Comparing one-step m-estimators of location corresponding to two independent groups

Experience with real data indicates that psychometric measures often have heavy-tailed distributions. This is known to be a serious problem when comparing the means of two independent groups because heavy-tailed distributions can have a serious effect on power. Another problem that is common in some areas is outliers. This paper suggests an approach to these problems based on the one-step M-estimator of location. Simulations indicate that the new procedure provides very good control over the probability of a Type I error even when distributions are skewed, have different shapes, and the variances are unequal. Moreover, the new procedure has considerably more power than Welch's method when distributions have heavy tails, and it compares well to Yuen's method for comparing trimmed means. Wilcox's median procedure has about the same power as the proposed procedure, but Wilcox's method is based on a statistic that has a finite sample breakdown point of only 1/n, wheren is the sample size. Comments on other methods for comparing groups are also included.     

The consequence of ignoring a nested factor on measures of effect size in analysis of variance

Although the consequences of ignoring a nested factor on decisions to reject the null hypothesis of no treatment effects have been discussed in the literature, typically researchers in applied psychology and education ignore treatment providers (often a nested factor) when comparing the efficacy of treatments. The incorrect analysis, however, not only invalidates tests of hypotheses, but it also overestimates the treatment effect. Formulas were derived and a Monte Carlo study was conducted to estimate the degree to which the F statistic and treatment effect size measures are inflated by ignoring the effects due to providers of treatments. These untoward effects are illustrated with examples from psychotherapeutic treatments.     

A multivariate projection‐type analogue of the Wilcoxon — Mann — Whitney test

The problem of comparing two independent groups based on mulitivariate data is considered. Many such methods have been proposed, but it is difficult to gain a perspective on the extent to which the groups differ. The basic strategy here is to determine a robust measure of location for each group, project the data onto the line connecting these measures of location, and then compare the groups based on the ordering of the projected points. In the univariate case the method uses the same measure of effect size employed by the Wilcoxon — Mann — Whitney test. Under general conditions, the projected points are dependent, causing difficulties when testing hypotheses. Two methods are found to be effective when trying to avoid Type I error probabilities above the nominal level. The relative merits of the two methods are discussed. The projected data provide not only a useful (numerical) measure of effect size, but also a graphical indication of the extent to which groups differ.     

On Detecting a Minimal Important Difference among Standardized Means

As a generalization of the standardized mean difference between two independent populations, two different effect size measures have been proposed to represent the degree of disparity among several treatment groups. One index relies on the standard deviation of the standardized means and the second formula is the range of the standardized means. Despite the obvious usage of the two measures, the associated test procedures for detecting a minimal important difference among standardized means have not been well explicated. This article reviews and compares the two approaches to testing the hypothesis that treatments have negligible effects rather than that of no difference. The primary emphasis is to reveal the underlying properties of the two methods with regard to power behavior and sample size requirement across a variety of design configurations. To enhance the practical usefulness, a complete set of computer algorithms for calculating the critical values, p-values, power levels, and sample sizes is also developed.     

Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: sample size planning via narrow confidence intervals

Contrasts of means are often of interest because they describe the effect size among multiple treatments. High-quality inference of population effect sizes can be achieved through narrow confidence intervals (CIs). Given the close relation between CI width and sample size, we propose two methods to plan the sample size for an ANCOVA or ANOVA study, so that a sufficiently narrow CI for the population (standardized or unstandardized) contrast of interest will be obtained. The standard method plans the sample size so that the expected CI width is sufficiently small. Since CI width is a random variable, the expected width being sufficiently small does not guarantee that the width obtained in a particular study will be sufficiently small. An extended procedure ensures with some specified, high degree of assurance (e.g., 90% of the time) that the CI observed in a particular study will be sufficiently narrow. We also discuss the rationale and usefulness of two different ways to standardize an ANCOVA contrast, and compare three types of standardized contrast in the ANCOVA/ANOVA context. All of the methods we propose have been implemented in the freely available MBESS package in R so that they can be easily applied by researchers.     

