Showing papers on "Bonferroni correction published in 1996"

Adjusting for multiple testing when reporting research results: the Bonferroni vs Holm methods.

Abstract: Public health researchers are sometimes required to make adjustments for multiple testing in reporting their results, which reduces the apparent significance of effects and thus reduces statistical power. The Bonferroni procedure is the most widely recommended way of doing this, but another procedure, that of Holm, is uniformly better. Researchers may have neglected Holm's procedure because it has been framed in terms of hypothesis test rejection rather than in terms of P values. An adjustment to P values based on Holm's method is presented in order to promote the method's use in public health research.

Bonferroni-type inequalities with applications

Abstract: Contents: Introduction.- The method of polynomials.- The Geometric method.- The linear programming method.- Multivariate Bonferroni-type inequalities.- Classical problems of probability and applications in combinatorics.- Applications in number theory.- Statistical applications.- Extreme value theory.- Miscellaneous topics.

Is the Simes improved Bonferroni procedure conservative

Abstract: SUMMARY Simes (1986) proposed a modified Bonferroni procedure for conducting multiple tests of significance. He proved that, when the n test statistics are independent, his procedure has exact size a. Already Hommel (1983) had considered a similar procedure and shown that it need not be conservative. He gave an attainable upper bound for its anticonservativeness. Here we show that, for one-sided tests based on positively correlated bivariate normal test statistics, the procedure is conservative, and for negatively correlated such variables it is anticonservative. Two-sided tests based on bivariate normal variables are always conservative. Some numerical values are given, which show that for all practical purposes the nominal a-value can be used.

Control of familywise errors in multiple endpoint assessments via stepwise permutation tests.

Abstract: We describe permutation based sequentially rejective multiple comparison procedures useful in multiple endpoint assessments. We used Monte Carlo methods to compare the power of these newly devised tests to that of tests due to Holm and Rom as well as to the classical Bonferroni method. We illustrate applications of the methods with analysis of visual field data collected from optic neuritis patients. We conclude that the new methods are particularly useful when there are many endpoints involved, the data are significantly correlated, and/or the distributional assumptions are questionable.

A Path Length Inequality for the Multivariate-t Distribution, with Applications to Multiple Comparisons

Abstract: This article presents a new inequality for the multivariate-t distribution, which implies a new method for multiple comparisons whose foundation rests on a recent inequality due to Naiman. The new method is promising in view of the fact that it utilizes information (estimator intercorrelations) ignored by the most widely used multiple comparison methods yet is not computationally prohibitive, requiring only the numerical evaluation of a single one-dimensional integral. In this article the validity of the new method in the normal-theoretic general linear model is established, and efficiency studies relative to the methods of Scheffe, Bonferroni, Sidak, and Hunter-Worsley are presented. The new method is shown to always improve on Scheffe's method. The new method is also shown to perform well; that is, to lead to a smaller critical point than its competitors, with low degrees of freedom. But the method is not as efficient as the Hunter-Worsley method for high degrees of freedom. In addition, the me...

Interaction contrasts in repeated measures designs.

Abstract: Specific information concerning the nature of interaction effects in factorial designs may be obtained through the use of tetrad contrasts. Empirical familywise Type I error rates and power rates associated with 10 procedures for conducting tetrad contrasts in groups-by-trials repeated measures designs were obtained when the assumptions of multisample sphericity and multivariate normality were not satisfied. Only three procedures provided acceptable control of familywise Type I error rates under the assumption violation conditions. These procedures relied on a test statistic formed using an estimate of the standard error of the contrast which was based on only that data used in defining the contrast, in combination with either a Studentized maximum modulus, Hochberg (1988) step-up Bonferroni, or Shaffer (1986) modified sequentially rejective Bonferroni critical value. Minimal power differences between these three procedures were observed.

18 Multiple comparisons

Abstract: Publisher Summary This chapter discusses the basic concepts of multiple comparisons. It presents several methods for constructing multiple testing procedures along with the p-value based procedures, which are modifications of the simple Bonferroni procedure. A multiple comparison procedure (MCP) is a statistical procedure for making all or selected inferences from a given family while controlling or adjusting for the increased incidence of type I errors because of multiplicity of inferences. Reporting p-values for individual hypotheses is a standard practice. These p-values may be obtained by using different tests for different hypotheses. The Bonferroni procedure is the simplest MCP. The Bonferroni procedure is a completely general procedure requiring no assumptions concerning the joint distribution or the correlations among the test statistics. The chapter discusses the problem of multiple endpoints along with several miscellaneous problems associated with multiple comparisons.

Power evaluation of various modified Bonferroni procedures by a Monte Carlo study.

Abstract: Various modified Bonferroni procedures (MBPs) have been proposed in order to improve the power of the classical Bonferroni procedure (CBP). In the present paper, powers of these MBPs are investigated by a Monte Carlo study for pairwise comparisons. It is shown that they can be remark-ably more powerful than the CBP and Tukey's procedure with respect to all-pairs power, whereas all these procedures with respect to any-pair power are almost the same. Therefore, we recommend the use of MBPs rather than the CBP or Tukey's procedure. Shaffer's procedure sometimes shows higher power than other MBPs and would be the best choice for pairwise comparisons.

