General Linear Test Research Articles

The relationship of cataract maturity to intraocular pressure in dogs.

To determine the distribution of intraocular pressure, as measured by applanation tonometry, in dogs with cataracts, and compare these tonometric results to the different stages of cataract formation (incipient, immature, mature, and hypermature). Animals studied Retrospection study of canine clinical patients (86 dogs). All records of dogs presented from 1991 to 1996 to the university veterinary medical teaching hospital for diagnosis of cataracts and evaluation for cataract surgery were reviewed. The tonometric measurements from the initial ophthalmic examination were selected in cataractous and nonglaucomatous eyes either receiving no topical or no systemic medications. The stage of cataracts was based on the degree of opacification, tapetal reflection, clinical vision, and visibility of the ocular fundus by indirect ophthalmoscopy. The distribution of tonometric results were grouped by the cataract maturity, and compared by anova and Tukey's general linear tests. Intraocular pressure with incipient cataracts ranged from 9 to 17 mmHg (mean 12.7 +/- 1.2 mmHg). Intraocular pressure with immature cataracts ranged from 3 to 27 mmHg (mean 13.6 +/- 0.6 mmHg). For the mature cataracts, IOP ranged from 5 to 22 mmHg (mean 11.9 +/- 0.7 mmHg). For the hypermature cataract group, IOP ranged from 4 to 23 mmHg (mean 10.8 +/- 0.6 mmHg). Comparison of the tonometric results among the different stages of cataract formation indicated a significant difference (P = 0.0086) between only the immature and hypermature groups. Intraocular pressure in lens-induced uveitis (LIU) is lowered but the relationship to the stage of cataract maturity is less clear. Significant tonometric differences were present between the immature and hypermature cataract groups, but these differences are too small to be clinically useful. Decreased intraocular pressure of dogs with all stages of cataract formation suggests concurrent LIU during all stages of cataract formation, especially with the mature and hypermature stages. The average tonometric measurements in dogs with these cataracts were about two standard deviations below the mean IOP reported in normal dogs.

Predictors of Condom Use Among African American Males at High Risk for HIV1

This study compared the influence of HIV risk behaviors and condom use attitudes on condom use among heterosexual African American males. Three models were tested: (a) HIV risk, (b) condom use attitudes, and (c) a model combining the previous two. Brief street intercept interviews were administered to African American males in 2 matched pairs of census tracts. Results are based on 589 males reporting vaginal sex in the last 30 days. The General Linear Test (GLT) was used to test the ability of regression models to reduce error variance. The condom use, attitude model was sufficient to predict frequency of condom use regardless of partner type. The strongest predictors of condom use were condom use enjoyment, social norms, self‐efficacy, and social influence.

Bootstrapping the general linear hypothesis test

We discuss the use of bootstrap methodology in hypothesis testing, focusing on the classical F-test for linear hypotheses in the linear model. A modification of the F-statistics which allows for resampling under the null hypothesis is proposed. This approach is specifically considered in the one-way analysis of variance model. A simulation study illustrating the behaviour of our proposal is presented.

Leverage Plots for General Linear Hypotheses

Abstract Leverage plots are a generalization of partial-regression leverage plots, extending the idea to apply to general linear hypothesis tests. Leverage plots can show the point-by-point composition of the sum of squares for a hypothesis test. They are valuable in revealing the degree of fit, the parameter estimates, the residuals, a measure of the variance of the fit, influential points, nonfitting points, nonlinearities, and even collinearity.

Review of methods and criteria for the evaluation of bioequivalence studies

Guidelines for the performance and analysis of bioequivalence studies are not very specific. The advantages and disadvantages of the following methods and tests are discussed: analysis of variance by summation or by use of general linear models, nonparametric procedures, aposteriori probabilities and tests on the normality of residuals and on the variability of the results. Arguments for or against an analysis of data after logarithmic transformation versus analysis of untransformed data are presented. If the confidence intervals lie within certain limits, preparations may be considered equivalent. The criteria leading to those limits are discussed. It is recommended that concentration-dependent data of bioequivalence studies be evaluated by analysis of variance after logarithmic transformation, applying general linear models. Data that by theoretical reasons cannot be normally or log-normally distributed should be analysed by nonparametric methods. Otherwise these methods can only be recommended if a significant deviation from normality has been noted and only for two-way cross-over designs. For a geometric evaluation (after logarithmic transformation) the regions of acceptance should be symmetrical in the logarithm, e.g. (80%, 125%).