基于两水平被试内设计的中介效应分析方法

在心理学和其他社科研究领域,通常的中介效应分析都基于被试间设计,研究者对于如何分析基于被试内设计的中介效应往往并不清楚。本文阐述了两水平被试内设计的中介效应分析方法(依次检验法和路径分析法),综合各方法优缺点给出一个分析流程,并用应用研究实例演示如何分析两水平被试内中介效应,最后展望了基于被试内设计的中介效应分析研究的拓展方向。     

Variable criteria sequential stopping rule: Validity and power with repeated measures ANOVA,multiple correlation,MANOVA and relation to Chi-square distribution

The variable criteria sequential stopping rule (vcSSR) is an efficient way to add sample size to planned ANOVA tests while holding the observed rate of Type I errors, α_o, constant. The only difference from regular null hypothesis testing is that criteria for stopping the experiment are obtained from a table based on the desired power, rate of Type I errors, and beginning sample size. The vcSSR was developed using between-subjects ANOVAs, but it should work with p values from any type of F test. In the present study, the α_o remained constant at the nominal level when using the previously published table of criteria with repeated measures designs with various numbers of treatments per subject, Type I error rates, values of ρ, and four different sample size models. New power curves allow researchers to select the optimal sample size model for a repeated measures experiment. The criteria held α_o constant either when used with a multiple correlation that varied the sample size model and the number of predictor variables, or when used with MANOVA with multiple groups and two levels of a within-subject variable at various levels of ρ. Although not recommended for use with χ² tests such as the Friedman rank ANOVA test, the vcSSR produces predictable results based on the relation between F and χ². Together, the data confirm the view that the vcSSR can be used to control Type I errors during sequential sampling with any t- or F-statistic rather than being restricted to certain ANOVA designs.     

预测视角下双因子模型与高阶模型的模拟比较

双因子模型和高阶因子模型,作为既有全局因子又有局部因子的两个竞争模型,在研究中得到了广泛应用。本文采用Monte Carlo模拟方法,在模型拟合比较的基础上,比较了效标分别为外显变量和内潜变量时,两个模型在各种负荷水平下预测准确度的差异。结果发现,两种模型在拟合效果方面无显著差异;但在预测效度方面,当效标为显变量时,两个模型的结构系数估计值皆为无偏估计;而效标为潜变量时,高阶因子模型表现优于双因子模型:高阶因子模型的结构系数为无偏估计,双因子模型的结构系数估计值则在50%左右的情况下存在偏差。     

Intraday reliability of ground reaction force data

Based upon independent parameter reliability and minimum sample size evaluations, a sample size of 25 trials was identified as necessary to provide accurate ground reaction force (GRF) data describing a subject's running performance. Intraday parameter reliability based on this sample size was approximately 75% indicating that subject variability must be acknowledged when comparing the effects of different running shoes. The minimum differences in GRF parameter values that are biomechanically significant have been estimated at 1 N/kg and 2% for force and relative temporal measures, respectively.     

调节模式对选择超载的影响及其机制：一个有中介的调节模型

当前,选择超载领域研究的焦点已从验证其是否存在,转向至其何时存在,即边界条件的探讨。本研究基于调节模式理论,分别以决策后悔和延迟选择作为选择超载的指标,开展两个实验探查选择超载存在的调节模式条件及所涉及的内在机制。实验1以决策后悔作指标,运用量表测试法操纵调节模式,初步探讨调节模式对选择超载的影响,结果发现调节模式调节了选项集与决策后悔的关系,即对评估模式的个体来说,面对大选项集比小选项集时体验到更强的后悔情绪,出现了选择超载,而对运动模式的个体而言,两种条件下的决策后悔无显著差异;实验2以延迟选择作指标,通过任务启动法操纵调节模式,进一步探讨调节模式对选择超载的影响及其机制,结果发现调节模式调节了选项集与延迟选择的关系,即对评估模式的个体来说,面对大选项集比小选项集时更倾向于延迟选择,出现了选择超载,而对运动模式的个体而言,两种条件下的延迟选择偏好无显著差异,进一步有中介的调节模型分析表明选择难度可以部分解释这种效应。总之,通过采用不同方法操纵调节模式,选取不同的选择超载指标,数据结果都一致支持：评估模式的个体比运动模式的个体更容易出现选择超载,选择难度在其中发挥着一定的中介作用。     

Development of a short form of the Treatment Evaluation Inventory for acceptability of psychological interventions

The Treatment Evaluation Inventory of Kazdin, French, and Sherick is a 19-item measure of the perceived acceptability of behavioural treatments. Development of two brief forms was based on data from two sources. For Study 1, data from 218 completed questionnaires were used to develop internally consistent brief scales. In Study 2 internal consistency and the validity of the brief forms were estimated for a set of 131 questionnaires. Item reduction was achieved by analysis of item-total minus item correlations. Brief forms with 3, 6, 9, and 12 items were proposed. Their internal consistency (Cronbach alpha) and construct validity were based on correlations of scores on each short form with the full scale scores and on comparing means of different forms. Discriminant validity was based on the difference between two groups (estimated effect size 0.7). Scores for all forms showed high internal consistency and correlated highly with total scale scores. Only the 12-item brief scale yielded mean scores similar to the full scale. The 3-item form could be used as a quick screen, and the 12-item form for more intensive purposes as it is most similar to the full-scale.     

