Moving Beyond Univariate Post-Hoc Testing in Exercise Science: A Primer on Descriptive Discriminate Analysis

Historically, behavior analytic research and practice have been grounded in the single subject examination of behavior change. Within the behavior analytic community, there remains little doubt that the graphing of behavior is a powerful strategy for demonstrating functional control by the independent variable; however, during the past thirty years, various statistical techniques have become a popular alternative form of evidence for demonstrating a treatment effect. Concurrently, a mounting number of behavior analytic investigators are measuring multiple dependent variables when conducting statistical analyses. Without employing strategies that protect the experimentwise error rate, evaluation of multiple dependent variables within a single experiment is likely to inflate the Type I error rate. In fact, with each additional dependent variable examined in univariate fashion, the probability of “incorrectly” identifying statistical significance increases exponentially as a function of chance. Multivariate analysis of variance (MANOVA) and several other statistical techniques can preclude this common error. We provide an overview of the procedural complications arising from methodologies that might inflate the Type I error rate. Additionally, we provide a sample of reviewer comments and suggestions, and an enrichment section focusing on this somewhat contentious issue, as well as a number of statistical and neural network techniques that enhance power and preclude the inflation of Type I error rates

Multivariate analysis refers to statistical techniques that simultaneously look at three or more variables in relation to the subjects under investigation with the aim of identifying or clarifying the relationships between them. These techniques have been broadly classified as dependence techniques, which explore the relationship between one or more dependent variables and their independent predictors, and interdependence techniques, that make no such distinction but treat all variables equally in a search for underlying relationships. Multiple linear regression models a situation where a single numerical dependent variable is to be predicted from multiple numerical independent variables. Logistic regression is used when the outcome variable is dichotomous in nature. The log-linear technique models count type of data and can be used to analyze cross-tabulations where more than two variables are included. Analysis of covariance is an extension of analysis of variance (ANOVA), in which an additional independent variable of interest, the covariate, is brought into the analysis. It tries to examine whether a difference persists after “controlling” for the effect of the covariate that can impact the numerical dependent variable of interest. Multivariate analysis of variance (MANOVA) is a multivariate extension of ANOVA used when multiple numerical dependent variables have to be incorporated in the analysis. Interdependence techniques are more commonly applied to psychometrics, social sciences and market research. Exploratory factor analysis and principal component analysis are related techniques that seek to extract from a larger number of metric variables, a smaller number of composite factors or components, which are linearly related to the original variables. Cluster analysis aims to identify, in a large number of cases, relatively homogeneous groups called clusters, without prior information about the groups. The calculation intensive nature of multivariate analysis has so far precluded most researchers from using these techniques routinely. The situation is now changing with wider availability, and increasing sophistication of statistical software and researchers should no longer shy away from exploring the applications of multivariate methods to real-life data sets.

Means comparisons using multivariate analysis of variance (MANOVA) is a useful though somewhat complex statistical approach for comparing independent groups across multiple dependent measures. In the field of applied linguistics, studies using MANOVA remain few, though its application has been seen across many areas including language assessment, acquisition, psycholinguistics, and textual analysis. As with any statistical method of this relative complexity, MANOVA relies upon several empirical assumptions that need to be examined prior to analysis, though the interpretations that it can provide in terms of both statistical significance and effect can offer a unique approach to examining the effects of group differences across a number of separate but related measured variables. To that end, this entry will cover the main considerations necessary for setting up, running, and interpreting MANOVA in practical and theoretical terms.

Re-examining the ontogeny of the context preexposure facilitation effect in the rat through multiple dependent variables

Multivariate regression is known as a multivariate extension of multiple regression, which explain/predict the variations in multiple dependent variables by multiple independent variables. Recently, various procedures for Sparse Multivariate Regression (SMR) have been proposed, in which a sparse regression coefficient matrix (having a number of zero elements) is obtained aiming to facilitate its interpretation. The procedures for SMR can be classified into the following two types; penalized and cardinality-constrained procedures. In them, the resulting number of zeros in the regression coefficient matrix is controlled/constrained by a prespecified penalty parameter or cardinality value. In this research, we propose another approach for SMR, referred to as Layered Multivariate Regression (LMR). In LMR, the regression coefficient matrix is assumed to be a sum of several sparse matrices, which is called layer. Therefore, the sparseness of the resulting coefficient matrix is controlled by how many layers are used. In LMR, k-th layer can be viewed as the coefficient matrix in the regression of a partial residual (i.e., the residual for all but k-th layer) on independent variables, and thus the variance explained by LMR gets closer to that for the unconstrained regression as the number of layers increases. We present an alternating least squares algorithm for LMR and a procedure for determining how many layers should be used. LMR is assessed in a simulation study and illustrated with a real data example. As an application of LMR, procedures for sparse estimation in some multivariate analysis techniques (e.g., principal component analysis) are also presented.

