Jinadasa K. Gamage

Generalized p -values and generalized confidence regions for the multivariate Behrens-Fisher problem and MANOVA

For two multivariate normal populations with unequal covariance matrices, a procedure is developed for testing the equality of the mean vectors based on the concept of generalized p-values. The generalized p-values we have developed are functions of the sufficient statistics. The computation of the generalized p-values is discussed and illustrated with an example. Numerical results show that one of our generalized p-value test has a type I error probability not exceeding the nominal level. A formula involving only a finite number of chi-square random variables is provided for computing this generalized p-value. The formula is useful in a Bayesian solution as well. The problem of constructing a confidence region for the difference between the mean vectors is also addressed using the concept of generalized confidence regions. Finally, using the generalized p-value approach, a solution is developed for the heteroscedastic MANOVA problem.

Size performance of some tests in one-way anova

Tsui and Weerahandi (1989) introduced the notion of generalized p-values and since then this idea is used to solve many statistical testing problems. Heteroskedasticity is one of the major practical problems encountered in ANOVA problems. To compare the means of several groups under heteroskedasticity approximate tests are used in the literature. Weerahandi (1995a) introduced a test using the notion of generalized p-values for comparing the means of several populations when the variances are not equal. This test is referred to as a generalized F-test. In this paper we compare the size performance of the Generalized F-test and four other widely used procedures: the Classical F-test for ANOVA, the F-test obtained by the weighted least-squares to adjust for heteroskedasticity, the Brown-Forsythe-test, and the Welch-test. The comparison is based on a simulation study of size performance of tests applied to the balanced one-way model. The intended level of the tests is set at 0.05. While the Generalized F-test...

Using MRI for assessing velopharyngeal structures and function.

Objective Direct visualization of the velopharynx and, in particular, the levator muscle is particularly important in the assessment of velopharyngeal function and normal speech production. The purpose of this study is to demonstrate the development of a static and dynamic magnetic resonance imaging protocol for evaluation of velopharyngeal structures and function. Methods A high-resolution, T2-weighted turbo-spin-echo three-dimensional anatomical scan (sampling perfection with application optimized contrasts using different flip angle evolution) was used to acquire a large field of view covering the velopharyngeal anatomy. Dynamic speech assessment was obtained using a fast-gradient echo, fast low-angle shot, multi-shot spiral technique to acquire 15.8 frames per second (FPS) of the sagittal and oblique coronal image planes. Results Using a three-dimensional data set, as opposed to two-dimensional data, the full contour of the levator muscle can be appreciated. Dynamic images were obtained at 15.8 FPS in the sagittal and oblique coronal planes, enabling visualization of the movements of the velum, posterior pharyngeal wall, lateral pharyngeal walls, and levator muscle during speech. Conclusions A three-dimensional magnetic resonance imaging sequence, such as that used in the present study, may provide better analyses and more precise measurements. A dynamic fast low-angle shot sequence allows for visualization of the levator muscle and the velum during speech at a high image rate. This protocol could have a significant impact in improving the process of visualizing pathology and promoting clinical treatment plans for individuals born with cleft lip and palate.

Anthropometric Analysis of the Velopharynx and Related Craniometric Dimensions in Three Adult Populations Using MRI

Objective The purpose of this study is to examine effects of sex, race, and craniometry among three distinct racial groups of adults with normal velopharyngeal anatomy and to determine whether craniofacial structures could be used to predict velopharyngeal structures. Methods A total of 88 adults across three racial groups including white, black, and Asian (Japanese) participated. Magnetic resonance images were obtained using a high-resolution, three-dimensional anatomical scan. Measurements were obtained on the levator veli palatini muscle, velum, and craniofacial structures. Results Head circumference was used as a covariate to control the effect of overall cranial size on the analyses. Palate height, linear cranial base, and face height and width vary based on sex, with men demonstrating larger values compared with women. Linear base values, cranial base angle, and face width vary significantly based on race, with Japanese subjects showing the smallest anterior to posterior measures and larger face-width values. Levator muscle measures, excluding angle measures, vary significantly (P < .0001) based on sex. There was no statistically significant difference (P > .05) among racial groups in the levator muscle measures. Velar length and thickness varied significantly based on race and sex. Conclusions This is the first study to examine the interaction of race and sex on levator muscle morphology. In spite of the differences in velar dimensions, no significant differences were found in muscle size, specifically the levator veli palatini, which is contained within the velum.

