The Study Of Effects In Manova

A particular strategy for investigating effects resulting from a MANOVA is proposed. The strategy involves multiple two-group multivariate analyses. The two groups result from considering multivariate pairwise group contrasts or multivariate complex group contrasts. Assuming a given two-group analysis yields real effects, the resultant single linear discriminant function (LDF) may be studied. A rationale based on a transformation of LDF weights, due to V. Y. Urbakh, is recommended for assessing variable relative contribution. The analysis strategy is described in detail and illustrated with real data sets.     

Comparison of sport achievement orientation of male professional, amateur, and wheelchair basketball athletes

To examine the differences in sport achievement orientation among 35 professional, 36 amateur, and 35 wheelchair basketball athletes, these men completed three subscales of Competitiveness, Win orientation, and Goal orientation of the 25-item Sport Orientation Questionnaire. A multivariate analysis of variance indicated significant differences among groups. Win orientation was the factor, through discriminant function analysis, that significantly separated the athletes into the three groups. The highest win score was obtained by the professional, followed by the amateur and wheelchair groups. Replication study is necessary to confirm the present findings.     

A Multivariate Profile Analysis of MMPIs of Suicidal and Nonsuicidal Neuropsychiatric Hospital Patients

Using six MMPI scales and a multivariate discriminant analysis, the question was asked whether differences existed between nonsuicidal and threatened, attempted, and committed suicides. The results indicated that there were significant differences between the mean score of the four groups. The application of the various identification rates to populations with different suicidal base rates and the implication of the findings for the prediction of different types of suicidal behavior was discussed.     

Multiple bi-serial and multiple point bi-serial correlation

Normal equations, using data in various forms, are presented for securing the regression weights for prediction of a dichotomized criterion, and a simplified equation for the estimation of the multiple bi-serial or multiple point bi-serial, depending upon the proper assumption as to the nature of the distribution of the criterion, on the basis of these maximal weights is given also. The weights, unaffected by the assumption as to the nature of the criterion, are identical (or proportional) to those found by the discriminant function approach based upon analysis of variance. The author holds that the present multiple correlation approach is both easier and more informative than the discriminant function (analysis of variance) approach and suggests that the discriminant function be abandoned in favor of multiple bi-serial and/or multiple point bi-serial correlation and regression.     

Influence of Generational Status and Financial Stress on Academic and Career Self‐Efficacy

The importance of a college degree is underscored by higher unemployment rates of individuals who have not completed college (Bureau of Labor Statistics, 2014 ). Academic and career self‐efficacy influence students' completion of college, and 1st‐generation college students and those under financial strain may experience decreased self‐efficacy (Wohlgemuth et al., 2007 ). Participants in this study (N = 383) were college students at a 4‐year university. Results from a 2 × 3 multivariate analysis of variance and discriminant function analysis revealed significant differences in academic and career self‐efficacy based on financial stress, but not generational status.     

Oblique factors and components with independent clusters

Relationships between the results of factor analysis and component analysis are derived when oblique factors have independent clusters with equal variances of unique factors. The factor loadings are analytically shown to be smaller than the corresponding component loadings while the factor correlations are shown to be greater than the corresponding component correlations. The condition for the inequality of the factor/component contributions is derived in the case with different variances for unique factors. Further, the asymptotic standard errors of parameter estimates are obtained for a simplified model with the assumption of multivariate normality, which shows that the component loading estimate is more stable than the corresponding factor loading estimate.     

Diagnosing Autism using ICD-10 criteria: A comparison of neural networks and standard multivariate procedures

In a sample of 976 consecutive cases derived from the recent world-wide Field Trial of Autism and other Pervasive Developmental Disorders, we tested the accuracy of the 15 ICD-10 criteria for the diagnosis of Autism, by comparing neural network models (NN) to more conventional multivariate competitors, namely, linear and quadratic discriminant function analyses and logistic regression. NNs were less accurate than competitors, both in terms of cross-validation results as well as in levels of shrinkage from training to test conditions. The clinical research implications of these results are discussed.     

The Fisher-Pitman permutation test when testing for differences in mean and variance

The Fisher-Pitman permutation test can detect any type of difference between two samples: hence, a significant Fisher-Pitman permutation test does not necessarily provide evidence for a difference in means. It is possible, however, to test separately for differences in means and variances. Here, we present a recently proposed two-stage procedure to decide whether there are differences in means or variances that can be applied when samples may come from nonnormal distributions with possibly unequal variances.     

FOUR METHODS OF ANALYZING BETWEEN VARIATION FOR THE K-GROUP MANOVA PROBLEM

Four methods of analyzing between variation in the k-group MANOVA problem are considered. Specifically, they are (1) discriminant analysis, (2) stepdown analysis, (3) contrasts on the classification variable and (4) a two group breakdown. These methods are discussed briefly, with certain basic com- puting equations being given. Then a sample problem is used to illustrate how the methods may be applied and interpreted. The univariate h2 (squared correlation ratio) is related t o a corresponding multivariate measure. Also, a variant of h2 is introduced to indicate the proportion of variance in each of the dependent variables which is accounted for by the classification variable.     

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.     

Variances and Covariances of Kendall's Tau and Their Estimation

We generalize the formulas derived by Daniels and Kendall (1947) for the variance of the sample tau correlation. It is assumed that multivariate data are sampled from a population, and sample taus between pairs of variables are being used to estimate their population counterparts. Expressions for the variance of tau-a are generalized to allow for ties on either variable, and we further provide an expression for the covariance between two taus, including the special case where there is a variable in common. Unbiased estimators of the variance and the covariances are also derived for use in small samples. The variances and covariances of tau-a are used to provide asymptotic variances for tau-b and Somers' d.     