An empirical study of the type I error rate and power for some selected normal-theory and nonparametric tests of the independence of two sets of variables

Normal-theory tests of the hypothesis of no relationship among two sets of variables require assumptions of independence, hamoscedasticity, and normality. If, however, the assumption of normality is not tenable, there are few guidelines for properly using these tests. Historically, the lack of a comprehensive hypothesis-testing framework in the nonparametric case has provided few alternatives to normal-theory procedures. Fortunately, this situation has changed with the introduction of nonparametric, general linear model-based tests that can be used with existing computing packages. Multivariate-nonparametric tests due to Puri and Sen (1969, 1971, 1985) and Conover and Iman (1981) are outlined, and the results of a simulation study of the performance of three nonparametric and one normal-theory test of the hypothesis of no relationship among two sets of variables are presented. These results suggest that multivariate-nonparametric tests should be considered for a variety of data conditions. especially heav...

Deformation analyses of Florida highway subgrade sand subjected to repeated load triaxial tests: Pumphrey, N D; Lentz, R W Trans Res RecN1089, 1986, P49–56

Laboratory repeated load triaxial tests are conducted to estimate the effects of highway traffic on the permanent and resilient deformation of a subgrade sand commonly used as a foundation for a flexible highway pavement structure in Florida. Combinations of confining stress and cyclic principal stress difference (test variables) and of dry unit weight and moisture content (sample variables) are used for each sample and loaded to 10,000 cycles. Confining stress, cyclic principal stress difference, and dry unit weight are correlated with permanent strain and resilient modulus and thus affect deformation properties of these soils. However, moisture content correlates with neither permanent strain nor resilient modulus. Static tests are conducted on various samples similar to those used in the cyclic tests. These results are used to normalize cyclic stress and strain at 10,000 cycles. A regression model is developed for predicting cyclic strain in the sand from satic tests by using a technique previously developed by Lenz. The model is compared to one for Michigan highway subgrade sand. Using a general linear test at a level of significance of 0.05, it is found that the data sets from each sand cannot be pooled to form one reression model. Values of resilient modulus after 10,000 loading cycles for the Florida sand ranged from 16,000 psi (110 240 kPa) at 5 psi (34.5 kPa) confining stress to 56,000 psi (385 840 kPa) at 50 psi (344.5 kPa) confining stress.

Practical methods for computing power in testing the multivariate general linear hypothesis

Four test statistics are commonly used in multivariate general linear hypothesis tests such as MANOVA: Roy's largest root, Wilks' Lambda, Hotelling-Lawley trace and Pillai-Bartlett trace. Closed form, finite series expressions do not exist for the distribution functions in either the null or non-null case (except for special cases). In practice, asymptotic approximations, based on F or chi square distributions, are used for the null case. It is not widely known that similarly accurate and general approximations have been published for the non-null case, for all except the largest root [15,38]. In this paper new approximations, based on noncentral F's, are provided for power for all but the largest root. These generalize existing F approximations for the central case. Much less calculation is needed than for earlier approximations and accuracy appears not to suffer in practice. An upper bound F approximation is provided for the largest root power. Power calculation can be used to help choose a test statistic as well as for experimental design. A particularly convenient method for estimating power, using standard linear models programs [20], is generalized to the multivariate case.

Model determination for use in automated control of drug dosages: application to d-tubocurarine.

