Multivariate Analysis of Variance and Repeated Measures: A Practical Approach for Behavioural Scientists

Assessments by Patients With Schizophrenia and Psychiatrists of Relative Risk of Research Procedures

Clinical psychology is a prominent career goal among psychology undergraduates, yet the mechanisms shaping this preference remain understudied. Guided by Social Cognitive Career Theory (SCCT), this study examined how personality traits, psychological distress, and motivational dimensions influence students’ intentions to pursue graduate studies in clinical psychology within the Turkish context. A total of 1,072 undergraduate psychology students (86.6% women; M = 21.97, SD = 3.08) completed an online survey assessing their motivations for pursuing clinical psychology, personality traits (as measured by the Big Five), and psychological distress (GHQ-12). Exploratory factor analysis (EFA) was conducted to identify motivational dimensions, followed by Pearson’s correlations to examine associations among variables. One-way multivariate analysis of variance (MANOVA) was conducted to find the prevalent motivating themes and compare students intending to specialize in clinical psychology with those preferring other subfields. EFA showed eight motivational factors (e.g., personal growth, helping others, professional prestige, becoming a psychotherapist). MANOVA indicated significant group differences in personality traits and psychological distress. Higher psychological distress among those interested in clinical psychology did not translate into a self-healing motivation but may reflect heightened empathic sensitivity. Preliminary construct validity of the newly developed Reasons for Choosing Clinical Psychology Questionnaire (RCCPQ) was supported through theoretically consistent correlations with personality traits and distress. Results underscore the interplay of personality dispositions, contextual factors, and goal-oriented motivations, consistent with SCCT. Clinical psychology appears to attract students not merely for self-oriented reasons but for culturally and socially shaped aspirations related to caregiving and professional meaning. Findings refining the wounded healer conceptualization, revealing a more complex and non-linear approach toward becoming a psychotherapist, are discussed.

Multivariate repeated measures data naturally arise in clinical trials and other fields such as biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normality and homogeneity. This paper proposes a finite-sample test by modifying the sums of squares matrices to make them insensitive to the heterogeneity in MANOVA. The proposed test is invariant to affine transformation and robust against nonnormality. The proposed method can be used in various experimental designs, for example, factorial design and crossover design. Under various simulation settings, the proposed method outperforms the classical Doubly Multivariate Model and Multivariate Mixed Model proposed elsewhere, especially for unbalanced sample sizes with heteroscedasticity. The applications of the proposed method are illustrated with ophthalmology data in factorial and crossover designs. The proposed method successfully identified and validated a significant main effect and demonstrated that univariate analysis could be oversensitive to small but clinically unimportant interactions.

There has been a recent call to improve data reporting in kinesiology journals, including the appropriate use of univariate and multivariate analysis techniques. For example, a multivariate analysis of variance (MANOVA) with univariate post hocs and a Bonferroni correction is frequently used to investigate group differences on multiple dependent variables. However, this univariate approach decreases power, increases the risk for Type 1 error, and contradicts the rationale for conducting multivariate tests in the first place. Purpose: The purpose of this study was to provide a user-friendly primer on conducting descriptive discriminant analysis (DDA), which is a post-hoc strategy to MANOVA that takes into account the complex relationships among multiple dependent variables. Method: A real-world example using the Statistical Package for the Social Sciences syntax and data from 1,095 middle school students on their body composition and body image are provided to explain and interpret the results from DDA. Results: While univariate post hocs increased the risk for Type 1 error to 76%, the DDA identified which dependent variables contributed to group differences and which groups were different from each other. For example, students in the very lean and Healthy Fitness Zone categories for body mass index experienced less pressure to lose weight, more satisfaction with their body, and higher physical self-concept than the Needs Improvement Zone groups. However, perceived pressure to gain weight did not contribute to group differences because it was a suppressor variable. Conclusion: Researchers are encouraged to use DDA when investigating group differences on multiple correlated dependent variables to determine which variables contributed to group differences.

In obesity research it is common to have repeated measures on subjects. Traditional statistical analyses of repeated measures data are analysis of variance (ANOVA) for random effects, and multivariate analysis of variance (MANOVA). Each assume that every subject was measured (i) the same number of times, and (ii) at the same time points. Another typical complication of many research designs is the presence of time-varying covariates. The usual ANOVA approach to repeated measures does not allow such covariates, and the MANOVA approach usually treats them as dependent variables. Hierarchical linear models deal with all of the above issues in a natural manner, making them an important tool for obesity research. This paper discusses some simple hierarchical models, and shows their application using two real data sets.