Hierarchical linear models for the quantitative integration of effect sizes in single-case research

In this article, the calculation of effect size measures in single-case research and the use of hierarchical linear models for combining these measures are discussed. Special attention is given to meta-analyses that take into account a possible linear trend in the data. We show that effect size measures that have been proposed for this situation appear to be systematically affected by the duration of the experiment and fail to distinguish between effects on level and slope. To avoid these flaws, we propose to perform a multivariate meta-analysis on the standardized ordinary least squares regression coefficients from the study-specific regression equations describing the response variable.     

Personal need for structure and creative performance: the moderating influence of fear of invalidity

Previous research has suggested that personal need for structure (PNS) is negatively related to creative performance. In this article, it is argued that this relation, in fact, depends on another personality variable: personal fear of invalidity (PFI). When PFI is high, PNS should indeed be negatively associated with creativity. However, PNS should be positively associated with creativity when PFI is low, because this combination enables people to take a structured approach to creative tasks and this can be helpful to overcome their reliance on conventional and accessible task strategies. In four studies, this hypothesis is tested using different measures of creative performance. The expected interaction effect is found for measures of ideational fluency and measures of originality but not for measures of flexibility. Moreover, it is shown that the interaction effect between PNS and PFI is mediated by perseverance within thought categories.     

Using response ratios for meta-analyzing single-case designs with behavioral outcomes

Methods for meta-analyzing single-case designs (SCDs) are needed to inform evidence-based practice in clinical and school settings and to draw broader and more defensible generalizations in areas where SCDs comprise a large part of the research base. The most widely used outcomes in single-case research are measures of behavior collected using systematic direct observation, which typically take the form of rates or proportions. For studies that use such measures, one simple and intuitive way to quantify effect sizes is in terms of proportionate change from baseline, using an effect size known as the log response ratio. This paper describes methods for estimating log response ratios and combining the estimates using meta-analysis. The methods are based on a simple model for comparing two phases, where the level of the outcome is stable within each phase and the repeated outcome measurements are independent. Although auto-correlation will lead to biased estimates of the sampling variance of the effect size, meta-analysis of response ratios can be conducted with robust variance estimation procedures that remain valid even when sampling variance estimates are biased. The methods are demonstrated using data from a recent meta-analysis on group contingency interventions for student problem behavior.     

Efficacy of functional analysis for informing behavioral treatment of inappropriate mealtime behavior: A systematic review and meta‐analysis

Children diagnosed with a feeding disorder often exhibit inappropriate mealtime behavior such as throwing or swiping food, which can exacerbate feeding difficulties during treatment. We conducted a meta‐analysis of 86 behavioral treatments for inappropriate mealtime behavior from 23 studies to assess the extent to which treatments based on a pretreatment functional analysis were more efficacious than those treatments not based on a functional analysis. Procedural escape extinction and attention extinction for inappropriate mealtime behavior, as well as differential reinforcement for food acceptance or consumption, represented the most common treatments independent of whether a functional analysis was conducted. No difference was detected between treatments that were and were not based on a functional analysis, and mean effect size across measures was identical (79%). The requirement of a pretreatment functional analysis for inappropriate mealtime behavior is equivocal given that standard care often includes efficacious treatment components that are not informed by a functional analysis.     

An effect size measure and Bayesian analysis of single-case designs

This article describes a linear modeling approach for the analysis of single-case designs (SCDs). Effect size measures in SCDs have been defined and studied for the situation where there is a level change without a time trend. However, when there are level and trend changes, effect size measures are either defined in terms of changes in R² or defined separately for changes in slopes and intercept coefficients. We propose an alternate effect size measure that takes into account changes in slopes and intercepts in the presence of serial dependence and provides an integrated procedure for the analysis of SCDs through estimation and inference based directly on the effect size measure. A Bayesian procedure is described to analyze the data and draw inferences in SCDs. A multilevel model that is appropriate when several subjects are available is integrated into the Bayesian procedure to provide a standardized effect size measure comparable to effect size measures in a between-subjects design. The applicability of the Bayesian approach for the analysis of SCDs is demonstrated through an example.     

