An empirical study of a proposed test of nonparametric analysis of covariance.

Puri and Sen (1969b) introduced a nonparametric test statistic that, because of its relationship to the general linear model, subsumes many commonly performed hypothesis tests. Following the work of Puri and Sen, Harwell and Serlin (1985) proposed a test of the nonparametric analysis of covariance (ANCOVA) hypothesis. In order to use this statistic, ranks (or some other transformation) are substituted for the original scores. Standard statistical packages can then be used to perform the analysis, and the results of the test are referred to the appropriate reference distribution. The similarity of the rank transformation of Conover and Iman (1981) to this procedure is noted, and the results of a Monte Carlo study investigating the distributional properties (i.e., Type I error rate and power) of the proposed test and other nonparametric analyses of covariance models are presented. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An order-directed score test for trend in ordered 2 X K tables

This paper presents a new test procedure for detecting trend in ordered 2 X K tables. Using an order-directed score statistic, the procedure does not require a set of scores preassigned to the ordinal categories under consideration. Thus the problem of varying p-values of linear rank tests, due to choices of different scoring systems, is avoided. The proposed test procedure can be easily generalized to handle stratified analysis where data are represented by several 2 x K tables. Examples are given to illustrate the method.     

An elastic computerized brain atlas for the analysis of clinical PET/SPET data

An elastic computerized brain atlas was developed for the analysis of positron emission tomography/single-photon emission tomography (PET/SPET) data. It consists of a set of digital anatomical contours and a template of regions of interest, schematically describing the brain, derived from a currently used anatomical/functional brain atlas. A warping algorithm, matching equivalent contours, was implemented to elastically fit the atlas to individual brain images. The elastic computerized brain atlas was applied to representative magnetic resonance imaging (MRI)-PET/SPET studies, MRI providing the anatomical information used by the matching procedure. The atlas is suited for clinical use in a nuclear medicine environment.     

Statistical methods in computational anatomy

This paper reviews recent developments by the Washington/Brown groups for the study of anatomical shape in the emerging new discipline of computational anatomy. Parametric representations of anatomical variation for computational anatomy are reviewed, restricted to the assumption of small deformations. The generation of covariance operators for probabilistic measures of anatomical variation on coordinatized submanifolds is formulated as an empirical procedure. Populations of brains are mapped to common coordinate systems, from which template coordinate systems are constructed which are closest to the population of anatomies in a minimum distance sense. Variation of several one-, two- and three-dimensional manifolds, i.e. sulci, surfaces and brain volumes are examined via Gaussian measures with mean and covariances estimated directly from maps of templates to targets. Methods are presented for estimating the covariances of vector fields from a family of empirically generated maps, posed as generalized spectrum estimation indexed over the submanifolds. Covariance estimation is made parametric, analogous to autoregressive modelling, by introducing small deformation linear operators for constraining the spectrum of the fields.     

Estimating the rate constants in a two-compartment stochastic model

A procedure is described for estimating the rate constants of a two-compartment stochastic model for which the covariance structure over time of the observations is known. The proposed estimation procedure, by incorporating the known (as a function of the parameters to be estimated) covariance structure of the observations, produces regular best asymptotically normal (RBAN) estimators for the parameters. In addition, the construction of approximate confidence intervals and regions for the parameters is made possible by identification of the asymptotic covariance matrix of the estimators. The explicit form of the inverse of the covariance matrix, which is required in the estimation procedure, is presented. The procedure is illustrated by application to real as well as simulated data, and a comparison is made to the widely used nonlinear least squares procedure, which does not account for correlations over time.     

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.     

Regional cerebral blood flow during the Wisconsin Card Sorting Test in normal subjects studied by xenon-133 dynamic SPECT: comparison of absolute values, percent distribution values, and covariance analysis

We studied regional cerebral blood flow (rCBF) by xenon-133 dynamic single photon emission computed tomography (SPECT) in 17 normal volunteers who were performing the Wisconsin Card Sorting Test (WCST), a task that is particularly sensitive to disturbance of the prefrontal cortex, and a simple matching-to-sample task (BAR) as a sensorimotor control. Three methods for statistical analysis of regional "subtraction" data were used: absolute rCBF values, percent distribution values, and means adjusted for global CBF changes (covariance analysis). The absolute values had high variance, due to the combination of interindividual differences in global flow and intra-individual variation, and showed no statistically significant regional changes. This variation was greatly reduced by percent values and covariance analysis, which had quite similar outcomes. With both methods, significant increases of rCBF during the WCST as compared with the BAR were seen in the right anterior dorsolateral prefrontal and left occipital cortices, and reduction of rCBF in the left pararolandic region. Moreover, significant correlations with performance were found in the medial regions of the frontal lobes, with opposite trends for the right and left hemisphere. The posterior dorsolateral prefrontal region showed a negative correlation with sensory-motor frequency, an index related to the task's difficulty. These results are consistent with previous findings using other rCBF techniques and confirm the statistical advantage of normalization and covariance methods, which yield practically identical results, at least in this analysis based on regions of interest.     

