items. The items that cause a significant change of the MLEs are responsible for the NMAR mechanism. Normal distribution is used for obtaining the MLEs; a sandwich-type covariance matrix is used to account for distribution violations. The class of nonnormal distributions within which the procedure is valid is provided. Both saturated and structural models are considered. Effect sizes are also defined and studied. The results indicate that more missing data in a sample does not necessarily imply more significant test statistics due to smaller effect sizes. Knowing the true population means and covariances or the parameter values in structural equation models may not make things easier either. The research was supported by NSF grant DMS04-37167, the James McKeen Cattell Fund.     

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution then requires an integral equation that is of dimension equal to the number of nonlinear terms. For nonlinear functions that have linear coefficients, the improvement in computational speed and accuracy using the new algorithm can be dramatic. An illustration of the method with repeated measures data from a learning experiment is presented.     

Human operant performance: Sensitivity and pseudosensitivity to contingencies

Undergraduates' button presses occasionally produced points exchangeable for money. Left and right buttons were initially correlated with multiple random-ratio (RR) and random-interval (RI) components, respectively. During interruptions of the multiple schedule, students filled out sentence-completion guess sheets describing the schedules, and points were contingent upon the accuracy of guesses. To test for sensitivity to schedule contingencies, schedule components were repeatedly reversed between the two buttons. Pressing rates were consistently higher in ratio than in interval components even when feedback for guesses was discontinued, demonstrating sensitivity to the difference between ratio and interval contingencies. The question was whether this sensitivity was based directly on the contingencies or whether it was rule-governed. For two students, when multiple RR RI schedules were changed to multiple RI RI schedules, rates became low in both components of the multiple RI RI schedule; however, subsequent prevention of point deliveries for the first few responses in any component produced high rates in that component. For a third student, response rates became higher in the RI component that provided the lower rate of reinforcement. In each case, performance was inconsistent with typical effects of the respective schedules with nonhuman organisms; it was therefore plausible to conclude that the apparently contingency-governed performances were instead rule-governed.     

Measuring misinformation in repeat trial pick 1 of 2 tests

An extension is described to a product testing model to account for misinformation among subjects. A misinformed subject is one who associates the taste of product A with product B and vice-versa; thus, the subject would tend to perform incorrectly on pick 1 of 2 tests. A likelihood ratio test for the presence of misinformation is described. The model is applied to a data set, and misinformation is found to exist. Biases due to model misspecificationand other implications for product testing are discussed.The first author is currently on leave from Carnegie Mellon University.     

Round-robin analysis of social interaction: Exact and estimated standard errors

Kenny has proposed a variance-components model for dyadic social interaction. His Social Relations model estimates variances and covariances from a round-robin of two-person interactions. The current paper presents a matrix formulation of the Social Relations model. It uses the formulation to derive exact and estimated standard errors for round-robin estimates of Social Relations parameters.We are grateful to George Gilbert for comments on an earlier draft.