Objectives The purposes of this study were to investigate the attitudes toward physical education and physical activity levels of middle school students in Jiangxi Province, China, and explore the relationship between these two factors. Methods The subjects consisted of 722 middle school students (male: 371 and female: 351) from 7th to 9th grade at four public middle schools in Jiangxi Province, China. The measurement tools were used the Chinese version of Students' Attitude Toward Physical Education (Hu et al., 2014) and the Chinese version of Physical Activity Questionnaire for Adolescents (Li, 2015). For data analysis, confirmatory factor analysis (CFA), descriptive statistics, univariate analysis of variance (ANOVA), multivariate analysis of variance (MANOVA) were performed, using SPSS 26 and AMOS 27 statistical program. Results The results showed that first, participants' attitudes toward physical education were generally positive across all grades and genders, with average scores above 3.0 for all sub-factors. According to the result of MANOVA, gender had a significant impact on all dependent variables [CE: F(1, 716)=21.795, p<.05; CU: F(1, 716)=14.818, p<.05; TE: F(1, 716)=18.150, p<.05; TU: F(1, 716)=8.130, p<.05]; however, grade did not significantly affect attitudes. Second, physical activity levels varied by gender and grade, with males generally exhibiting higher (2.34) scores than females (1.88). According to a multivariate analysis of variance (MANOVA), both gender [F(1, 716)=80.342, p＜.05] and grade [F(2, 716)=24.351, p＜.05) had significant effects on physical activity scores, while the interaction effect between grade and gender was not significant [F(2, 716)=1.659, p＞.05]. Third, correlation analysis revealed slightly positive relationships between physical activity and the four sub-scales of attitude [CE (r=.290, p<.05); CU (r=.299, p<.05); TE (r=.326, p<.05); TU (r=.283, p<.05)]. Conclusions The results of this study are expected to enhance the understanding of middle school students by schools and physical education teachers for the development of physical education in China, and to contribute to the development of future physical education programs by providing theoretical evidence.

PART ONE: FROM THEORY TO METHODOLOGY Types of Research Problems and Research Situations A Classification of Classical Techniques of Multivariate Analysis The Analysis Technique as the Mirror of the Research Problem PART TWO: FROM METHODOLOGY TO ANALYSIS The Experimental Design The Effect of Humour on Financial Concession Multiple Regression Analysis The Causes of Childlessness Partial Correlation and Path Analysis The Causal Influence of Christian Beliefs on Anti-Semitism Analysis of Variance and Covariance The Effect of Interaction of Monetary Rewards and Task Interest on Motivation Two-Group Discriminant Analysis Poor and Rich Neighbourhoods Factor Analysis The Investigation of Marital Adjustment Canonical Correlation Analysis The Study of Economic Inequality and Political Instability Techniques with Multiple Dependent Variables

In this article, we describe a multistudy project designed to explain observed cross-national differences in risk taking between respondents from the People's Republic of China and the United States. Using this example, we develop the following recommendations for cross-cultural investigations. First, like all psychological research, cross-cultural studies should be model based. Investigators should commit themselves to a model of the behavior under study that explicitly specifies possible causal constructs or variables hypothesized to influence the behavior, as well as the relationship between those variables, and allows for individual, group, or cultural differences in the value of these variables or in the relationship between them. This moves the focus from a simple demonstration of cross-national differences toward a prediction of the behavior, including its cross-national variation. Ideally, the causal construct hypothesized and shown to differ between cultures should be demonstrated to serve as a moderator or a mediator between culture and observed behavioral differences. Second, investigators should look for converging evidence for hypothesized cultural effects on behavior by looking at multiple dependent variables and using multiple methodological approaches. Thus, the data collection that will allow for the establishment of conclusive causal connections between a cultural variable and some target behavior can be compared with the creation of a mosaic.