To implement a feedback control system to achieve satisfactory muscle relaxation during surgical procedures, a mathematical formalism, based on linear compartmental theory, is derived to model the input/output response between the dosage of a drug administered and its neuromuscular effect as measured by the train-of-four (T4) ratio twitch response. The effect (T4 ratio) is related directly to the dosage schedule, and no attempt is made to include the plasma concentration of the neuromuscular blocking drug in the formalism. The neuromuscular blocking data of 24 patients, in whom the muscle relaxant d-tubocurarine (curare) was used, were fitted using a nonlinear least-squares data fitting routine. The number of compartments necessary to fit the data for each patient was determined using the general linear test. In all but three cases a biexponential model was sufficient to fit the data. Simulation studies also show that a biexponential model gives satisfactory control even for those patients for whom a triexponential model was necessary to fit the data. Further simulation shows that because of interindividual variation the application of adaptive control techniques will be needed.

Local comparison of linear rank tests, in the Bahadur sense

As continuation ofKremer [1979a] a theory of asymptotic comparison based on local Bahadur efficiency is derived for general linear rank tests of the one-sample symmetry problem and thek-sample problem (k≥2). The results are similar to former considerations based on Pitman efficiency but hold under weaker conditions on the scores-generating functions or local alternatives.

A Model for Use in Automated Control of Muscle Relaxation During Surgical Procedures

It is proposed to use an automatated feedback control system to solve the clinical problems associated with the achievement of muscle relaxation during surgical procedures. Due to the variability between individuals a 1 self-tuning' control system would" be required. This paper deals with the problems of determining a suitable model structure and model order for the human response to the muscle relaxant drug curare (or d-Tubocurarine) for use in such a self-tuning control loop. We present a formalism based on linear compartmental theory, and show by examining its structural identiflability how it can be commpared with existing clinical models. We then use off-line non-linear least-squares fitting and the general linear test to obtain a simple bi-compartment model structure, which we show by simulation to be suitable for control purposes and an improvement over existing models.

A Note on the Multivariate General Linear Test

Abstract The general linear test approach for testing hypotheses concerning parameters of a full-rank multivariate regression model is often not sufficiently discussed in applied multivariate analysis textbooks. This note makes mention of this approach and suggests that major emphasis of this topic in an applied multivariate analysis course provides students with a unifying structure for the analysis of statistical models.

A Note on the Multivariate General Linear Test

A Note on the Multivariate General Linear Test

Sequential Tests in Industrial Statistics

Summary After an introductory and an historical note, an elementary problem of simple qualitative inspection of a box of components is treated by using a “lattice diagram representation.” This leads to the consideration of sequential tests for such cases. Procedures for determining “Target-Handicap” forms of inspection, and their operating and sample size properties are given. This leads to a consideration of general linear sequential tests, which are those test procedures which can be formulated in terms of a “score.” Such procedures are shown to be similar to classical games of chance, and to physical diffusion processes. The diffusion analogy leads to a differential equation which gives the approximate characteristics of any such linear test. In many cases, Wald’s “Probability Ratio Sequential Test” takes the form of a linear test. The conditions for this are determined. The P.R.S. test is seen to be “best possible linear test,” in the sense of minimizing average sample size. The effects of deviations from normality, and general distributions are considered. Reference is made to Wald’s work on tests which involve parameters other than those being estimated, and then consideration is restricted to tests for the mean of normal populations where the variance is unknown. Methods of reducing such tests to simple binomial tests are indicated. A number of procedures for use with 2 × 2 comparative trials, and double dichotomies, are given, and their properties discussed. Returning to general inspection problems, the paper indicates that these are not always to be identified with problems involving merely tests of statistical hypotheses. The notions of Consumer’s Lot, Producer’s Batch, the Lot Quality Curve, the Process Curve, are explained, and their importance indicated. A distinction is made between Acceptance Inspection schemes and Rectifying Inspection schemes, and the notions of Operating Characteristic Curve, Operating Characteristic Matrix, and the Sample Size distribution function are explained. The lattice diagram is used to bring out relationships between notions involved in general inspection, and some other uses are also indicated. Finally, some reflections on the relevance of the matters discussed to matters of current debate among statisticians are given.