Asymptotic confidence intervals for the Pearson correlation via skewness and kurtosis

When bivariate normality is violated, the default confidence interval of the Pearson correlation can be inaccurate. Two new methods were developed based on the asymptotic sampling distribution of Fisher's z′ under the general case where bivariate normality need not be assumed. In Monte Carlo simulations, the most successful of these methods relied on the (Vale & Maurelli, 1983, Psychometrika, 48, 465) family to approximate a distribution via the marginal skewness and kurtosis of the sample data. In Simulation 1, this method provided more accurate confidence intervals of the correlation in non-normal data, at least as compared to no adjustment of the Fisher z′ interval, or to adjustment via the sample joint moments. In Simulation 2, this approximate distribution method performed favourably relative to common non-parametric bootstrap methods, but its performance was mixed relative to an observed imposed bootstrap and two other robust methods (PM1 and HC4). No method was completely satisfactory. An advantage of the approximate distribution method, though, is that it can be implemented even without access to raw data if sample skewness and kurtosis are reported, making the method particularly useful for meta-analysis. Supporting information includes R code.     

Bias-corrected estimation of the Rudas–Clogg–Lindsay mixture index of fit

Rudas, Clogg, and Lindsay (1994, J. R Stat Soc. Ser. B, 56, 623) introduced the so-called mixture index of fit, also known as pi-star (π*), for quantifying the goodness of fit of a model. It is the lowest proportion of ‘contamination’ which, if removed from the population or from the sample, makes the fit of the model perfect. The mixture index of fit has been widely used in psychometric studies. We show that the asymptotic confidence limits proposed by Rudas et al. (1994, J. R Stat Soc. Ser. B, 56, 623) as well as the jackknife confidence interval by Dayton ( 2003 , Br. J. Math. Stat. Psychol., 56, 1) perform poorly, and propose a new bias-corrected point estimate, a bootstrap test and confidence limits for pi-star. The proposed confidence limits have coverage probability much closer to the nominal level than the other methods do. We illustrate the usefulness of the proposed method in practice by presenting some practical applications to log-linear models for contingency tables.     

Why cannot reasons change your moral decisions? Because they are not persuasive enough: A comment on Stanley et al. (2018)

Stanley et al. (2018) found that the consideration of reasons rarely induced people to change their moral decisions. We challenged this article by assuming what caused such a null or weak effect was that the persuasiveness of reasons provided to oppose the initial decisions was not strong enough. To verify our assumption, this study used Stanley et al.’s (2018) experimental paradigm and manipulated the levels of persuasiveness of reasons. The results revealed (1) that not only strong opposing reasons but also weak affirming reasons could induce changes in moral decision-making and increase decision confidence after altering the decisions; (2) that people with a weak decision confidence tended to change their initial decisions after evaluation of reasons; and (3) that people who maintained their decisions after considering weak opposing reasons enhanced rather than reduced their decision confidence. Overall, these findings demonstrated that moral decision change was a composite outcome of the interaction among reason type, reason persuasiveness and initial decision confidence and that low-quality argumentation had a boomerang effect on moral persuasion. This study re-lifted the role of rational reasoning in moral decision-making and revising, thus posing important amendments to Stanley et al.’s (2018) findings.     

Confidence interval-based sample size determination formulas and some mathematical properties for hierarchical data

The use of hierarchical data (also called multilevel data or clustered data) is common in behavioural and psychological research when data of lower-level units (e.g., students, clients, repeated measures) are nested within clusters or higher-level units (e.g., classes, hospitals, individuals). Over the past 25 years we have seen great advances in methods for computing the sample sizes needed to obtain the desired statistical properties for such data in experimental evaluations. The present research provides closed-form and iterative formulas for sample size determination that can be used to ensure the desired width of confidence intervals for hierarchical data. Formulas are provided for a four-level hierarchical linear model that assumes slope variances and inclusion of covariates under both balanced and unbalanced designs. In addition, we address several mathematical properties relating to sample size determination for hierarchical data via the standard errors of experimental effect estimates. These include the relative impact of several indices (e.g., random intercept or slope variance at each level) on standard errors, asymptotic standard errors, minimum required values at the highest level, and generalized expressions of standard errors for designs with any-level randomization under any number of levels. In particular, information on the minimum required values will help researchers to minimize the risk of conducting experiments that are statistically unlikely to show the presence of an experimental effect.     

