Statistical analysis of repeated measures data using SAS procedures

Mixed linear models were developed by animal breeders to evaluate genetic potential of bulls. Application of mixed models has recently spread to all areas of research, spurred by availability of advanced computer software. Previously, mixed model analyses were implemented by adapting fixed-effect methods to models with random effects. This imposed limitations on applicability because the covariance structure was not modeled. This is the case with PROC GLM in the SAS System. Recent versions of the SAS System include PROC MIXED. This procedure implements random effects in the statistical model and permits modeling the covariance structure of the data. Thereby, PROC MIXED can compute efficient estimates of fixed effects and valid standard errors of the estimates. Modeling the covariance structure is especially important for analysis of repeated measures data because measurements taken close in time are potentially more highly correlated than those taken far apart in time.     

Discriminant analysis: A comment.

Discusses 3 topics related to the interpretation of discriminant analyses (DAs): (a) partial F ratios and partial Wilks's lambdas for predictor variables in standard, step-down and stepwise DAs; (b) relation of goals of classification to the definition and evaluation of classification rules; and (c) significance tests for total hit rates in internal versus external analyses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Stability of nonlinear principal components analysis: An empirical study using the balanced bootstrap.

Principal components analysis (PCA) is used to explore the structure of data sets containing linearly related numeric variables. Alternatively, nonlinear PCA can handle possibly nonlinearly related numeric as well as nonnumeric variables. For linear PCA, the stability of its solution can be established under the assumption of multivariate normality. For nonlinear PCA, however, standard options for establishing stability are not provided. The authors use the nonparametric bootstrap procedure to assess the stability of nonlinear PCA results, applied to empirical data. They use confidence intervals for the variable transformations and confidence ellipses for the eigenvalues, the component loadings, and the person scores. They discuss the balanced version of the bootstrap, bias estimation, and Procrustes rotation. To provide a benchmark, the same bootstrap procedure is applied to linear PCA on the same data. On the basis of the results, the authors advise using at least 1,000 bootstrap samples, using Procrustes rotation on the bootstrap results, examining the bootstrap distributions along with the confidence regions, and merging categories with small marginal frequencies to reduce the variance of the bootstrap results. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical procedures and the justification of knowledge in psychological science.

Justification, in the vernacular language of philosophy of science, refers to the evaluation, defense, and confirmation of claims of truth. In this article, we examine some aspects of the rhetoric of justification, which in part draws on statistical data analysis to shore up facts and inductive inferences. There are a number of problems of methodological spirit and substance that in the past have been resistant to attempts to correct them. The major problems are discussed, and readers are reminded of ways to clear away these obstacles to justification. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating the correlation coefficient: The bootstrap approach.

Reviews B. Efron's (1979, 1982) bootstrap proposal, an approach to nonparametric statistics that resamples from a set of observations to establish a basis for inference. The bootstrap approach is adapted to the bivariate correlation situation and illustrated by developing nonparametric confidence intervals for the Pearson product-moment correlation. The technique is shown to be within the capabilities of microcomputers readily available to psychologists. (16 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Pattern analysis as simultaneous statistical inference.

Investigated the problem that most forms of pattern analysis of the Wechsler scales are essentially varieties of simultaneous statistical inference (i.e., multiple comparisons in the same sense that this term is used in the literature on ANOVA). A solution is presented for a special case of one–many comparisons, namely, the comparison of each subtest score with the average Verbal or Performance subtest score, or with the overall average. Tables are provided to facilitate this form of pattern analysis of the WISC, the WAIS, the Wechsler Preschool and Primary Scale of Intelligence, the WISC-R, and the WAIS-R. (21 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A longitudinal analysis of logical reasoning relationships: Conservation and transitive inference.