Simultaneous studies of multiple health conditions over geographic areas can be enhanced by the principal component analysis (PCA). However, the presence of spatial autocorrelation may induce nonlinearity that compromises PCA. This article presents an approach that combines the residual standardization method in PCA with a spatial regression method to account for spatial autocorrelation. It first estimates a multivariate simultaneous autoregressive model for parameter estimates and residuals. It then uses the residuals to formulate a standardized matrix for singular value decomposition. Simulation in various scenarios demonstrates that the proposed approach can effectively remove spatial dependent effects between spatial units to capture pure correlation effects within spatial units. Two case studies examine hospitalization and cancer data in Nebraska. The first demonstrates a way to account for spatial dependency in 39 hospitalization conditions over 156 census tracts. The second applies regression residuals to PCA to evaluate potentially elevated cancer risks near two nuclear power plants. The results show that accounting for spatial dependency and explanatory variables can help reveal information about multiple health outcomes.

This book describes a practical aproach to univariate and multivariate analysis of variance. It starts with a general non-mathematical account of the fundamental theories and this is followed by a discussion of a series of examples using real data sets from the authors' own work in clinical trials, psychology and industry. Included are discussions of factorial and nested designs, structures on the multiple dependent variables measured on each subject, repeated measures analyses, covariates, choice of text statistic and simultaneous test procedures.

Social media has become an integral part of modern communication, with millions of users worldwide. While it facilitates connectivity and information sharing, its psychological effects, particularly on selfesteem and body image, have raised significant concerns. This study investigates the impact of social media use on self-esteem and body image among female young adults in Sri Lanka. Using convenience sampling, the study included 251 females with ages ranging from 18 to 26. A Google form that included a demographic questionnaire, the Social Media Use Scale, the Body Image Questionnaire, and the Rosenberg Self-Esteem Scale was shared through social media platforms to collect data. A one-way multivariate analysis of variance (MANOVA) confirmed a statistically significant multivariate effect of social media use on both body image and self-esteem, with social media use explaining 8.5% of the variance in the combined dependent variables. Follow-up analysis of variance (ANOVA) indicated a significant effect of social media use on body image and self-esteem separately, with small to moderate effect sizes. Further analysis using Welch’s t-test showed that individuals with Low social media use had significant and higher self-esteem (d = 0.459) and more positive body image (d = 0.580) compared to those with High social media use. Findings highlight that social media use has a significant effect on both self-esteem and body image, with higher social media use associated with lower self-esteem and poor body image. Future research should examine usage patterns and cultural influences. Keywords: Social media use, body image, self-esteem, Sri Lankan female young adults

Objectives: To determine if online team-based learning (TBL) is effective in improving knowledge outcomes and confidence about hyponatremia in its clinical recognition, classification, diagnostic work up, and management among fourth year medical students Study design: A quantitative evaluative design. Population and Setting: Fourth year medical students (medical clerks) rotating in the Department of Medicine, Faculty of Medicine and Surgery, University of Santo Tomas, Manila, Philippines from July to December 2020. Methodology: A modified TBL workshop is adopted in teaching fourth year medical clerks about hyponatremia. The TBL session was held with a group of medical clerks weekly from July to December 2020. As a pre-workshop preparation, the medical clerks were assigned to read ahead of time the clinical practice guidelines on the diagnosis and treatment of hyponatremia developed by the European Renal Best Practice. After reading it, they were asked to answer an Individual Readiness Assessment Test (IRAT) composed of 20 case-based multiple-choice questions (MCQ). The group was thereafter divided into 4 subgroups and asked to discuss the same MCQ-based exam and present it as a Team Readiness Assessment Test (TRAT). As each subgroup presented their IRAT, the facilitator discussed the underlying concepts for each question and its application in actual cases of hyponatremia. The facilitator then summarized the learning outcomes at the end of the TBL workshop. For team application (TAPP), the students created a concept map and formulated admitting orders. The medical clerks were then surveyed on their confidence in hyponatremia diagnosis and management during pre-TBL workshop, after IRAT, after TRAT, and after discussion with the facilitator. Statistical Design: Descriptive statistics were used to summarize the study variables and included the mean, standard deviation, frequency, and percentage. Within-group comparisons of different outcomes across the different timeframes were conducted using one-way multivariate analysis of variance (one-way MANOVA). Cognizant that the study has multiple outcomes or dependent variables which were compared at four different timeframes, multivariate analysis was utilized to minimize the inflation of family-wise errors (FWE). Results: Comparative analysis indicated that the mean readiness scores of the respondents after TRAT was significantly higher (t=–91.61, p=0.001) compared to the mean readiness scores after IRAT. Comparative analysis using paired t-test indicated that the mean confidence scores of the respondents in the recognition, diagnosis, and treatment of hyponatremia were significantly higher among the respondents after the IRAT (t=–24.26, p=0.001), TRAT (t=–34.58, p=0.001), and facilitator discussion (t=–42.72, p=0.001) approaches compared to the mean pre-TBL confidence score. The mean knowledge score of the respondents on the creation of a concept map and the formulation of admission orders of patients with hyponatremia was 25.54±1.98 (95% CI 25.26-25.82). Conclusion: Findings of this study are not to be interpreted as demonstrating a causal relationship. Furthermore, the results are only hypothesis-generating at best. The study showed that online TBL has the potential to be an effective method in improving knowledge outcomes and confidence about hyponatremia in its clinical recognition, classification, diagnostic work-up, and management among fourth year medical students. As a preliminary evaluation of TBL, further studies can be conducted to determine its effectiveness as a teaching modality in the medical curricula in comparison to the traditional method before being adopted as a teaching-learning activity. Key words: team-based learning, online learning, COVID-19, hyponatremia, medical education