情景预见对跨期决策的影响机制

为了探究情景预见对跨期决策的影响机制, 研究采用延迟折扣任务范式, 检验了在情景预见对跨期决策的影响中延迟时间知觉起到的中介作用。两个实验分别操纵了情景预见中未来事件与自我有关的信息和未来事件的情绪特征, 结果均发现情景预见通过改变个体对延迟等待时间的时距知觉影响了跨期决策。想象与自己、与母亲有关的未来事件, 想象积极、中性情绪效价的未来事件都使得被试将延迟等待时间知觉为较短的时间段, 更倾向于选择延迟奖励。想象消极情绪效价的未来事件使得被试将延迟等待时间知觉为较长的时间段, 更加偏好即时奖励。本研究有助于增进人们对情景预见影响跨期决策现象的理解。     

Fourteen-month-olds’ imitation is influenced more strongly by a model’s competence than by a model’s certainty

Research has shown that infants are more likely to learn from certain and competent models than from uncertain and incompetent models. However, it is unknown which of these cues to a model’s reliability infants consider more important. In Experiment 1, we investigated whether 14-month-old infants (n = 35) imitate and adopt tool choices selectively from an uncertain but competent compared to a certain but incompetent model. Infants watched videos in which an adult expressed either uncertainty but acted competently or expressed certainty but acted incompetently with familiar objects. In tool-choice tasks, the adult then chose one of two objects to operate an apparatus, and in imitation tasks, the adult then demonstrated a novel action. Infants did not adopt the model’s choice in the tool-choice tasks but they imitated the uncertain but competent model more often than the certain but incompetent model in the imitation tasks. In Experiment 2, 14-month-olds (n = 33) watched videos in which an adult expressed only either certainty or uncertainty in order to test whether infants at this age are sensitive to a model’s certainty. Infants imitated and adopted the tool choice from a certain model more than from an uncertain model. These results suggest that 14-month-olds acknowledge both a model’s competence and certainty when learning novel actions. However, they rely more on a model’s competence than on his certainty when both cues are in conflict. The ability to detect reliable models when learning how to handle cultural artifacts helps infants to become well-integrated members of their culture.     

Asking an eyewitness to predict their later lineup performance could harm the confidence–accuracy relationship

Few studies have investigated eyewitnesses' ability to predict their later lineup performance, known as predecision confidence. We applied calibration analysis in two experiments comparing predecision confidence (immediately after encoding but prior to a lineup) to postdecision confidence (immediately after a lineup) to determine which produces a superior relationship with lineup decision accuracy. Experiment 1 (N = 177) featured a multiple-block lineup recognition paradigm featuring several targets and lineups; Experiment 2 featured an eyewitness identification paradigm with a mock-crime video and a single lineup for each participant (N = 855). Across both experiments, postdecision confidence discriminated well between correct and incorrect lineup decisions, but predecision confidence was a poor predictor of accuracy. Moreover, simply asking for predecision confidence weakened the postdecision confidence–accuracy relationship. This implies that police should exercise caution when interviewing eyewitnesses, as they should not be asked to predict their ability to make an accurate lineup decision.     

Poor peer work does not boost student confidence

Students' low confidence, particularly in numerical topics, is thought to be a barrier to keeping them engaged with education. We studied the effects on confidence of exposure to a peer's work of varying quality (very good or bad) and neatness (messy or neat). Previous research underpinned our hypothesis that a peer's bad-quality work—which students rarely see—might boost student confidence more than very good work. We also predicted that a peer's very good work—which students are often shown—might be less discouraging if it were messy, suggesting it required effort and struggle. However, in experiments with university students and low-educated adults, these hypotheses were not supported, and all participants decreased in confidence after seeing any peer work. The failure to find support for these hypotheses can inform future research into social comparison effects on self-confidence in numerical topics. These results also have practical implications for teachers and managers who are expected to provide examples of peer work.     

Bootstrap confidence intervals for principal covariates regression

Principal covariate regression (PCOVR) is a method for regressing a set of criterion variables with respect to a set of predictor variables when the latter are many in number and/or collinear. This is done by extracting a limited number of components that simultaneously synthesize the predictor variables and predict the criterion ones. So far, no procedure has been offered for estimating statistical uncertainties of the obtained PCOVR parameter estimates. The present paper shows how this goal can be achieved, conditionally on the model specification, by means of the bootstrap approach. Four strategies for estimating bootstrap confidence intervals are derived and their statistical behaviour in terms of coverage is assessed by means of a simulation experiment. Such strategies are distinguished by the use of the varimax and quartimin procedures and by the use of Procrustes rotations of bootstrap solutions towards the sample solution. In general, the four strategies showed appropriate statistical behaviour, with coverage tending to the desired level for increasing sample sizes. The main exception involved strategies based on the quartimin procedure in cases characterized by complex underlying structures of the components. The appropriateness of the statistical behaviour was higher when the proper number of components were extracted.     

The Effect of Information Strength and Weight on Behavior in Financial Markets

Griffin and Tversky (1992) explain evidence of individual over- and underconfidence as resulting from attending too much to the strength (i.e., extremity) of information and not enough to the weight (i.e., statistical reliability) of information. We report two experiments that demonstrate how information strength and weight affect confidence, trading, prices, and wealth in laboratory markets. Our results indicate that information strength and weight affect individual over- and underconfidence and that market participants lack sufficient self-insight to avoid trading when they are biased. As a consequence, market prices are biased, and market participants with high-strength, low-weight information systematically transfer wealth to participants with low-strength, high-weight information.