Conventional F-test Research Articles

Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects

ABSTRACTThis article examines the use of ranked set sampling (RSS) with cluster randomized designs (CRDs), for potential improvement in estimation and detection of treatment or intervention effects. Outcome data in cluster randomized studies typically have nested structures, where hierarchical linear models (HLMs) become a natural choice for data analysis. However, nearly all theoretical developments in RSS to date are within the structure of one-level models. Thus, implementation of RSS at one or more levels of an HLM will require development of new theory and methods. Under RSS-structured CRDs developed to incorporate RSS at different levels, a nonparametric estimator of the treatment effect is proposed; and its theoretical properties are studied under a general HLM that has almost no distributional assumptions. We formally quantify the magnitude of the improvement from using RSS over SRS (simple random sampling), investigate the relationship between design parameters and relative efficiency, and establish connections with one-level RSS under completely balanced CRDs, as well as studying the impact of clustering and imperfect ranking. Further, based on the proposed RSS estimator, a new test is constructed to detect treatment effects, which is distribution-free and easy to use. Simulation studies confirm that in general, the proposed test is more powerful than the conventional F-test for the original CRDs, especially for small or medium effect sizes. Two empirical studies, one using data from educational research (i.e., the motivating application) and the other using human dental data, show that our methods work well in real-world settings and our theory provides useful predictions at the stage of experimental design, and that substantial gains may be obtained from using RSS at either level. Supplementary materials for this article are available online.

ON SIZE AND POWER OF HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS

Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and autocorrelation robust tests. Using these results we show that nonparametrically as well as parametrically corrected F-type tests in time series regression models with stationary disturbances have either size equal to one or nuisance-infimal power equal to zero under very weak assumptions on the covariance model and under generic conditions on the design matrix. In addition we suggest an adjustment procedure based on artificial regressors. This adjustment resolves the problem in many cases in that the so-adjusted tests do not suffer from size distortions. At the same time their power function is bounded away from zero. As a second application we discuss the case of heteroskedastic disturbances.

Generalized [formula omitted] test for high dimensional linear regression coefficients

To test the regression coefficients of linear models, the conventional F-test has been suggested. This paper investigates the performance of the generalized F-test for testing regression coefficients in high dimensional linear regression under the case of p/n⟶ρ(0<ρ<1). The asymptotic normality of generalized F-statistic is obtained under some regular conditions, and then the power of the F-test is derived. Some comparisons and an illustrated example are also presented.

Analysis of Variance in Neuroreceptor Ligand Imaging Studies

Radioligand positron emission tomography (PET) with dual scan paradigms can provide valuable insight into changes in synaptic neurotransmitter concentration due to experimental manipulation. The residual t-test has been utilized to improve the sensitivity of the t-test in PET studies. However, no further development of statistical tests using residuals has been proposed so far to be applied in cases when there are more than two conditions. Here, we propose the residual f-test, a one-way analysis of variance (ANOVA), and examine its feasibility using simulated [11C]raclopride PET data. We also re-visit data from our previously published [11C]raclopride PET study, in which 10 individuals underwent three PET scans under different conditions. We found that the residual f-test is superior in terms of sensitivity than the conventional f-test while still controlling for type 1 error. The test will therefore allow us to reliably test hypotheses in the smaller sample sizes often used in explorative PET studies.

Tests for High-Dimensional Regression Coefficients With Factorial Designs

We propose simultaneous tests for coefficients in high-dimensional linear regression models with factorial designs. The proposed tests are designed for the “large p, small n” situations where the conventional F-test is no longer applicable. We derive the asymptotic distribution of the proposed test statistic under the high-dimensional null hypothesis and various scenarios of the alternatives, which allow power evaluations. We also evaluate the power of the F-test for models of moderate dimension. The proposed tests are employed to analyze a microarray data on Yorkshire Gilts to find significant gene ontology terms which are significantly associated with the thyroid hormone after accounting for the designs of the experiment.

A New Test for Large Dimensional Regression Coefficients

In the article, hypothesis test for coefficients in high dimensional regression models is considered. I develop simultaneous test statistic for the hypothesis test in both linear and partial linear models. The derived test is designed for growing p and fixed n where the conventional F-test is no longer appropriate. The asymptotic distribution of the proposed test statistic under the null hypothesis is obtained.

