Effects of question formats on causal judgments and model evaluation

Evaluation of causal reasoning models depends on how well the subjects' causal beliefs are assessed. Elicitation of causal beliefs is determined by the experimental questions put to subjects. We examined the impact of question formats commonly used in causal reasoning research on participant's responses. The results of our experiment (Study 1) demonstrate that both the mean and homogeneity of the responses can be substantially influenced by the type of question (structure induction versus strength estimation versus prediction). Study 2A demonstrates that subjects' responses to a question requiring them to predict the effect of a candidate cause can be significantly lower and more heterogeneous than their responses to a question asking them to diagnose a cause when given an effect. Study 2B suggests that diagnostic reasoning can strongly benefit from cues relating to temporal precedence of the cause in the question. Finally, we evaluated 16 variations of recent computational models and found the model fitting was substantially influenced by the type of questions. Our results show that future research in causal reasoning should place a high priority on disentangling the effects of question formats from the effects of experimental manipulations, because that will enable comparisons between models of causal reasoning uncontaminated by method artifact

A Simple Statistic for Comparing Moderation of Slopes and Correlations

Given a linear relationship between two continuous random variables X and Y that may be moderated by a third, Z, the extent to which the correlation ρ is (un)moderated by Z is equivalent to the extent to which the regression coefficients β(y) and β(x) are (un)moderated by Z iff the variance ratio [Formula: see text] is constant over the range or states of Z. Otherwise, moderation of slopes and of correlations must diverge. Most of the literature on this issue focuses on tests for heterogeneity of variance in Y, and a test for this ratio has not been investigated. Given that regression coefficients are proportional to ρ via this ratio, accurate tests, and estimations of it would have several uses. This paper presents such a test for both a discrete and continuous moderator and evaluates its Type I error rate and power under unequal sample sizes and departures from normality. It also provides a unified approach to modeling moderated slopes and correlations with categorical moderators via structural equations models

Imprecise compositional data analysis: Alternative statistical methods

This paper briefly describes statistical methods for analyzing imprecise compositional data that might be elicited from approximate measurement or from expert judgments. Two alternative approaches are discussed: Log-ratio transforms and probability-ratio transforms. The first is well-established and the second is under development by the author. The primary focus in this paper is on generalized linear models for predicting imprecise compositional data

RAPID CLOCK RECOVERY ALGORITHMS FOR DIGITAL MAGNETIC RECORDING AND DATA COMMUNICATIONS

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Asymmetries in responses to attitude statements: the example of "zero-sum" beliefs

While much has been written about the consequences of zero-sum (or fixed-pie) beliefs, their measurement has received almost no systematic attention. No researchers, to our awareness, have examined the question of whether the endorsement of a zero-sum-like proposition depends on how the proposition is formed. This paper focuses on this issue, which may also apply to the measurement of other attitudes. Zero-sum statements have a form such as "The more of resource X for consumer A, the less of resource Y for consumer B." X and Y may be the same resource (such as time), but they can be different (e.g., "The more people commute by bicycle, the less revenue for the city from car parking payments"). These statements have four permutations, and a strict zero-sum believer should regard these four statements as equally valid and therefore should endorse them equally. We find, however, that three asymmetric patterns routinely occur in people's endorsement levels, i.e., clear framing effects, whereby endorsement of one permutation substantially differs from endorsement of another. The patterns seem to arise from beliefs about asymmetric resource flows and power relations between rival consumers. We report three studies, with adult samples representative of populations in two Western and two non-Western cultures, demonstrating that most of the asymmetric belief patterns are consistent across these samples. We conclude with a discussion of the implications of this kind of "order-effect" for attitude measurement.The research for this project was supported by Australian Research Council Discovery Project grant DP102101095, awarded to MS in 2012

Randomly stopped sums: models and psychological applications

This paper describes an approach to modeling the sums of a continuous random variable over a number of measurement occasions when the number of occasions also is a random variable. A typical example is summing the amounts of time spent attending to pieces of information in an information search task leading to a decision to obtain the total time taken to decide. Although there is a large literature on randomly stopped sums in financial statistics, it is largely absent from psychology. The paper begins with the standard modeling approaches used in financial statistics, and then extends them in two ways. First, the randomly stopped sums are modeled as "life distributions" such as the gamma or log-normal distribution. A simulation study investigates Type I error rate accuracy and power for gamma and log-normal versions of this model. Second, a Bayesian hierarchical approach is used for constructing an appropriate general linear model of the sums. Model diagnostics are discussed, and three illustrations are presented from real datasets

Adapting to an uncertain world: Cognitive capacity and causal reasoning with ambiguous observations

Ambiguous causal evidence in which the covariance of the cause and effect is partially known is pervasive in real life situations. Little is known about how people reason about causal associations with ambiguous information and the underlying cognitive mechanisms. This paper presents three experiments exploring the cognitive mechanisms of causal reasoning with ambiguous observations. Results revealed that the influence of ambiguous observations manifested by missing information on causal reasoning depended on the availability of cognitive resources, suggesting that processing ambiguous information may involve deliberative cognitive processes. Experiment 1 demonstrated that subjects did not ignore the ambiguous observations in causal reasoning. They also had a general tendency to treat the ambiguous observations as negative evidence against the causal association. Experiment 2 and Experiment 3 included a causal learning task requiring a high cognitive demand in which paired stimuli were presented to subjects sequentially. Both experiments revealed that processing ambiguous or missing observations can depend on the availability of cognitive resources. Experiment 2 suggested that the contribution of working memory capacity to the comprehensiveness of evidence retention was reduced when there were ambiguous or missing observations. Experiment 3 demonstrated that an increase in cognitive demand due to a change in the task format reduced subjects' tendency to treat ambiguous-missing observations as negative cues. Copyright: © 2015 Shou, Smithson.This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Moderator effects differ on alternative effect-size measures

This paper discusses largely ignored issues regarding moderation of effect-sizes. We show that, under commonly-occurring conditions, popular alternatives for effect-size measures in ANOVA and multiple regression are not moderated identically across independent samples. Effects may appear to be unmoderated according to one effect-size measure but not according to another, or may even be moderated in opposite directions. We identify the conditions under which differential effect-size moderation can occur, and show that they are commonplace. We then review techniques for detecting and dealing with differential moderation of alternative effect-size measures. Finally, we discuss implications for research practice, reporting, replication, and meta-analysis