This article reviews and compares different existing statistical tests utilized in significance analysis of gene expression from DNA microarray data. Microarray gene expression study facilitates the investigation of genes that are differentially expressed with respect to different classes of samples. Many gene expression studies also aim to find groups of genes that do something together, or to find out molecular similarities among a group of samples. In all respects, it is very important to know whether there is a difference between two sets of results, and whether that difference is likely to occur due to random variations of the datasets. Hence instead of simple data analysis, statistical tests are the proper way to check statistical relevance. Basically, the statistical significance test is compulsory for yielding an ordered list of relevant genes in terms of differential expression to the investigator. This article surveys a few important statistical tests which include both parametric and nonparametric tests and compares those statistical tests with respect to different performance metrics. The statistical tests have been applied on several artificial and real-life microarray gene expression datasets. Most of the time, real-life datasets contain noise and noisy data can have undesirable effect on the results of any data mining analysis. Therefore, performance analysis on noisy datasets for different statistical tests has also been performed to facilitate the comparative study. Furthermore, correlation analysis of the resultant genes from different statistical methods has been accomplished. Keywords: Analysis, correlation analysis, eigenvector, nonparametric tests, P-value, parametric tests, principal component, statistical tests.

A total of 1,482 videos of lessons performed by teachers, whose performance was assessed as satisfactory and outstanding in the teaching assessment and teacher accreditation programs implemented in Chile, were examined. The videos were recorded between 2005 and 2010, at the middle school level, in language and mathematics lessons. The Good Teaching Practices Scheme was applied and 151 videos presenting at least one episode with 2 or more practices highlighted in the scheme were selected. Descriptive and correlational analyses were performed, along with multivariate analyses of variance, to assess differences by sex and education sector, and a repeated measures analysis between the moments of the lesson in the identified variables. Most of the identified good practices are implemented during the development phase of the lesson and seek to promote student participation. The most frequently used teaching strategy involves making reasoning processes explicit. These teaching practices are linked to a notion of teaching as transmission and are compatible with the externalist pattern of teaching that prevails in Chile.

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

Parametric statistical tests, as opposed to nonparametric or distribution‐free tests, are based on various assumptions regarding the characteristics, properties, and forms of the distributions of populations from which the data are drawn. A large number of statistical tests are included among the parametric tests, primarily hypothesis testing procedures derived from the general linear model. These include both univariate and multivariate statistical tests: the t test, univariate and multivariate analysis of variance (ANOVA) and covariance (including repeated measures), Pearson product‐moment correlation, simple and multiple regression (and variants including logistic regression), Hotelling's T 2 , discriminant function analysis, canonical correlation, and multivariate set correlation.

Symptom Severity Cut Points for the MD Anderson Symptom Inventory for CML (MDASI-CML)

Current analytic methods applied to multidimensional health-related quality of life (HRQOL) data do not borrow strength across analyses and do not produce summary estimates of effect. To compare a random effects modelling approach for the analysis of multidimensional HRQOL data to the following: (1) separate analyses for each dimension; (2) O'Brien's global test procedure; and (3) multivariate analysis of variance (MANOVA). Randomized clinical trial comparing 3 treatments (Trimethoprim-Sulfamethoxazole [TS], Dapsone-Trimethoprim [DT], and Clindamycin-Primaquine [CP] for Pneumocystis carinii pneumonia [PCP]). Patients with PCP enrolled in AIDS Clinical Trials Group Protocol 108. A 33-item battery assessing 7 dimensions of HRQOL: physical functioning, pain, energy, general health perceptions, disability, pulmonary symptoms, and constitutional symptoms. Analyses focused on changes in score from baseline to Day 7 (n = 145). Separate analyses for each dimension suggested a trend favoring CP versus TS, but using a Bonferroni correction no differences were statistically significant. O'Brien's global procedure for a test of no-treatment effect versus superiority of one treatment yielded P = 0.07. MANOVA did not reveal significant differences among treatment groups. A random effects model using fixed treatment and dimension effects and separate random effects for each person showed a significant overall treatment effect (P = 0.02); changes in scores for CP averaged 10 points greater than for TS. Random-effects models provide a flexible class of models for analyzing multidimensional quality of life data and estimating treatment effects because they borrow strength across dimensions.

