A score method of constructing asymmetric confidence intervals for the mean of a rating scale item

This article presents a generalization of the Score method of constructing confidence intervals for the population proportion (E. B. Wilson, 1927) to the case of the population mean of a rating scale item. A simulation study was conducted to assess the properties of the Score confidence interval in relation to the traditional Wald (A. Wald, 1943) confidence interval under a variety of conditions, including sample size, number of response options, extremeness of the population mean, and kurtosis of the response distribution. The results of the simulation study indicated that the Score interval usually outperformed the Wald interval, suggesting that the Score interval is a viable method of constructing confidence intervals for the population mean of a rating scale item.     

性别对工作→家庭冲突的影响机制:基于社会角色理论的实证分析

采用问卷调查法,对来自上海地区的261名企业管理者进行调查,探讨了性别与组织分割供给、工作中心度及工作→家庭冲突的关系。结果表明:⑴性别对工作→家庭冲突的预测作用显著,男性比女性经历的工作→家庭冲突更多;⑵组织分割供给和工作中心度在性别与工作→家庭冲突之间的中介效应均显著。相比女性而言,男性员工因获得的组织分割供给较少且其自身的工作中心度较高,导致其经历的工作→家庭冲突更多。     

Improved Test–retest Reliability Criteria as Applied to Probability Assessments

Test–retest reliability is a common indicator of response consistency. It is argued that using regression coefficients for detecting systematic response error is less appropriate than testing for shifts in the mean (median) and variance. This procedure is exemplified using probability response data. For this data, shifts in centrality were found to be about 2.5 times more likely than shifts in variability. The shifts in centrality did not favor any particular direction; however, variability tended to decrease over time in early sessions.     

Confidence intervals for standardized linear contrasts of means

Most psychology journals now require authors to report a sample value of effect size along with hypothesis testing results. The sample effect size value can be misleading because it contains sampling error. Authors often incorrectly interpret the sample effect size as if it were the population effect size. A simple solution to this problem is to report a confidence interval for the population value of the effect size. Standardized linear contrasts of means are useful measures of effect size in a wide variety of research applications. New confidence intervals for standardized linear contrasts of means are developed and may be applied to between-subjects designs, within-subjects designs, or mixed designs. The proposed confidence interval methods are easy to compute, do not require equal population variances, and perform better than the currently available methods when the population variances are not equal.     

Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant

An approach to sample size planning for multiple regression is presented that emphasizes accuracy in parameter estimation (AIPE). The AIPE approach yields precise estimates of population parameters by providing necessary sample sizes in order for the likely widths of confidence intervals to be sufficiently narrow. One AIPE method yields a sample size such that the expected width of the confidence interval around the standardized population regression coefficient is equal to the width specified. An enhanced formulation ensures, with some stipulated probability, that the width of the confidence interval will be no larger than the width specified. Issues involving standardized regression coefficients and random predictors are discussed, as are the philosophical differences between AIPE and the power analytic approaches to sample size planning.     

Standard errors and confidence intervals for correlations corrected for indirect range restriction: A simulation study comparing analytic and bootstrap methods

A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation. Monte Carlo simulation studies involving both normal and non-normal data were conducted to examine the empirical performance of the bootstrap and analytic methods. Results indicated that with both normal and non-normal data, the bootstrap standard error and confidence interval were generally accurate across simulation conditions (restricted sample size, selection ratio, and population correlations) and outperformed estimates of the analytic method. However, with certain combinations of distribution type and model conditions, the analytic method has an advantage, offering reasonable estimates of the standard error and confidence interval without resorting to the bootstrap procedure's computer-intensive approach. We provide SAS code for the simulation studies.     

Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach

The accuracy in parameter estimation approach to sample size planning is developed for the coefficient of variation, where the goal of the method is to obtain an accurate parameter estimate by achieving a sufficiently narrow confidence interval. The first method allows researchers to plan sample size so that the expected width of the confidence interval for the population coefficient of variation is sufficiently narrow. A modification allows a desired degree of assurance to be incorporated into the method, so that the obtained confidence interval will be sufficiently narrow with some specified probability (e.g., 85% assurance that the 95 confidence interval width will be no wider than to units). Tables of necessary sample size are provided for a variety of scenarios that may help researchers planning a study where the coefficient of variation is of interest plan an appropriate sample size in order to have a sufficiently narrow confidence interval, optionally with somespecified assurance of the confidence interval being sufficiently narrow. Freely available computer routines have been developed that allow researchers to easily implement all of the methods discussed in the article.     

α系数的区间估计方法比较

多数情况下,α系数可以用来评价测验信度。诸多研究建议,在报告测验信度的时候应当包括其置信区间。通过蒙特卡洛模拟研究,比较了7种α系数区间估计方法,包括Fisher法、Bonett-02法、Bonett-10法、精确Koning-Franses法、渐近ID法、渐近Koning-Franses法和ADF法。结果发现Bonett-10法和精确Koning-Franses法较好,它们的结果相差很小。这两种方法都比较简单,只需要样本的α值、测验题数、被试人数及F临界值,通过简单的运算便可得到α系数的置信区间。     

The Making of Female Presidents and Prime Ministers: The Impact of Birth Order, Sex, of Siblings, and Father-Daughter Dynamics

Although research into the factors that may affect male achievement of political leadership is relatively robust, very few studies on the making of female presidents and prime ministers exist. This paper examines the literature on birth order, sex of siblings, and parent-daughter dynamics to see whether the findings for male political leaders—that first-born individuals will be overrepresented as compared with later-born siblings—also hold for female ones. Two other hypotheses were tested concerning differences in birth order and sex of siblings between female political leaders and a larger sample of women. A review of the literature on parent-daughter dynamics suggests that this may be another important variable for future research into explanations for the success of women who achieve senior-level positions of power. The findings suggest that first-born women, like first-born men, are overrepresented among political leaders; that first-born women are overrepresented among female political leaders as compared with their numbers in a larger sample population; and that fewer female political leaders have an older brother than would be expected to occur in a larger sample population. The last finding applies only for women who come to power in the period 1960–1989, not those who gained office more recently.     

Association of Economic Internality With Saving Behavior and Motives,Financial Confidence,and Attitudes Toward State Intervention1

This study investigates economic locus of control (ELOC) in a Greek sample using Furnham's (1986) scale. In particular, it examines the association between ELOC and saving behavior and motives, attitudes toward state intervention in the economic field, and factors engendering confidence in economic matters. The main hypotheses predicted that internal ELOC should be associated with (a) desire for less state intervention; (b) confidence in factors under one's own control (knowing the other party in transactions, being well informed) more strongly than with other factors of economic trust, such as the state and the law; (c) more saving; and (d) that respondents with internal and external ELOC should be differentiated with respect to saving motives. Analysis was based on a sample of 135 participants from Athens. Principal components analysis of the Greek translation of Furnham's ELOC questionnaire gave results similar to those reported from England, yielding 4 factors interpretable as chance, internal, external/denial, and powerful others. The findings of the study include confirmation of all of the hypotheses.     

Sample size planning for composite reliability coefficients: accuracy in parameter estimation via narrow confidence intervals

Composite measures play an important role in psychology and related disciplines. Composite measures almost always have error. Correspondingly, it is important to understand the reliability of the scores from any particular composite measure. However, the point estimates of the reliability of composite measures are fallible and thus all such point estimates should be accompanied by a confidence interval. When confidence intervals are wide, there is much uncertainty in the population value of the reliability coefficient. Given the importance of reporting confidence intervals for estimates of reliability, coupled with the undesirability of wide confidence intervals, we develop methods that allow researchers to plan sample size in order to obtain narrow confidence intervals for population reliability coefficients. We first discuss composite reliability coefficients and then provide a discussion on confidence interval formation for the corresponding population value. Using the accuracy in parameter estimation approach, we develop two methods to obtain accurate estimates of reliability by planning sample size. The first method provides a way to plan sample size so that the expected confidence interval width for the population reliability coefficient is sufficiently narrow. The second method ensures that the confidence interval width will be sufficiently narrow with some desired degree of assurance (e.g., 99% assurance that the 95% confidence interval for the population reliability coefficient will be less than W units wide). The effectiveness of our methods was verified with Monte Carlo simulation studies. We demonstrate how to easily implement the methods with easy-to-use and freely available software.     