两类常见的类别变量调节效应分析

类别变量在心理学和其他社科研究领域经常遇到,当自变量或调节变量为类别变量时,应当如何分析调节效应呢？详述了多类别变量的被试间设计和两水平被试内设计（因变量重复测量2次）的调节效应分析方法,并给出了分析流程。先进行调节效应的显著性检验,后用选点法或Johnson-Neyman法进行简单斜率检验。多类别变量被试间设计的简单斜率检验是先进行整体检验,后进行配对检验。用两个实际例子演示如何进行类别变量的调节效应分析,最后展望了两类设计的类别变量的调节研究的拓展方向,例如更复杂的类别变量的调节模型等。     

Global and local precedence: selective attention in form and motion perception

This study explores the perception of stimuli at two levels: local parts and the wholes that comprise these parts. Previous research has produced contradictory results. Some studies (e.g., Pomerantz & Sager, 1975) show local precedence, in which the local parts are more difficult to ignore in selective attention tasks. Other studies (e.g., Navon, 1977) have shown the opposite effect, global precedence. The present five experiments trace the causes of this discrepancy by exploring the effects of the relative discriminabilities of the local and global levels of the stimuli and the differences between two different measures of selective attention, namely, Stroop-type interference (attributable to incongruity on the irrelevant dimension) and Garner-type interference (attributable to variability on the irrelevant dimension). The experiments also examine whether the precedence effects previously examined in form perception generalize to motion perception. The results show that (a) some cases of global precedence are due solely to the greater perceptual discriminability of the global level and thus demonstrate only that more discriminable stimuli are harder to ignore; (b) instances of both local and global precedence can be demonstrated for certain types of stimuli, even when the discriminabilities of their local and global levels have been equated; and (c) the Stroop and Garner measures of selective attention are not equivalent but instead measure different types of interference. In addition, a distinction is made between two fundamentally different types of part-whole relationships that exist in visual configurations, one based only on the positions of the parts (Type P) and one based also on the nature of the parts (Type N). Previous research has focused on Type P, which appears to be irrelevant to the broader questions of Gestalt and top-down effects in perception. It is concluded that bona fide cases of both local and global precedence have been amply documented but that no general theory can account for why or when these effects will appear until we better understand both the nature of part-whole relationships and the perceptual processes that are tapped by different measures of selective attention.     

Direct and indirect perception of size

Three experiments, using a reaction time paradigm, examine the direct (stimulus bound) and indirect (mediational inference) approaches to size perception. Subjects determine which of two stimuli is the larger when the two can be at different egocentric distances. The effects of two variables on reaction times are examined—distal ratio, the ratio of physical sizes of the stimuli, and proximal ratio, the ratio of the angular projections of the stimuli on the retina. In Experiment 1, both ratios are found to affect reaction times, with the proximal ratios yielding the larger effect, more in line with the predictions of the indirect approach. But the results of Experiments 2 and 3 indicate that distance is taken into greater account, the more similar the distal sizes of the stimuli. In one stimulus condition, distance appears not to affect reaction times. It is suggested that direct size perception occurs for large stimulus differences, indirect size perception for smaller differences. The identical results of the two experiments, one with and one without texture, point to some variable other than texture occlusion or interception as the stimulus for direct size perception. Some aspect of distance from the eye-level plane is suggested as an alternative.     

Concurrent variable‐interval variable‐ratio schedules in a dynamic choice environment

Most studies of operant choice have focused on presenting subjects with a fixed pair of schedules across many experimental sessions. Using these methods, studies of concurrent variable‐ interval variable‐ratio schedules helped to evaluate theories of choice. More recently, a growing literature has focused on dynamic choice behavior. Those dynamic choice studies have analyzed behavior on a number of different time scales using concurrent variable‐interval schedules. Following the dynamic choice approach, the present experiment examined performance on concurrent variable‐interval variable‐ratio schedules in a rapidly changing environment. Our objectives were to compare performance on concurrent variable‐interval variable‐ratio schedules with extant data on concurrent variable‐interval variable‐interval schedules using a dynamic choice procedure and to extend earlier work on concurrent variable‐interval variable‐ratio schedules. We analyzed performances at different time scales, finding strong similarities between concurrent variable‐interval variable‐interval and concurrent variable‐interval variable‐ ratio performance within dynamic choice procedures. Time‐based measures revealed almost identical performance in the two procedures compared with response‐based measures, supporting the view that choice is best understood as time allocation. Performance at the smaller time scale of visits accorded with the tendency seen in earlier research toward developing a pattern of strong preference for and long visits to the richer alternative paired with brief “samples” at the leaner alternative (“fix and sample”).