Case control. To use modified NFL Combine testing methodology to test for functional deficits in athletes following anterior cruciate ligament (ACL) reconstruction following return to sport. There is a need to develop objective, performance-based, on-field assessment methods designed to identify potential lower extremity performance deficits and related impairments in this population. Eighteen patients (mean ± SD age, 16.9 ± 2.1 years; height, 170.0 ± 8.7 cm; body mass, 71.9 ± 21.8 kg) who returned to their sport within a year following ACL reconstruction (95% CI: 7.8 to 11.9 months from surgery) participated (ACLR group). These individuals were asked to bring 1 or 2 teammates to serve as control participants, who were matched for sex, sport, and age (n = 20; mean ± SD age, 16.9 ± 1.1 years; height, 169.7 ± 8.4 cm; body mass, 70.1 ± 20.7 kg). Functional performance was tested using the broad jump, vertical jump, modified long shuttle, modified pro shuttle, modified agility T-test, timed hop, triple hop, single hop, and crossover hop tests. A 1-way multivariate analysis of variance (MANOVA) was used to evaluate group differences for dependent performance variables. The functional performance measurements of skills requiring bilateral involvement of both lower extremities showed no group differences between the ACLR and control groups (P>.05). An overall group difference (P = .006) was observed for the combined limb symmetry index (LSI) measures. However, the modified double-limb performance tasks (long shuttle, modified agility T-test, and pro shuttle) were not, independently, sufficiently sensitive to detect limb deficits in individuals with ACL reconstruction. Conversely, the LSI on the distance measures of the single-limb performance tasks all provided moderate to large effect sizes to differentiate between the ACLR and control groups, as the individuals who had ACL reconstruction demonstrated involved limb deficits on all measures (P<.05). Finally, the LSI for the timed hop test was not different between groups (P>.05). These findings indicate that, while unilateral deficits are present in individuals following ACL reconstruction, they may not be evident during bipedal performance or during modified versions of double-limb performance activities. Isolation of the involved limb with unilateral hopping tasks should be used to identify deficits in performance.

Longitudinal variations in maximal oxygen intake with age and activity.

A model for analyzing multiple categorical dependent variables is presented and developed for use in organizational research. A primary example occurs in the foreign market entry literature, in which choice of ownership (majority, equal, or minority) and function (acquisition or joint venture) are simultaneously endogenous; only separate univariate ownership-based and function-based choice models are considered in the literature. Another example is in the comparison of gender and race across organizational units, controlling for confounders such as experience and qualification. Subsuming univariate categorical dependent variables as a special case, the model unifies existing organizational research methods, mitigates bias associated with univariate methods, provides more powerful testing methods, and provides a flexible modeling framework that allows hypotheses to be modeled and tested that are not possible with univariate models. Standard software may be used for estimation and testing; examples are given.