Names,concepts, features and the living/nonliving things dissociation

The present paper evaluates different hypotheses for explaining the living/nonliving things dissociation phenomenon in terms of feature type, considering the role of this dimension in the organization of conceptual semantic representations and in the activation of name representations. For this purpose we used Sloman and associates' (Memory and Cognition 27(3) (1999) 526; Cognitive Science 22(2) (1998) 189) name centrality and conceptual centrality tasks and asked subjects to judge functional and perceptual/visual features of living and nonliving items. Conceptual centrality results are more in accordance with a "single feature-domain connection hypothesis" where visual features are more important than functional features for the representation of living things and no feature type advantage is found for nonliving things. Name centrality results show that functional features are more important than sensory/visual features overall, a result that is not predicted by any of the hypotheses considered. The fact that the two judgments diverge emphasizes their importance for evaluating the role of feature type in the living/nonliving dissociation. Implications for explaining this phenomenon are also discussed.     

Accuracy in parameter estimation for targeted effects in structural equation modeling: sample size planning for narrow confidence intervals

In addition to evaluating a structural equation model (SEM) as a whole, often the model parameters are of interest and confidence intervals for those parameters are formed. Given a model with a good overall fit, it is entirely possible for the targeted effects of interest to have very wide confidence intervals, thus giving little information about the magnitude of the population targeted effects. With the goal of obtaining sufficiently narrow confidence intervals for the model parameters of interest, sample size planning methods for SEM are developed from the accuracy in parameter estimation approach. One method plans for the sample size so that the expected confidence interval width is sufficiently narrow. An extended procedure ensures that the obtained confidence interval will be no wider than desired, with some specified degree of assurance. A Monte Carlo simulation study was conducted that verified the effectiveness of the procedures in realistic situations. The methods developed have been implemented in the MBESS package in R so that they can be easily applied by researchers.     

Point-biserial correlation: Interval estimation,hypothesis testing,meta-analysis,and sample size determination

The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.     

The self-consistency model of subjective confidence

How do people monitor the correctness of their answers? A self-consistency model is proposed for the process underlying confidence judgments and their accuracy. In answering a 2-alternative question, participants are assumed to retrieve a sample of representations of the question and base their confidence on the consistency with which the chosen answer is supported across representations. Confidence is modeled by analogy to the calculation of statistical level of confidence (SLC) in testing hypotheses about a population and represents the participant's assessment of the likelihood that a new sample will yield the same choice. Assuming that participants draw representations from a commonly shared item-specific population of representations, predictions were derived regarding the function relating confidence to inter-participant consensus and intra-participant consistency for the more preferred (majority) and the less preferred (minority) choices. The predicted pattern was confirmed for several different tasks. The confidence-accuracy relationship was shown to be a by-product of the consistency-correctness relationship: It is positive because the answers that are consistently chosen are generally correct, but negative when the wrong answers tend to be favored. The overconfidence bias stems from the reliability-validity discrepancy: Confidence monitors reliability (or self-consistency), but its accuracy is evaluated in calibration studies against correctness. Simulation and empirical results suggest that response speed is a frugal cue for self-consistency, and its validity depends on the validity of self-consistency in predicting performance. Another mnemonic cue-accessibility, which is the overall amount of information that comes to mind-makes an added, independent contribution. Self-consistency and accessibility may correspond to the 2 parameters that affect SLC: sample variance and sample size.     

Centrality of women's multiple roles: beneficial and detrimental consequences for psychological well-being

Theorists have proposed that greater centrality (personal importance) of a social role is associated with better psychological well-being but that role centrality exacerbates the negative effects of stress in that same social role on well-being. The present study found evidence to support both hypotheses in a sample of 296 women who simultaneously occupied the roles of parent care provider, mother, wife, and employee. Greater centrality of all four roles was related to better psychological well-being. As predicted, wife centrality exacerbated the effects of wife stress on life satisfaction, and employee centrality exacerbated the effects of employee stress on depressive symptoms. Contrary to prediction, centrality of the mother role buffered women from the negative effects of mother stress on depressive symptoms. These findings point to an aspect of role identity that can benefit well-being but that has complex effects in the context of role stress.     