Regression models: calculating the confidence interval of effects in the presence of interactions

The main goal of regression analysis (multiple, logistic, Cox) is to assess the relationship of one or more exposure variables to a response variable, in the presence of confounding and interaction. The confidence interval for the regression coefficient of the exposure variable, obtained through the use of a computer statistical package, quantify these relationships for models without interaction. Relationships between variables that present interactions are represented by two or more terms, and the corresponding confidence intervals can be calculated 'manually' from the covariance matrix. This paper suggests an easy procedure for obtaining confidence intervals from any statistical package. This procedure is applicable for modifying variables which are continuous as well as categorical.     

Group composition as a determinant of job analysis outcomes.

The purpose of this study was to determine if different groups of job incumbents would provide different job analysis outcomes. Patrolpersons from 12 university police departments served as subjects. Subject-matter-expert groups were formed on the basis of a multidimensional scaling (MDS) procedure, seniority level, and educational level. The job analysis technique used was the critical incident technique. Multivariate analysis of variance indicated that MDS groups differed on ratings and rank orderings of job dimension importance. These MDS group differences were probed via discriminant analysis, which revealed that the MDS groups differed on one discriminant function for the job dimension importance ratings and on two discriminant functions for the job dimension importance rank orderings. The MDS group's discriminant function differences were also related to supervisor rank orderings. Job analysis outcomes were not affected by subject-matter-expert groups of seniority and educational level. Results are discussed in terms of their implications for the job analysis practitioner. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The use of covariance functions and random regressions for genetic evaluation of milk production based on test day records

In the analysis of test day records for dairy cattle, covariance functions allow a continuous change of variances and covariances of test day yields on different lactation days. The equivalence between covariance functions as an infinite dimensional extension of multivariate models and random regression models is shown in this paper. A canonical transformation procedure is proposed for random regression models in large-scale genetic evaluations. Two methods were used to estimate covariance function coefficients for first parity test day yields of Holsteins: 1) a two-step procedure fitting covariance functions to matrices with estimated genetic and residual covariances between predetermined periods of lactation and 2) REML directly from data with a random regression model. The first method gave more reliable estimates, particularly for the periphery of the trajectory. The goodness of fit of a random regression model based on covariables describing the shape of the lactation curve was nearly the same as random regression on Legendre polynomials. In the latter model, two and three regression coefficients were sufficient to fit the covariance structure for additive genetic and permanent environment, respectively. The eigenfunction pattern revealed the possibility of selection for persistency. Covariance functions can be usefully implemented in large-scale test day models by means of random regressions.     

Cluster analysis with constraints: its use with breast cancer mortality rates in Argentina

One approach to analyse geographic variations of a disease within a country is through mortality rates in administrative areas. In some geographical areas the rates can be unstable due to their low population. Thus, the statistical analysis of the rate could be not significant due to low population, not because of the real value. An alternative approach to this problem is to set a minimum level of population that enables valid statistical comparisons with the national rate to be made. It is decided to apply an algorithm that groups neighbouring geographical units that reach the minimum population. In the resulting regions, mortality rates are calculated, and the geographic patterns are analysed through the Moran's I coefficient of spatial clustering. This paper presents an application of this approach to mortality rates from breast cancer by Argentine departments, political administrative units into which a province is divided. Applying this procedure, 217 regions were obtained. In two of the regions the rates were significantly higher than the national rate, while in 40 regions they were significantly lower. Significant spatial grouping, reflected by a Moran I coefficient of O-47, was observed.     

Testing differences between nested covariance structure models: Power analysis and null hypotheses.

For comparing nested covariance structure models, the standard procedure is the likelihood ratio test of the difference in fit, where the null hypothesis is that the models fit identically in the population. A procedure for determining statistical power of this test is presented where effect size is based on a specified difference in overall fit of the models. A modification of the standard null hypothesis of zero difference in fit is proposed allowing for testing an interval hypothesis that the difference in fit between models is small, rather than zero. These developments are combined yielding a procedure for estimating power of a test of a null hypothesis of small difference in fit versus an alternative hypothesis of larger difference. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Martingales without tears

This pedagogical paper presents a casual introduction to martingales, or fair gambling processes. Our objective is to describe the concept of a martingale and its application to common statistical tests used in the analysis of survival data, but without the mathematical rigor required for formal proofs. We use heuristic arguments to demonstrate that the logrank statistic evaluated over followup time is a fair gambling process, and introduce some mathematical notation and terminology along the way. We then employ the counting process approach to show that the logrank statistic computed over followup time can be expressed as the difference of two martingale transforms, and thus is a martingale. These ideas are first time introduced in the context of a discrete time process, and are then generalized to a continuous time process. With slight modifications, the same idea extends from the logrank to other weighted Mantel-Haenszel statistics computed over time.     

