{"title":"Sequential analysis of variance: Increasing efficiency of hypothesis testing.","authors":"Meike Steinhilber,Martin Schnuerch,Anna-Lena Schubert","doi":"10.1037/met0000677","DOIUrl":"https://doi.org/10.1037/met0000677","url":null,"abstract":"Researchers commonly use analysis of variance (ANOVA) to statistically test results of factorial designs. Performing an a priori power analysis is crucial to ensure that the ANOVA is sufficiently powered, however, it often poses a challenge and can result in large sample sizes, especially if the expected effect size is small. Due to the high prevalence of small effect sizes in psychology, studies are frequently underpowered as it is often economically unfeasible to gather the necessary sample size for adequate Type-II error control. Here, we present a more efficient alternative to the fixed ANOVA, the so-called sequential ANOVA that we implemented in the R package \"sprtt.\" The sequential ANOVA is based on the sequential probability ratio test (SPRT) that uses a likelihood ratio as a test statistic and controls for long-term error rates. SPRTs gather evidence for both the null and the alternative hypothesis and conclude this process when a sufficient amount of evidence has been gathered to accept one of the two hypotheses. Through simulations, we show that the sequential ANOVA is more efficient than the fixed ANOVA and reliably controls long-term error rates. Additionally, robustness analyses revealed that the sequential and fixed ANOVAs exhibit analogous properties when their underlying assumptions are violated. Taken together, our results demonstrate that the sequential ANOVA is an efficient alternative to fixed sample designs for hypothesis testing. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
David Trafimow,Tingting Tong,Tonghui Wang,S T Boris Choy,Liqun Hu,Xiangfei Chen,Cong Wang,Ziyuan Wang
{"title":"Improving inferential analyses predata and postdata.","authors":"David Trafimow,Tingting Tong,Tonghui Wang,S T Boris Choy,Liqun Hu,Xiangfei Chen,Cong Wang,Ziyuan Wang","doi":"10.1037/met0000697","DOIUrl":"https://doi.org/10.1037/met0000697","url":null,"abstract":"The standard statistical procedure for researchers comprises a two-step process. Before data collection, researchers perform power analyses, and after data collection, they perform significance tests. Many have proffered arguments that significance tests are unsound, but that issue will not be rehashed here. It is sufficient that even for aficionados, there is the usual disclaimer that null hypothesis significance tests provide extremely limited information, thereby rendering them vulnerable to misuse. There is a much better postdata option that provides a higher grade of useful information. Based on work by Trafimow and his colleagues (for a review, see Trafimow, 2023a), it is possible to estimate probabilities of being better off or worse off, by varying degrees, depending on whether one gets the treatment or not. In turn, if the postdata goal switches from significance testing to a concern with probabilistic advantages or disadvantages, an implication is that the predata goal ought to switch accordingly. The a priori procedure, with its focus on parameter estimation, should replace conventional power analysis as a predata procedure. Therefore, the new two-step procedure should be the a priori procedure predata and estimations of probabilities of being better off, or worse off, to varying degrees, postdata. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Consistency of Bayes factor estimates in Bayesian analysis of variance.","authors":"Roland Pfister","doi":"10.1037/met0000703","DOIUrl":"https://doi.org/10.1037/met0000703","url":null,"abstract":"Factorial designs lend themselves to a variety of analyses with Bayesian methodology. The de facto standard is Bayesian analysis of variance (ANOVA) with Monte Carlo integration. Alternative, and readily available methods, are Bayesian ANOVA with Laplace approximation as well as Bayesian t tests for individual effects. This simulation study compared the three approaches regarding ordinal and metric agreement of the resulting Bayes factors for a 2 × 2 mixed design. Simulation results indicate remarkable disagreement of the three methods in certain cases, particularly when effect sizes are small and studies include small sample sizes. Findings further replicate and extend previous observations of substantial variability of ANOVAs with Monte Carlo integration across different runs of one and the same analysis. These observations showcase important limitations of current implementations of Bayesian ANOVA. Researchers should be mindful of these limitations when interpreting corresponding analyses, ideally applying multiple approaches to establish converging results. (PsycInfo Database Record (c) 2024 APA, all rights reserved).","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142165971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling construct change over time amidst potential changes in construct measurement: A longitudinal moderated factor analysis approach.","authors":"Siyuan Marco Chen, Daniel J