Measuring Parallelism, Linearity, and Relative Potency in Bioassay and Immunoassay Data

ABSTRACT There is often a need to determine parallelism or linearity between pairs of dose–response data sets for various biological applications. This article describes a technique based on a modification of the well-known extra-sum-of-squares principle of statistical regression. The standard extra-sum-of-squares method uses an F-distributed ratio as a statistic and an F-test based on this statistic as the parallelism test. It is shown here that this metric does not directly measure the parallelism between the two curves and can often vary in opposition to actual parallelism. To overcome this problem, a metric based on a chi-square test applied directly on the chi-square–distributed extra-sum-of-squares statistic is developed, which is shown to correspond directly to parallelism. This parallelism metric does not suffer from the shortcomings of the conventional F-test–based metric, and is a more reliable and appropriate measure of parallelism. The article also shows that the choice of curve model has a large effect on the sensitivity of either metric, and that using an asymmetric model, such as the asymmetric five-parameter logistic function, a generalization of the commonly used symmetric four-parameter logistic function, is necessary when working with asymmetric dose–response data. The effect of noise, as well as the importance of correct weighting on the parallelism metrics and the relative potency, is also studied.

The government revenue and government expenditure nexus: empirical evidence from nine Asian countries

The nexus between government revenue and government expenditure has been an important topic in public economics. In this paper, we investigate evidence for cointegration and causality between government revenue and government expenditure for nine Asian countries. We use the recently developed bounds testing approach to cointegration and the conventional F-test to examine Granger causality. Our empirical results suggest that for three out of the nine countries government revenue and government expenditure are cointegrated. Our results on the direction of causation are mixed: (a) for Indonesia, Singapore, Sri Lanka in the short-run and for Nepal in both the short- and long-run we find support for the tax-and-spend hypothesis; (b) Indonesia and Sri Lanka are in conformity with the spend-and-tax hypothesis in the long-run; and (c) for other countries there is evidence of neutrality.

Uniformity test of bias when the reference value contains experimental error.

The uniformity test of biases for analytical methods must address uncertainties in the reference method. If the uncertainty associated with the estimates of true values is significant but ignored in the test of bias equality, the type I error can exceed the prespecified error rate. In general, when biases at each concentration level are confounded with a random component (confounding bias), the usual test of bias equality tests the uniformity of the combined bias, rather than the uniformity of fixed bias-the bias without the random component. Based on a confounding model that takes both the fixed and the confounding biases into account, the actual type I error rate of the uniformity test can be calculated. To eliminate the impact of confounding bias on the uniformity test of fixed biases, a new F'-test is proposed. The new F'-test is simply adding a correction factor to the conventional F-test. The correction factor is directly related to the uncertainty associated with the estimates of true values. A simulation study is conducted to show that the proposed test can bring the type I error rate down to the prespecified level. Data from two aldehyde methods are used to demonstrate how the proposed F'-test works. Recommendations on optimal sample allocation are also provided.

Exact and Approximate Tests for Unbalanced Random Effects Designs

SUMMARY In the three stage nested design with random effects, let ?A2 be the variance of factor A (the top stage). It is often desirable to test the hypothesis HA: GA2 = 0. In the unbalanced case, the conventional F-test for HA does not in general have the expected null distribution, and the expected mean squares are not in general equal under HA . Tietjen and Moore [1968] proposed that a Satterthwaite-like procedur-e be used to construct a denominator (and D.F.) which would have, under HA , the same expected mean square as the numerator. It was pointed out by W. H. Kruskal, however, that such a procedure had no justification since the mean squares were not independent and did not have chi-square distributions. This paper is an attempt to revisit the question by investigatiing the properties of this approximation and those of the conventional F-test. It is shown that the conventional F-test does considerably better as an approximation under imbalance than does the Satterthwaite test.

Individual Degrees of Freedom for Testing Homogeneity of Regression Coefficients in a One-Way Analysis of Covariance

Homogeneity of the withini-treatment riegression coefficients is a necessary condition for the validity of the adjustments made to the treatment means in a one-way analysis of covariance These adjustments require that the within-treatment regression functions differ only with respect to their intercepts, or zero degree terms, and comparisons among adjusted treatment means are then in effect comparisons among the intercepts When the treatments and the factor represented by the covariate interact in producing their effect, heterogeneity of regression coefficients results and the treatment effects adjusted in the usual manner no longer estimate the true effects. The assumption of linear regressions within treatments, which is implicit in any test of homogeneity of linear regressions, limits the type of interaction which can occur between treatment and covariate. In this case the null hypothesis being tested is characterized by families of parallel straight lines, and the alternative interaction-hypotheses, against which a homogeneity test is designed to have power, are represented by families of intersecting but still linear regression lines. The power of the conventional F-test of homogeneity is then an increasing function of the weighted variance among the slopes of these intersecting straight lines, E wi(f,i ,)2, where the weighting coefficients w; are determined by the levels of the covariate used in the experiment. Under some circumstances it seems reasonable to restrict the class of alternative hypotheses even further by imposing some regularity condition on the families of intersecting straight lines, and then to modify the structure of the homogeneity test so as to increase the power against this restricted class of alternatives. For example, in situations where the dependent variable is logically zero at the zero-level of the