102 children originally assessed in 1973 were retested 1 yr later on a series of conservation and transitive inference tasks (length and weight content areas). An additional sample of matched cohort/grade Ss (1st- and 4th-grade levels) were assessed in the 2nd yr only to permit evaluation of repeated measurement biases for the longitudinal sample. Results indicate that there were no effects of presentation order, selective survival, repeated measurement, sex, or content area; these variables did not interact with each other. Analyses of the longitudinal Ss' conservation task performances over the annual interval indicated significant grade-level distinctions, Yr 1 vs Yr 2 differences, and type of conservation distinctions (identity vs equivalence). Identity conservation scores were consistently superior to equivalence conservation scores, a superiority most notable for the youngest Ss. Transitive inference tasks were significantly less difficult than equivalence conservation tasks. Most importantly, evidence for a developmental mastery sequence (transitivity-conservation) was demonstrated. Identity-equivalence conservation task distinctions were most apparent for the without verbal justification response criterion. (26 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical analysis: Summarizing evidence versus establishing facts.

Comments on the contention of T. A. Ryan (see record 1985-21808-001) that the purpose of statistics is to establish new facts that will contribute to the development of theory. It is argued that the primary role of statistical analysis is summarizing the current state of knowledge about scientific questions under study. The present authors do not share the following views expressed by Ryan: (1) Nonsignificant results should not be published; (2) the importance of Type II errors has been overemphasized relative to Type I; and (3) avoiding consideration of importance and interest in the weighting of contrasts is possible. The reasons for the disagreements are discussed. (7 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical procedures for evaluating the practical utility of a moderator approach to prediction.

Describes 3 statistical procedures for evaluating the practical utility of a moderator approach. Each procedure gives tests of significance for the comparison of 3 prediction strategies: (a) using the moderator variable as a basis for subgrouping Ss and computing separate regression equations, (b) using the moderator variable as a predictor variable, or (c) excluding the moderator variable from the prediction model. It is concluded that when job performance is measured along a continuum, the average y score of the selected group (Procedure 1) should be considered. However, when 2 levels of job performance are measured, (e.g., pass-fail grades) then either the number of selection errors (Procedure 2) or the number of selection errors when a selection ratio constraint is present (Procedure 3) should be used. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Principles and procedures of exploratory data analysis.

Exploratory data analysis (EDA) is a well-established statistical tradition that provides conceptual and computational tools for discovering patterns to foster hypothesis development and refinement. These tools and attitudes complement the use of significance and hypothesis tests used in confirmatory data analysis (CDA). Although EDA complements rather than replaces CDA, use of CDA without EDA is seldom warranted. Even when well-specified theories are held, EDA helps one interpret the results of CDA and may reveal unexpected or misleading patterns in the data. This article introduces the central heuristics and computational tools of EDA and contrasts it with CDA and exploratory statistics in general. EDA techniques are illustrated using previously published psychological data. Changes in statistical training and practice are recommended to incorporate these tools. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Discriminant analysis of the Ullrich-Turner syndrome neurocognitive profile

OBJECTIVES: To evaluate the effect of fetal behavioral states on the relationship between fetal heart rate (FHR) and middle cerebral artery resistance index (MCA RI) in normal fetuses. METHODS: The FHR and MCA RI of 10 normal cases from 37 to 40 weeks of gestation were recorded consecutively over a 45-min period. Correlations between the MCA RI and FHR during resting and active phases, classified by an actocardiotocogram, were analyzed by simple regression analysis. RESULTS: The mean FHR and MCA RI were significantly higher during the active phase (140.3 +/- 6.6 bpm, 0.79 +/- 0.06) than those during the resting phase (137.4 +/- 6.8 bpm, 0.75 +/- 0.07, P < 0.01, two sample t-test). There was a significant negative correlation (r = - 0.22, n = 2642, P < 0.01) between RI and FHR during the active phase and a significant positive correlation (r = 0.28, n = 2066, P < 0.001) during the resting phase. CONCLUSIONS: The relationship between FHR and the MCA RI during the resting phase is different from during the active phase.     

Statistical methods in factor analysis.