The use of smallest space analysis in studying scale structure: An application to the California Psychological Inventory.

Smallest space analysis is a nonmetric technique for analysis of proximity relations, e.g., intercorrelation matrices. The variables are represented as points in Euclidean space so that the rank order of the interpoint distances corresponds to the rank order of the intercorrelations. A nonmetric technique developed by L. Guttman and J. C. Lingoes, G-L SSA-1, was applied for analysis of the structure of the intercorrelation matrix of the CPI. 2 dimensions provided a good fit to the data. The space can be partitioned into several regions. The central region includes scales related to general adjustment. 3 peripheral regions include measures of "person orientation," "value orientation," and "self-orientation." Results correspond to those obtained in factor analytic studies, but the nonmetric solution is simpler and more parsimonious. Applications to prediction problems, scale construction, and formulation of research hypotheses are discussed. (18 ref.) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A new wave of behavior genetic modeling using covariance structure analysis

A number of useful methods for analyzing covariance structure have been proposed in the studies of human behavior genetics, reflecting the fact that the behavior genetic studies are one of the main origins of covariance structure model. In this paper, I review recent progress on methodology for behavior genetic studies of twins and families from the standpoint of the structural equation modeling. Especially, genetic ACE (additive genetic, common environment and random environment) model, multivariate ACE model, genetic factor analysis model and twin-parent model are focused upon. This review also discusses how to construct applied structural equation models which are useful for psychological research.     

A quasi-experimental approach to assessing treatment effects in the nonequivalent control group design.

Evaluates 4 statistical tests of treatment effect for the nonequivalent control group design. This design consists of pre- and posttreatment measures of a dependent variable with biased assignments to treatment groups. The biased assignment creates a treatment-pretest confounding for which different statistical techniques adjust. The different statistical tests discussed are the analysis of covariance, analysis of covariance with reliability correction, raw change score analysis, and standardized change score analysis. If assignment to treatment groups is based on the pretest score (a very infrequent event), analysis of covariance is the appropriate mode of analysis. Selection based on the pretest true scores necessitates a reliability correction procedure. Selection based on stable group differences and selection that occurs midway between the pre- and posttest necessitates change score analysis. (35 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Anterior cruciate ligament-plasty and high valgus tibial osteotomy as a combined procedure in anterior instability and varus deviation

Besides patients having an acute rupture of the ACL with a clear therapeutical strategy there are increasingly young patients with chronical anterior instability and degenerative arthritis of the medial compartment and varus malalignment. This constellation is taxing severely the operative procedure considering that there is not only the instability which has to be treated but that also an improvement of the arthritis symptomatology has to be achieved. In this paper we present a therapeutical concept of high tibial osteotomy combined with an arthroscopic assisted reconstruction of the ACL which is performed as a single procedure since the early 80-ies. The goal is to remove two severe arthrogenic factors correcting the instability and the pathological anatomical axis, to reduce the medial knee pain and to improve the use of the knee in life activities.     

A note on analysis of covariance.

S. H. Evans and E. J. Anastasio (see record 1968-09688-001) constructed 2 sets of hypothetical data to show ways in which the analysis of covariance can yield erroneous results. It is argued that analysis of covariance does not give incorrect results for either set of their data. Analysis of covariance correctly (within rounding error) recovered the form of the models used to construct their data and also provided accurate estimates of parameters for both sets of data. Although analysis of covariance produces accurate results, it must be used cautiously because it may or may not answer the substantive question a researcher asks. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An analysis of radiating pain at lumbar discography

Internal illiac and ovarian artery ligation was performed in 7 patients as a life saving measure (group I) and in 12 patients as a prophylactic procedure (group II) in 116 pelvic operations for gynaecological malignancy. The author presents own surgical technique for internal iliac and ovarian arteries ligation. The purpose of analysis was to identify a surgical complications after the ligation in the study groups. Surgical complications in the group of prophylactic ligation were statistically significant low. It is advisable to adopt this procedure as a routine in all difficult pelvic operations, particularly radical operations for gynaecological malignancy.     

Localization of brain electrical activity via linearly constrained minimum variance spatial filtering

A spatial filtering method for localizing sources of brain electrical activity from surface recordings is described and analyzed. The spatial filters are implemented as a weighted sum of the data recorded at different sites. The weights are chosen to minimize the filter output power subject to a linear constraint. The linear constraint forces the filter to pass brain electrical activity from a specified location, while the power minimization attenuates activity originating at other locations. The estimated output power as a function of location is normalized by the estimated noise power as a function of location to obtain a neural activity index map. Locations of source activity correspond to maxima in the neural activity index map. The method does not require any prior assumptions about the number of active sources of their geometry because it exploits the spatial covariance of the source electrical activity. This paper presents a development and analysis of the method and explores its sensitivity to deviations between actual and assumed data models. The effect on the algorithm of covariance matrix estimation, correlation between sources, and choice of reference is discussed. Simulated and measured data is used to illustrate the efficacy of the approach.