Showing papers on "Bonferroni correction published in 1995"

Inference in models with nearly integrated regressors

Abstract: This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step procedures, with first stages that consistently classify x as I(1) or I(0), exhibit large size distortions when regressors have local-to-unit roots, because of asymptotic dependence on a nuisance parameter that cannot be estimated consistently. Several alternative procedures, based on Bonferroni and Scheffe methods, are therefore proposed and investigated. For many parameter values, the power loss from using these conservative tests is small.

Power and Type I Error Rates of New Pairwise Multiple Comparison Procedures Under Heterogeneous Variances

Abstract: The Type I error rates and statistical power of 9 selected multiple comparison procedures were compared in a Monte Carlo study. Data were generated for 3-, 4-, and 5-group ANOVA models, from simulated populations with both homogeneous and heterogeneous variances. A variety of patterns of population means were examined, including completely null, partial-null, and multiple-null patterns. None of the procedures was robust to violations of the assumption of variance homogeneity at nominal alpha levels lower than .10, even with equal sample sizes. The Dunn procedure and modified Bonferroni procedures showed better robustness properties than the Tukey procedure and recent modifications of it did. Power comparisons, conducted at a nominal alpha level of .10, showed the Peritz, Ryan, and Fisher-Hayter tests to be consistently most powerful across the variance conditions examined. However, power differences among these three procedures were minimal.

The Use of an Overall F Test to Control Type I Error Rates in Factorial Analyses of Variance: Limitations and Better Strategies

Abstract: The inflation of Type I error rates caused by the testing of multiple null hypotheses in factorial analyses of variance (ANOVAs) is a problem that is often not recognized in the behavioral sciences. Fletcher, Daw, and Young (1989) described the problem and conducted a limited simulation study to investigate the effectiveness of two strategies to correct the problem: use of an overall F test and use of a Bonferroni adjustment. Unfortunately, two limitations in the design of their simulation led these authors to conclusions about the overall F test that do not hold under all conditions. The present study was designed to overcome these limitations and to provide a more complete evaluation of such strategies. Our results indicated that the overall F test is effective only when all effects in the ANOVA are null. In contrast, the Bonferroni adjustment and recent modifications of the procedure control the Type I error rate regardless of the number of true null hypotheses in the ANOVA.

A full heteroscedastic one-way error components model for incomplete panel: maximum likelihood estimation and Lagrange multiplier testing

Abstract: In this paper, we study maximum likelihood estimation and Lagrange multiplier testing of a one-way error components regression model suitable for incomplete panel and including parametrically specified variance functions for both individual-specific and general error disturbances. All the required ingredients for obtaining the ML estimates are provided. We also derive two Lagrange multiplier test statistics (based on OLS residuals) for jointly testing the null of no individual effects and homoscedasticity. Further, we discuss a Bonferroni multiple comparison procedure intended for identifying the source(s) of departure from the joint null when it is rejected. The practical usefulness of the model and the testing procedures are illustrated by an empirical example in the production analysis field.

Factors Correlated with Adolescents' Use of Crack in Public Schools

Abstract: This study was undertaken to evaluate factors correlated with crack use by 479 adolescents in 1992 in Dade County, Florida public schools. Based upon self-reports, after application of the Bonferroni correction, only two variables were related to crack use, i.e., having friends who use crack and living alone.

Improved Bonferroni procedures for testing overall and pairwise homogeneity hypotheses

Abstract: Simes' (1986) improved Bonferroni test is verified by simulations ∗to control the α-level when testing the overall homogeneity hypothesis with all pairwise t statistics in a balanced parallel group design. Similarly, this result was found to hold (for practical purposes) in various underlying distributions other than the normal and in some unbalanced designs. To allow the use of step-up procedures based on pairwise t statistics, simulations were used to verify that Simes' test, when applied to testing multiple subset homogeneity hypotheses with pairwise t statistics also keeps the level ♣ α. Some robustness as above was found here too. Tables of the simulation results are provided and an example of a step-up Hommel-Shaffer type procedure with pairwise comparisons is given.

Detection of outliers in linear model when the regression parameters are stochastic

Abstract: Procedures for detection of outliers in linear model with stochastic regression parameters are given for mean-slippage and dispersion slippage outlier model. The distributions of the test statistics are derived and the values of significant probabilities are given using Bonferroni's bounds and Doornbos's bounds. Some simulation results are also presented.

Union-Intersection testing for outliers in multivariate normal data

Abstract: The union-intersection approach to multivariate test construction is used to develop an alternative to Wilks' likelihood ratio test statistic for testing for two or more outliers in multivariate normal data. It is shown that critical values of both statistics are poorly approximated by Bonferroni bounds. Simulated critical values are presented for both statistics for significance levels 1% and 5%, for sample sizes 10(5)30, 40, 50, 75 and 100 for 2, 3, 4 and 5 dimensions. A power comparison of the two tests in the slippage of the mean model for generating outliers indicates that the union-intersection test is the more powerful when the slippages are close to collinear. Although Wilks' test remains the preference for general use, the union-intersection test could be valuable when such special structure in the data is suspected.

A more practical scheffe-type multiple comparison procedure for commonly encountered numbers of comparisons

Abstract: Multiple comparison procedures are important tools used in the analysis and interpretation of linear combinations of means from several populations. These procedures are used for two different types of comparisons: 1) the comparisons of all possible pairs of means and 2) testing a set of “g” comparisons. The Scheffe procedure is one of several techniques available for multiple comparisons but is generally regarded as too conservative for most practical analyses. Some authors have suggested ad hoc adjustments to the significance level to overcome the conservative nature of the Scheffe method. A heuristic approach is proposed to achieve the same objective which is quite satisfactory for commonly encountered numbers of comparisons Simulations clearly indicate that the modification of the Scheffe test is always superior to the unmodi-fied Scheffe and has acceptable experimentwise error rates and more power than the Bonferroni test for the investigation of a moderate number of comparisons.