Bauer","doi":"10.1037/met0000685","DOIUrl":"https://doi.org/10.1037/met0000685","url":null,"abstract":"<p><p>In analyzing longitudinal data with growth curve models, a critical assumption is that changes in the observed measures reflect construct changes and not changes in the manifestation of the construct over time. However, growth curve models are often fit to a repeated measure constructed as a sum or mean of scale items, making an implicit assumption of constancy of measurement. This practice risks confounding actual construct change with changes in measurement (i.e., differential item functioning [DIF]), threatening the validity of conclusions. An improved method that avoids such confounding is the second-order growth curve (SGC) model. It specifies a measurement model at each occasion of measurement that can be evaluated for invariance over time. The applicability of the SGC model is hindered by key limitations: (a) the SGC model treats time as continuous when modeling construct growth but as discrete when modeling measurement, reducing interpretability and parsimony; (b) the evaluation of DIF becomes increasingly error-prone given multiple timepoints and groups; (c) DIF associated with continuous covariates is difficult to incorporate. Drawing on moderated nonlinear factor analysis, we propose an alternative approach that provides a parsimonious framework for including many time points and DIF from different types of covariates. We implement this model through Bayesian estimation, allowing for incorporation of regularizing priors to facilitate efficient evaluation of DIF. We demonstrate a two-step workflow of measurement evaluation and growth modeling, with an empirical example examining changes in adolescent delinquency over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142111363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Supplemental Material for Modeling Construct Change Over Time Amidst Potential Changes in Construct Measurement: A Longitudinal Moderated Factor Analysis Approach","authors":"","doi":"10.1037/met0000685.supp","DOIUrl":"https://doi.org/10.1037/met0000685.supp","url":null,"abstract":"","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141925494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Inference with cross-lagged effects-Problems in time.","authors":"Charles C Driver","doi":"10.1037/met0000665","DOIUrl":"https://doi.org/10.1037/met0000665","url":null,"abstract":"<p><p>The interpretation of cross-effects from vector autoregressive models to infer structure and causality among constructs is widespread and sometimes problematic. I describe problems in the interpretation of cross-effects when processes that are thought to fluctuate continuously in time are, as is typically done, modeled as changing only in discrete steps (as in e.g., structural equation modeling)-zeroes in a discrete-time temporal matrix do not necessarily correspond to zero effects in the underlying continuous processes, and vice versa. This has implications for the common case when the presence or absence of cross-effects is used for inference about underlying causal processes. I demonstrate these problems via simulation, and also show that when an underlying set of processes are continuous in time, even relatively few direct causal links can result in much denser temporal effect matrices in discrete-time. I demonstrate one solution to these issues, namely parameterizing the system as a stochastic differential equation and focusing inference on the continuous-time temporal effects. I follow this with some discussion of issues regarding the switch to continuous-time, specifically regularization, appropriate measurement time lag, and model order. An empirical example using intensive longitudinal data highlights some of the complexities of applying such approaches to real data, particularly with respect to model specification, examining misspecification, and parameter interpretation. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141634308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nicole Walasek, Ethan S Young, Willem E Frankenhuis
{"title":"A framework for studying environmental statistics in developmental science.","authors":"Nicole Walasek, Ethan S Young, Willem E Frankenhuis","doi":"10.1037/met0000651","DOIUrl":"https://doi.org/10.1037/met0000651","url":null,"abstract":"<p><p>Psychologists tend to rely on verbal descriptions of the environment over time, using terms like \"unpredictable,\" \"variable,\" and \"unstable.