Sexual dimorphism of the levator veli palatini muscle: an imaging study.

Objective Magnetic resonance imaging studies of the levator veli palatini muscle have used small numbers of subjects and have not consistently controlled for sex, race, or age. The purpose of this study was to conduct a structural assessment using a large homogeneous sample to examine the sex differences in the levator muscle morphology. Methods Thirty white adult subjects (15 men and 15 women) were imaged using a 3 Tesla MRI system. A high-resolution SPACE (sampling perfection with application-optimized contrasts using different flip-angle evolution) sequence was used to acquire images of the velopharyngeal anatomy. Levator muscle measurements were obtained. Results Men displayed significantly greater levator extravelar segment length (P = .003), levator intravelar segment muscle length (P < .001), greater distance between levator insertion points (P < .001), and greater angles of origin (P = .008) compared with women. There was no statistically significant variation between men and women in the distance between points of origin at the base of the skull. Conclusions This study provides normative data to improve understanding of levator dysmorphology such as that in cleft palate muscle anatomy. Results of the study demonstrate significant differences between white men and women across several levator muscle measures. Variations in the relative size of the cranium or height of the individual were not proportionate to the variations observed in the levator muscle.

On steady state availability of a system with lognormal repair time

Assuming two-parameter lognormal distribution for repair times, statistical inference for the steady state availability of a system is considered. For the failure time distribution, weibull, gamma, and lognormal distributions were considered. Using the generalized p-value approach, we propose confidence intervals and exact tests for the steady state availability of a system. A couple of examples are given to illustrate the proposed procedures.

Generalized prediction intervals for BLUPs in mixed models

A prediction interval is derived for the BLUP (Best Linear Unbiased Predictor) in mixed models involving a single random effect of interest, using the generalized inference approach. The resulting prediction interval is referred to as a generalized prediction interval. The solution in the case of the simplest balanced random effects model is first derived to provide better insight into the approach. Extensions to the unbalanced case as well as to a general model are then provided. A simulation study is carried out to show the advantage of the proposed interval compared to the ML and REML based intervals available from widely used software packages such as SAS and R/S+. The estimated coverage probabilities show that the generalized prediction interval exhibits substantially better performance compared to ML and REML based intervals; the latter intervals were found to be highly conservative.

GENERALIZED P-VALUES AND THE MULTIVARIATE BEHRENS-FISHER PROBLEM

Abstract Tsui and Weerahandi (1989) defined generalized p-values for testing statistical hypothesis in the presence of nuisance parameters and applied to obtain an exact solution to the univariate Behrens-Fisher problem. Johnson and Weerahandi (1988) provided a Bayesian solution to the multivariate Behrens-Fisher problem. With the help of the Cauchy-Schwarz inequality we provide an upper bound for the generalized p-value for the multivariate case. Also we extend the result of Tsui and Weerahandi to present a second upper bound.

A general method of inference for two-parameter continuous distributions

Abstract This article presents a general method of inference of the parameters of a continuous distribution with two unknown parameters. Except in a few distributions such as the normal distribution, the classical approach fails in this context to provide accurate inferences with small samples.Therefore, by taking the generalized approach to inference (cf. Weerahandi, 1995), in this article we present a general method of inference to tackle practically useful two-parameter distributions such as the gamma distribution as well as distributions of theoretical interest such as the two-parameter uniform distribution. The proposed methods are exact in the sense that they are based on exact probability statements and exact expected values. The advantage of taking the generalized approach over the classical approximate inferences is shown via simulation studies. This article has the potential to motivate much needed further research in non normal regressions, multiparameter problems, and multivariate problems for which basically there are only large sample inferences available. The approach that we take should pave the way for researchers to solve a variety of non normal problems, including ANOVA and MANOVA problems, where even the Bayesian approach fails. In the context of testing of hypotheses, the proposed method provides a superior alternative to the classical generalized likelihood ratio method.