Discriminant Analysis Using Mixed Continuous,Dichotomous, and Ordered Categorical Variables

This article proposes an intuitive approach for predictive discriminant analysis with mixed continuous, dichotomous, and ordered categorical variables that are defined via an underlying multivariate normal distribution with a threshold specification. The classification rule is based on the comparison of the observed data logarithm probability density functions. To reduce the computational burden, the analysis is conducted in the context of a confirmatory factor analysis model with independent error measurements. Identification of the dichotomous and ordered categorical variables is discussed. Results are obtained by implementations of a Monte Carlo expectation maximization (MCEM)algorithm and a path sampling procedure. Probabilities of misclassification are estimated via the idea of the “jackknife” method. A real example is given to illustrate the proposed method.     

Genetic and environmental effects on the covariance structure of the Norwegian army ability tests: A study of twins

The ability scores from all complete twin pairs recruited to the compulsory Norwegian military service during the period 1950–1954 were analysed, using a multivariate design. Three separate scores were obtained from the Army tests: general ability, technical comprehension and arithmetical skills. A chi- square model test and a maximum likelihood estimation were performed by the use of LISREL computer program. The total genetic variances varied from 40% to 66% in the three subttests. The environmental within family variances and the environmental between family variances were about equally large. The intra-correlations between the subtests were generally high, and the major part of the genetic variance was common, but specific genetic effects and specific environmental within family effects both explained about 20% of the total variances in technical comprehension and in arithmetical skills. Nearly no variance was specific for general ability. All the environmental between family variance was common for the three subtests.     

Enhancing job satisfaction perspectives: Combining Holland themes and basic interests

Investigations addressing the match between vocational interests and satisfaction have emphasized higher-order dimensions (e.g., Holland themes) and specific occupational scales. Although support exists at these levels of analysis for the hypothesis that congruence between interests and work environments yields satisfaction, limitations of these perspectives frequently result in small effect sizes or inconclusive results. This study examined the capacity of content scales of the 2005 Strong Interest Inventory, including the General Occupational Themes (GOTs) and Basic Interest Scales (BISs), in predicting job satisfaction across 22 samples comprising 9647 working adults. Hypothesized multivariate sets of content scales, and predicted individual GOTs and BISs demonstrated significant group differences. Sequential discriminant function analyses demonstrated that sets of hypothesized BISs significantly distinguished between satisfied and dissatisfied workers beyond the six Holland themes in 17 of the 22 occupational samples. The authors discuss practical implications of interpreting BISs to augment Holland themes related to job satisfaction.     

Morphological Knowledge in Children with Dyslexia

The phonological skills are not the only linguistic abilities which are observed to have some influence on reading achievement in dyslexics. In addition to phonological skills, morphological skills should be also taken in consideration. The aim of this study is to extend investigation the linguistic abilities of children with dyslexia to the morphological level through examination whether there is a lack of morphological knowledge in children with dyslexia for Bosnian language with transparent orthography. Testing sample included 45 children with dyslexia that are compared with chronological age and reading level controls. The dyslexic children performed significantly worse than same age controls on all forms of word and the most complex word formation tasks. Based on the examination of standardized discriminant function coefficients the variable with the highest weight in defining the first discriminant function was the suffixal formation, declination of personal pronouns, changing gender of adjectives with regard to the gender of a noun, and changing of gender of cardinal numbers with regard to the gender of a noun best differentiates groups. Results of multivariate analyses of variance also showed that chronological age and reading level groups outperformed dyslexics on all these tasks. Our results suggest that dyslexics have problems with morphological knowledge which indicate that certain actions regarding the development of morphological abilities in dyslexics should be taken in the elementary grades.     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

Statistical inferences about the error variance

This paper is a presentation of an essential part of the sampling theory of the error variance and the standard error of measurement. An experimental assumption is that several equivalent tests with equal variances are available. These may be either final forms of the same test or obtained by dividing one test into several parts. The simple model of independent and normally distributed errors of measurement with zero mean is employed. No assumption is made about the form of the distributions of true and observed scores. This implies unrestricted freedom in defining the population. First, maximum-likelihood estimators of the error variance and the standard error of measurement are obtained, their sampling distributions given, and their properties investigated. Then unbiased estimators are defined and their distributions derived. The accuracy of estimation is given special consideration from various points of view. Next, rigorous statistical tests are developed to test hypotheses about error variances on the basis of one and two samples. Also the construction of confidence intervals is treated. Finally, Bartlett's test of homogeneity of variances is used to provide a multi-sample test of equality of error variances.     

CAREER DEVELOPMENTS AND TRANSITIONS OF MIDDLE-AGED WOMEN

Job transition behaviors of women ( N = 71; M = 42.5 yrs.) in their middle years of professional careers who had changed jobs within the previous 3 years were investigated. They were employed in a major utility company in a midwestern city where 11% of the jobs had been eliminated. The women were classified according to job transition attitudes and behaviors into groups labeled Wanters-Planners or Creators ( n = 12); Wanters-Nonplanners or Maintainers ( n = 15); Nonwanters-Planners or Conventionalists ( n = 28); and Nonwanters-Nonplanners or Reactors ( n = 16). Significant differences were obtained from three developmental perspectives: Person, Situation, and Person-by-Situation aspects of job-leaving/job-procuring behaviors. Three multivariate analyses of variance were followed by appropriate one-way analyses of variance and post hoc chi-square and Tukey's tests to identify the variations among the groups. Three multivariate discriminant analyses correctly classified the women into the four groups.