Understanding the effects of sample size on the variability of the mean

In the first three experiments, we attempted to learn more about subjects' understanding of the importance of sample size by systematically changing aspects of the problems we gave to subjects. In a fourth study, understanding of the effects of sample size was tested as subjects went through a computerassisted training procedure that dealt with random sampling and the sampling distribution of the mean. Subjects used sample size information more appropriately for problems that were stated in terms of the accuracy of the sample average or the center of the sampling distribution than for problems stated in terms of the tails of the sampling distribution. Apparently, people understand that the means of larger samples are more likely to resemble the population mean but not the implications of this fact for the variability of the mean. The fourth experiment showed that although instruction about the sampling distribution of the mean led to better understanding of the effects of sample size, subjects were still unable to make correct inferences about the variability of the mean. The appreciation that people have for some aspects of the law of large numbers does not seem to result from an in-depth understanding of the relation between sample size and variability.     

Fisher transformation based confidence intervals of correlations in fixed- and random-effects meta-analysis

Meta-analyses of correlation coefficients are an important technique to integrate results from many cross-sectional and longitudinal research designs. Uncertainty in pooled estimates is typically assessed with the help of confidence intervals, which can double as hypothesis tests for two-sided hypotheses about the underlying correlation. A standard approach to construct confidence intervals for the main effect is the Hedges-Olkin-Vevea Fisher-z (HOVz) approach, which is based on the Fisher-z transformation. Results from previous studies (Field, 2005, Psychol. Meth., 10, 444; Hafdahl and Williams, 2009, Psychol. Meth., 14, 24), however, indicate that in random-effects models the performance of the HOVz confidence interval can be unsatisfactory. To this end, we propose improvements of the HOVz approach, which are based on enhanced variance estimators for the main effect estimate. In order to study the coverage of the new confidence intervals in both fixed- and random-effects meta-analysis models, we perform an extensive simulation study, comparing them to established approaches. Data were generated via a truncated normal and beta distribution model. The results show that our newly proposed confidence intervals based on a Knapp-Hartung-type variance estimator or robust heteroscedasticity consistent sandwich estimators in combination with the integral z-to-r transformation (Hafdahl, 2009, Br. J. Math. Stat. Psychol., 62, 233) provide more accurate coverage than existing approaches in most scenarios, especially in the more appropriate beta distribution simulation model.     

Sample size determination for confidence intervals of interaction effects in moderated multiple regression with continuous predictor and moderator variables

Moderated multiple regression (MMR) has been widely employed to analyze the interaction or moderating effects in behavior and related disciplines of social science. Much of the methodological literature in the context of MMR concerns statistical power and sample size calculations of hypothesis tests for detecting moderator variables. Notably, interval estimation is a distinct and more informative alternative to significance testing for inference purposes. To facilitate the practice of reporting confidence intervals in MMR analyses, the present article presents two approaches to sample size determinations for precise interval estimation of interaction effects between continuous moderator and predictor variables. One approach provides the necessary sample size so that the designated interval for the least squares estimator of moderating effects attains the specified coverage probability. The other gives the sample size required to ensure, with a given tolerance probability, that a confidence interval of moderating effects with a desired confidence coefficient will be within a specified range. Numerical examples and simulation results are presented to illustrate the usefulness and advantages of the proposed methods that account for the embedded randomness and distributional characteristic of the moderator and predictor variables.     

Fitting linear models to ordinal responses

The distribution of an ordinal response can be modelled as a grouping of an underlying quantitative variable whose mean is a linear function of explanatory variables. Possible distributional assumptions about the underlying quantitative response are compared. An iteratively reweighted least squares algorithm for parameter estimation in these models is described in detail and variances and tests of hypotheses are given. Two data sets are analysed to illustrate the methods.