"A recent investigation of the efficiency of the centroid method of analysis is noted, and a recommendation is made regarding a valid test of the significance of residual matrices when this method is employed. The 'simple structure' concept is criticized and an alternative approach in the search for psychologically meaningful factors is recommended." 44 refs. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements.

When the distribution of the response variable is skewed, the population median may be a more meaningful measure of centrality than the population mean, and when the population distribution of the response variable has heavy tails, the sample median may be a more efficient estimator of centrality than the sample mean. The authors propose a confidence interval for a general linear function of population medians. Linear functions have many important special cases including pairwise comparisons, main effects, interaction effects, simple main effects, curvature, and slope. The confidence interval can be used to test 2-sided directional hypotheses and finite interval hypotheses. Sample size formulas are given for both interval estimation and hypothesis testing problems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Influence and inference: What the active perceiver overlooks.

We propose that perceivers who engage in social influence tasks (inducers) concentrate primarily on the relation between their influencing behaviors and the responsive behaviors of their target and ignore other important sources of information relevant to social inference (e.g., other concurrent sources of influence on the target person). As a result, inducers' inferences about the target person are biased by their own personal power. In Experiment 1, weak inducers drew more dispositional inferences about the targets of their influence attempts than did strong inducers when the magnitude of the inducers' power was revealed in the course of the social interaction, but not when inducers were informed about the magnitude of their power prior to the social interaction. These results suggest that inducers concentrated on information that they considered relevant to the assessment of their personal power and ignored information about concurrent sources of influence on the target person's behavior. In Experiment 2, inducers' judgments were unaffected by the presence or absence of information about concurrent sources of influence, whereas observers' judgments were significantly affected. The results of both experiments suggest that active perceivers, who are immersed in the social interactions they seek to interpret, differ from passive perceivers in a variety of theoretically predictable ways. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Confidence intervals for a quantile contrast: Application of the bootstrap.

Notes that for those making choices among selection strategies, training programs, or other treatments it can be more important to understand the impact of the choice on individuals identified as the best or poorest rather than on the average. As there are not readily available techniques for making such comparisons, an approach that develops confidence intervals for quantile differences is illustrated based on the recently developed bootstrap principle of nonparametric inference. (14 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Discriminant and factor analysis of the WAIS and the Satz-Mogel Abbreviated WAIS on brain-damaged and psychiatric patients.

Used a multivariate approach to compare diagnostic classification (brain-damaged vs psychiatric) of the abbreviated and the standard WAIS, using 118 brain-damaged and 55 psychiatric patients. Results show that in terms of hit rates, agreement, and subtest accuracy, there is a fair degree of similarity between the short and standard WAIS. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Statistical analysis of dyadic social behavior.

Describes a method for determining the effects of sex (or any other dichotomous characteristic) from the individual correlated behavioral responses observed in dyadic interactional situations. In the illustration used, the dyads are of 3 types: girl–girl, girl–boy, and boy–boy. Main effects of sex of S and of sex of partner and interaction effects are estimated and tested, using a generalization of the matched-pair t-test approach. Intragroup correlations between paired responses are examined separately. Alternative procedures of analysis are discussed and compared. The present method is extended to interacting groups larger than dyads when the S characteristic remains dichotomous (e.g., boys and girls in groups of 3, 4, etc). In these cases there are 3 intragroup correlations of interest for responses within the same interacting groups: boys vs boys, boys vs girls, and girls vs girls. (12 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A goodness-of-fit approach to inference procedures for the kappa statistic: confidence interval construction, significance-testing and sample size estimation

We propose a new procedure for constructing a confidence interval about the kappa statistic in the case of two raters and a dichotomous outcome. The procedure is based on a chi-square goodness-of-fit test as applied to a model frequently used for clustered binary data. The procedure provides coverage levels that are accurate in samples of smaller size than those required for other procedures. The procedure also has use for significance-testing and the planning of corresponding sample size requirements.