Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.     

Considering too few alternatives: The mental model theory of extensional reasoning

When solving a simple probabilistic problem, people tend to build an incomplete mental representation. We observe this pattern in responses to probabilistic problems over a set of premises using the conjunction, disjunction, and conditional propositional connectives. The mental model theory of extensional reasoning explains this bias towards underestimating the number of possibilities: In reckoning with different interpretations of the premises (logical rules, mental model theoretical, and, specific to conditional premises, conjunction and biconditional interpretation) the mental model theory accounts for the majority of observations. Different interpretations of a premise result in a build-up of mental models that are often incomplete. These mental models are processed using either an extensional strategy relying on proportions amongst models, or a conflict monitoring strategy. The consequence of considering too few possibilities is an erroneous probability estimate akin to that faced by decision makers who fail to generate and consider all alternatives, a characteristic of bounded rationality. We compare our results to the results published by Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni [Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]–88 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. doi:10 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1037 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]/0033 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]-295X Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], and we observe lower performance levels than those in the original article.     

Evidence for a young adult face bias in accuracy and consensus of age estimates

Adults' face processing may be specialized for the dimensions of young adult faces. For example, young and older adults exhibit increased accuracy in normality judgments and greater agreement in attractiveness ratings for young versus older adult faces. The present study was designed to examine whether there is a similar young adult face bias in facial age estimates. In Experiment 1, we created a face age continuum by morphing an averaged young adult face with an averaged older adult face in 5% increments, for a total of 21 faces ranging from 0 to 100% old. Young and older adults estimated facial age for three stimulus age categories [young (morphs 0–30%), middle‐aged (morphs 35–65%), and older adult (morphs 70–100%)]. Both age groups showed the least differentiation in age estimates for young adult faces, despite showing greater consensus across participants in estimates for young faces. In Experiment 2, young and older adults made age estimates for individual young and older adult identities. Both age groups were more accurate and showed greater consensus in age estimates for young faces. Collectively, these results provide evidence for a bias in processing young adult faces beyond that which is often observed in recognition and normality/attractiveness judgment tasks.     

Scarce Foods are Perceived as Having More Calories

People vary dramatically in their calorie estimates of food depending on the information available to them. Prior research has focused on information that is normatively relevant to the number of calories a food contains (e.g., fat content, serving size). The current research examines whether information that is normatively irrelevant to the number of calories a food contains—such as its availability—might also shape people's calorie estimates. Three studies found that a food perceived as limited in availability leads people to estimate the food to contain more calories. Serial mediation analyses revealed that this effect occurs because scarce food is seen as more valuable and expensive, which subsequently induces feelings of resource deprivation. This sense of resource deprivation, in turn, leads to motivated perception, whereby higher calorie estimates are the result of people wanting to acquire more resources. The findings provide insight into the psychology of scarcity and underscore the importance of understanding how contextual factors shape people's calorie estimates and the psychological mechanisms that drive them.     

Using equivalence‐based instruction to teach the visual analysis of graphs

Previous research has demonstrated low rater agreement when visually inspecting trends in single‐subject design graphs (see Wolfe, Seaman, & Drasgow, 2016). Didactic instruction of visual analysis of practicing behavior analysts has resulted in generally poor and unreliable performances (Danov & Symons, 2008; Diller, Barry, & Gelino, 2016). Therefore, a refined instructional technology to improve the reliability among behavior analysts is warranted. Developing research has focused on the application of equivalence‐based instruction (Brodsky & Fienup, 2018; Rehfeldt, 2011) for a variety of complex human behaviors. In the current study, equivalence‐based instruction was used to train four participants to identify functional relations displayed in five different classes of graphs. Training resulted in the formation of five equivalence classes by all participants consisting of three members (graph, functional relation rule, and functional relation statement). In addition, the skills were maintained for up to 2 weeks and generalized to novel graphs.     

Addressing the “Replication Crisis”: Using Original Studies to Design Replication Studies with Appropriate Statistical Power

Psychology is undergoing a replication crisis. The discussion surrounding this crisis has centered on mistrust of previous findings. Researchers planning replication studies often use the original study sample effect size as the basis for sample size planning. However, this strategy ignores uncertainty and publication bias in estimated effect sizes, resulting in overly optimistic calculations. A psychologist who intends to obtain power of .80 in the replication study, and performs calculations accordingly, may have an actual power lower than .80. We performed simulations to reveal the magnitude of the difference between actual and intended power based on common sample size planning strategies and assessed the performance of methods that aim to correct for effect size uncertainty and/or bias. Our results imply that even if original studies reflect actual phenomena and were conducted in the absence of questionable research practices, popular approaches to designing replication studies may result in a low success rate, especially if the original study is underpowered. Methods correcting for bias and/or uncertainty generally had higher actual power, but were not a panacea for an underpowered original study. Thus, it becomes imperative that 1) original studies are adequately powered and 2) replication studies are designed with methods that are more likely to yield the intended level of power.     

Accommodating Small Sample Sizes in Three-Level Models When the Third Level is Incidental

Small samples sizes are a pervasive problem when modeling clustered data. In two-level models, this problem has been well studied, and several resources provide guidance for modeling such data. However, a recent review of small-sample clustered data methods has noted that no studies have investigated methods for modeling three-level data with small sample sizes. Furthermore, strategies for two-level models do not necessarily translate to the three-level context. Moreover, three-level models are prone to small samples because the “small sample” designation is primarily based on the sample size of the highest level, and large samples are increasingly difficult to amass as one progresses up a hierarchy. In this study, we focus on the case when the third level is incidental, meaning that the third level is important to consider but there are no explicit research questions at the third level. This study performs a simulation study to examine the performance of seven methods for modeling three-level data with a small sample at the third level. A motivating educational psychology example is also provided to demonstrate how the choice of method can greatly affect results.     

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。     

Clinical Validation of the Swedish Version of the Quality of Life Inventory in Crime Victims with Posttraumatic Stress Disorder and a Nonclinical Sample

The Swedish version of the Quality of Life Inventory (QOLI) was cross-culturally validated with a crime victim sample (N = 53) with posttraumatic stress disorder (PTSD) and a nonclinical group (N = 100) with no lifetime and current psychiatric disorder from the general population in the Stockholm county of Sweden. The QOLI showed excellent internal consistencies in the clinical and the nonclinical sample. In addition, PTSD participants displayed a significantly lower self-perceived quality of life in 13 out of 16 domains of life than the nonclinical individuals. Furthermore, the QOLI was inversely correlated with interview and self-report measures of PTSD symptoms, depression, and anxiety. Overall, the results support the utility of the Swedish QOLI version as a potentially useful measure of self-perceived quality of life in Swedish clinical and nonclinical samples. The results are discussed in relation to the Swedish cross-cultural validation of the QOLI, methodological limitations and future directions.     

群体水平IRT模型及其应用——兼与IRT的比较

传统上,群体评估都是以个体的评估结果的平均值为基础进行的。而群体水平IRT理论则可以避开对个体的评估,直接实现对群体的评估,它具有许多传统方法难以企及的优点。本文将群体水平IRT模型应用于2007年某省高考英语阅读理解的410所学校的能力评估,评估结果发现：410所学校的英语阅读理解能力几乎都在[-1,1]区间内,没有能力极高或极低的学校。对这些学校而言,测验中所有项目的难度较易,区分度适中。所有的评估结果与IRT模型的评估结果在 的水平上相关显著,表明GIRT模型在实践中是可以选择的一种群体评估方法。