Controversies in the Genetic Analysis of Hypertensive Diseases

Abstract: In this issue of Hypertension , an article appears that involved considerable discussion among the reviewers, editors, and statistical consultants.1 . The article reports an association between the transforming growth factor-β1 gene and hypertension. The contentious issues result from a meaningful academic statistical argument. If multiple genetic loci are investigated for possible association with a phenotype without an a priori hypothesis, should a correction for repeated comparisons (a la Bonferroni) be carried out? If so, what is …

Classification of non-stationary random signals using multiple hypotheses testing

Abstract: In this paper we introduce a new time-frequency based method for classifying non-stationary random signals. The method involves dividing the signal into overlapping or nonoverlapping segments considered to be subpopulations of the entire population. From each sub-population we calculate a test statistic which can be used to construct a single hypothesis test. To control the global type-I error it is necessary to consider the hypotheses from all subpopulations simultaneously. We use the generalised sequentially rejective Bonferroni multiple hypothesis test which provides an efficient method to simultaneously test multiple hypotheses while maintaining the global type-1 error. Finally, we show the results of classifying time-dependent AR(1) processes which have identical expected instantaneous power and power spectral densities but different time-frequency representations.

False-positive error rates in routine application of repeated measurements ANOVA.

Abstract: Failure to recognize the serious implications of heterogeneous correlations and disregard of the multiple test problem in interpreting the results from repeated measurements ANOVA of any single primary outcome measure can produce false-positive error rates that are more than five times the alpha level that is reported. Alternative analyses that do not depend on the symmetry assumption, together with a Bonferroni correction of the multiple tests of significance that are routinely accomplished by the repeated measurements ANOVA, appropriately control the probability of statistical support for a false-positive claim. The magnitudes of error inflation and appropriate procedures for error control are examined in this article using simulated clinical trials data.

Multivariate bonferroni-type lower bounds

Abstract: We derive multivariate Sobel-Uppuluri-Galambos-type lower bounds for the probability that at least a, and at least a2, and for the probability that exactly a, and a2, out of n and N events, occur. The lower bound presented here reduces to a sharper bound than that of Galambos and Lee (1992). Our approach is by way of indicator functions and bivariate binomial moments. A new concept, marginal Bonferroni summation, is introduced in this paper.

Different methods to analyze clinical experiments with multiple endpoints: a comparison on real data

Abstract: In many clinical experiments multiple measurements are required for evaluation of the results. Several methods have been illustrated in the literature to deal with this problem. Some of these solve the problem of multiple testing bias just by looking at the significance of the most pronounced difference. On the other hand, some other methods are designed to take into account all the information available from an experiment. The purpose of this paper is to review these methods and compare the results they gave when applied to a clinical trial in which drug efficacy was assessed by 14 outcome measures.

Bonferroni inequalities and deviations of discrete distributions

Abstract: In the paper we first show how to convert a generalized Bonferroni-type inequality into an estimation for the generating function of the number of occurring events, then we give estimates for the deviation of two discrete probability distributions in terms of the maximum distance between their generating functions over the interval [0, 1].

Bonferroni inequalities and negative cycles in large complete signed graphs

Abstract: In this paper the problem of characterizing extremal graphs K n relatively to the number of negative p- cycles, when the number of negative edges is fixed, is solved for large n. This number can be expressed as an alternating sum for which the Bonferroni inequalities hold. Finally, the asymptotic value of the probability that a p- cycle of K n is negative is found as n →∞, if the negative edges induce a subgraph the components of which are paths or cycles.

Non-stationary Gaussian signal classification

Abstract: We present a new non-stationary signal classification algorithm based on a time-frequency distribution and multiple hypothesis testing. The time-frequency distribution is used to construct a time-dependent quadratic discriminant function. At selected points in time we evaluate the discriminant function and form a set of statistics which are used to test multiple hypotheses. We show that the statistics are linear combinations of chi square random variables with constant coefficients and hence are not normally distributed. The multiple hypotheses are treated simultaneously using the generalised sequentially rejective Bonferroni test to control the probability of incorrect classification of one class.

The generalised sequentially rejective Bonferroni test applied to non-stationary, random signal classification

Abstract: We present a new non-stationary signal classification algorithm based on a time-frequency distribution and multiple hypothesis testing. The time-frequency distribution is used to construct a time-dependent quadratic discriminant function. At selected points in time we evaluate the discriminant function and form a set of statistics which are used to test multiple hypotheses. We show that the statistics are a linear combinations of chi square random variables with constant coefficients and hence are not normally distributed. The multiple hypotheses are treated simultaneously using the generalised sequentially rejective Bonferroni test to control the probability of incorrect classification of one class. Finally, we show the results of classifying time-varying AR(1) processes which have identical expected instantaneous power and power spectral densities but different time-frequency representations.

Some Remarks on Multivariate Multiple Tests

Abstract: The aim of this paper is show how to apply the fundamental theorem for closed test procedures to linear hypothesis about regression coefficients. We compared the closed test procedures to classical Bonferroni and Scheffe procedures. We show some ideas of constructing test procedures which control the multiple level α.

Optimal bivariate bonferroni-type inequalities via taking average

Abstract: Let $A_1, A_2, \cdots, A_m$ be a sequence of events on a given probability space and let $X_m(A)$ be the number of those A's which occur.

A Tighter Upper Bound for System Unavailability

Abstract: It is shown that with a very small computational overhead the error interval between the first two Bonferroni inequalities can be reduced, thus allowing for very much simpler approximate analysis of mincut-based fault trees in many cases than by Hunter’s tighter upper bound.