\" These terms are often open to different interpretations. This ambiguity blurs the match between constructs and measures, which creates confusion and inconsistency across studies. To better characterize the environment, the field needs a shared framework that organizes descriptions of the environment over time in clear terms: as statistical definitions. Here, we first present such a framework, drawing on theory developed in other disciplines, such as biology, anthropology, ecology, and economics. Then we apply our framework by quantifying \"unpredictability\" in a publicly available, longitudinal data set of crime rates in New York City (NYC) across 15 years. This case study shows that the correlations between different \"unpredictability statistics\" across regions are only moderate. This means that regions within NYC rank differently on unpredictability depending on which definition is used and at which spatial scale the statistics are computed. Additionally, we explore associations between unpredictability statistics and measures of unemployment, poverty, and educational attainment derived from publicly available NYC survey data. In our case study, these measures are associated with mean levels in crime rates but hardly with unpredictability in crime rates. Our case study illustrates the merits of using a formal framework for disentangling different properties of the environment. To facilitate the use of our framework, we provide a friendly, step-by-step guide for identifying the structure of the environment in repeated measures data sets. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141634306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Coefficients of determination measured on the same scale as the outcome: Alternatives to R² that use standard deviations instead of explained variance.","authors":"Mathias Berggren","doi":"10.1037/met0000681","DOIUrl":"https://doi.org/10.1037/met0000681","url":null,"abstract":"<p><p>The coefficient of determination, <i>R</i>², also called the explained variance, is often taken as a proportional measure of the relative determination of model on outcome. However, while <i>R</i>² has some attractive statistical properties, its reliance on squared variations (variances) may limit its use as an easily interpretable descriptive statistic of that determination. Here, the properties of this coefficient on the squared scale are discussed and generalized to three relative measures on the original scale. These generalizations can all be expressed as transformations of <i>R</i>², and alternatives can therefore also be calculated by plugging in related estimates, such as the adjusted <i>R</i>². The third coefficient, new for this article, and here termed the CoD<sub>SD</sub> (the coefficient of determination in terms of standard deviations), or <i>R</i><sub>π</sub> (<i>R</i>-pi), equals <i>R</i>²/(<i>R</i>²+1-<i>R</i>²). It is argued that this coefficient most usefully captures the relative determination of the model. When the contribution of the error is <i>c</i> times that of the model, the CoD<sub>SD</sub> equals 1/(1 + <i>c</i>), while <i>R</i>² equals 1/(1 + <i>c</i>²). (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141634307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Supplemental Material for Coefficients of Determination Measured on the Same Scale as the Outcome: Alternatives to R2 That Use Standard Deviations Instead of Explained Variance","authors":"","doi":"10.1037/met0000681.supp","DOIUrl":"https://doi.org/10.1037/met0000681.supp","url":null,"abstract":"","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141669123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Niek Stevenson, Reilly J Innes, Quentin F Gronau, Steven Miletić, Andrew Heathcote, Birte U Forstmann, Scott D Brown
{"title":"Using group level factor models to resolve high dimensionality in model-based sampling.","authors":"Niek Stevenson, Reilly J Innes, Quentin F Gronau, Steven Miletić, Andrew Heathcote, Birte U Forstmann, Scott D Brown","doi":"10.1037/met0000618","DOIUrl":"https://doi.org/10.1037/met0000618","url":null,"abstract":"<p><p>Joint modeling of decisions and neural activation poses the potential to provide significant advances in linking brain and behavior. However, methods of joint modeling have been limited by difficulties in estimation, often due to high dimensionality and simultaneous estimation challenges. In the current article, we propose a method of model estimation that draws on state-of-the-art Bayesian hierarchical modeling techniques and uses factor analysis as a means of dimensionality reduction and inference at the group level. This hierarchical factor approach can adopt any model for the individual and distill the relationships of its parameters across individuals through a factor structure. We demonstrate the significant dimensionality reduction gained by factor analysis and good parameter recovery, and illustrate a variety of factor loading constraints that can be used for different purposes and research questions, as well as three applications of the method to previously analyzed data. We conclude that this method provides a flexible and usable approach with interpretable outcomes that are primarily data-driven, in contrast to the largely hypothesis-driven methods often used in joint modeling. Although we focus on joint modeling methods, this model-based estimation approach could be used for any high dimensional modeling problem. We provide open-source code and accompanying tutorial documentation to make the method accessible to any researchers. (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":null,"pages":null},"PeriodicalIF":7.6,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141446886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}