To determine the impact of dry eye on quality of life, depression, anxiety, and stress in a healthy youthful clinical sample. This was a clinic-based cross-sectional study. Subjects were patients visiting the University of Cape Coast Eye Clinic for comprehensive eye examination. The age range for recruitment into the study was 16 to 35 years. Eligible participants completed three questionnaires namely the Ocular Surface Disease Index (OSDI), short version of the depression, anxiety, and stress scale (DASS-21), dry eye quality of life score (DEQS) questionnaire. All eligible participants underwent clinical assessment including meibomian gland expressibility, corneal staining, tear breakup time, and Schirmer 1 test. The Spearman correlation coefficient was used to determine the relationship between variables. Univariate and multivariate analyses of variance were used to determine the impact of the OSDI score on DASS-21 subscales scores and the dry eye quality of life scores. All 211 subjects who met the inclusion criteria were included in the analysis. The mean age for the entire sample was 21.6±3.0 years with a range of (17-31) years. Spearman correlation coefficient showed a statistically significant association between OSDI scores and DEQSs (P<0.001), anxiety scores (P<0.001), depression scores (P<0.001), and stress scores (P<0.001). Spearman correlation coefficient showed no statistically significant association between clinical test results and quality of life scores (P>0.05), DASS-21 subscales scores (P>0.05), except anxiety subscale and meibomian gland expressibility score (P=0.026). There were no statistically significant association between clinical test results and OSDI scores (P>0.05) except for the tear breakup time (P=0.018). Using Pillai's trace in the multivariate analysis of variance (MANOVA), there was a significant effect of OSDI severity classification on depression, anxiety, and stress subscales scores of the DASS-21, V=0.37, F(3, 207)=9.67, P<0.001. Furthermore, separate univariate analyses of variances on the outcome variables revealed a significant effect of OSDI severity classification on depression F(3, 207)=35.24, P<0.001, anxiety F(3, 207)=25.27, P<0.001, and stress F(3, 207)=13.08, P<0.001. The MANOVA was followed up with a discriminant analysis, which revealed three discriminant functions. When subjects were classified according to the OSDI grading of severity, there were a statistically significant difference between all levels of severity dry eye symptoms for the DEQSs (F(3, 207) = 63.9.3 P<0.001, η=0.48). The study showed that the severity of dry eye symptoms impacted on psychosomatic symptoms and quality of life. The study also revealed that the severity of dry eye symptoms impacted more on the depressive symptoms compared with other psychosomatic symptoms in this youthful clinical sample.

One of the applications of Fisher's linear discriminant function (FDF) is its use in transforming multivariate data into a new univariate variable. This then makes possible a new option for the variance analysis of multivariate data, in addition to the multivariate analysis of variance (MANOVA). The aim of this work was to select groups of seven characteristics of quality in coffee seedlings using six criteria for selection, to use the FDF to transform such groupings of characteristics into a new variable, and then to compare interpretation of the results obtained from the univariate and multivariate analyses of variance of the characteristics and this new variable, with a view to its use in evaluating coffee seedlings. A randomised block design was used to assess the effect of organic fertiliser on the formation of seedlings in coffee cv. Catuai Vermelho IAC-44, evaluating the following characteristics: seedling height, diameter, root length, dry weight of shoots and roots, leaf area, number of leaves and total dry weight. According to the selection criteria used, different subsets of the selected characteristics are possible. The use of the FDF is shown to be viable in discriminating between treatments. Univariate analysis of the new variable obtained with the FDF and multivariate analysis (MANOVA) was able to detect differences between the treatments, however, it is simpler to apply FDF methodology.

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.

the President Dr H. P. WYNN in the Chair) SUMMARY The problem of choosing appropriate models for multiply cross-classified data is examined. It is shown that a standard method of analysis used in many ANOVA programs, equivalent to Yates's method of weighted squares of means, may lead to inappropriate models. A simultaneous test procedure equivalent to one proposed in regression analysis is used to derive a class of acceptable models. The procedure is applied to an example. THIS paper presents a simple procedure for the analysis of multiply cross-classified data, for both normal and non-normal responses. The procedure is based on the hierarchical partition- ing of the total sum of squares or maximized likelihood, with a simultaneous test procedure, proposed in regression analysis, applied to the hierarchical partition to determine appropriate models for the data. This leads to a class of minimal adequate models; there may be several models in this class. The procedure is illustrated by applying it to a set of normal response data. Before discussing the general cross-classification, we consider some difficulties that have arisen in the treatment of the unbalanced two-way classification. 2. TIk TWO-WAY CLASSICATION 2.1. The2x2 Case Consider a 2 x 2 cross-classification with disproportionate subclass frequencies. We will be concerned with the case in which the disproportionality is considerable, so that approximate methods based on replacing the observed frequencies by proportional expected frequencies are inappropriate. Let A1, A2 and B1, B2 denote the levels of the cross-classifying factors, and let nU, j and ,uH be the sample size, and sample and population means in the (i,j) cell of the classifica- tion, and let n. and n 1 be the row and column marginal totals: B1 B2 B1 B2 B1 B2