Showing papers on "Bonferroni correction published in 2002"

Interpretation of glass composition measurements: the effects of match criteria on discrimination capability.

Abstract: The concentrations of ten elements in 209 unrelated glass specimens received as evidence were used to assess the frequencies of errors of false association (Type II errors) using several comparison criteria at specified significance levels (Type I errors). Pairwise comparisons of the samples using either the equal-variance t-test or Welch's modification (unequal variances) result in a small number of errors of false association, even when adjusting the significance level (Bonferroni correction) for multivariate comparisons. At the 95% confidence level (overall Type I error of 0.05, or individual element comparison error of 0.005), only two Type II errors are made in 21736 comparisons (0.009%) when using the equal-variance t-test for comparison of sample means. In this study, the range overlap test using three replicate measurements per specimen results in no errors of false association. Most specimen pairs in this data set are readily discriminated either by differences in the concentrations of several elements or by an extremely large difference in the concentrations of one or more element.

The Effectiveness of Methods for Analyzing Multivariate Factorial Data

Abstract: A Monte Carlo simulation was used to examine the effectiveness of univariate analysis of variance (ANOVA), multivariate analysis of variance (MANOVA), and multiple indicator structural equation (MISE) modeling to analyze data from multivariate factorial designs. The MISE method yielded downwardly biased standard errors for the univariate parameter estimates in the small sample size conditions. In the large sample size data conditions, the MISE method outperformed MANOVA and ANOVA when the covariate accounted for variation in the dependent variable and variables were unreliable. With multivariate statistical tests, MANOVA outperformed the MISE method in the Type I error conditions and the MISE method outperformed MANOVA in the Type II error conditions. The Bonferroni methods were overly conservative in controlling Type I error rates for univariate tests, but a modified Bonferroni method had higher statistical power than the Bonferroni method. Both the Bonferroni and modified methods adequately controlled m...

Determining Hit Rate in Pattern Search

Abstract: The problem of spurious apparent patterns arising by chance is a fundamental one for pattern detection. Classical approaches, based on adjustments such as the Bonferroni procedure, are arguably not appropriate in a data mining context. Instead, methods based on the false discovery rate - the proportion of flagged patterns which do not represent an underlying reality - may be more relevant. We describe such procedures and illustrate their application on a marketing dataset.

Correction of the p-value after multiple tests in a Cox proportional hazard model.

Abstract: We consider a situation which is common in epidemiology, in which several transformations of an explanatory variable are tried in a Cox model and the most significant test is retained. The p-value should then be corrected to take account of the multiplicity of tests. Bonferroni method is often too conservative because the tests may be highly positively correlated. We propose an asymptotically exact correction of the p-value. The method uses the fact that the tests are asymptotically normal to compute numerically the distribution of the maximum of several tests. Counting processes theory is used to derive estimators of the correlations between tests. The method is illustrated by a simulation and an analysis of the relation between concentration of aluminum in drinking water and risk of dementia.

Many-to-one Comparisons in Stratified Designs

Abstract: CHEUNG and HOLLAND (1992) extended Dunnett's procedure for comparing all active treatments with a control simultaneously within each of r groups while maintaining the Type I error rate at some designated level a allowing different sample sizes for each of the group-treatment categories. This paper shows that exact percentage points can be easily calculated with current available statistical software (SAS). This procedure is compared to resampling techniques and a Bonferroni corrected Dunnett-with-in-group procedure by means of a simulation study.

Support Approximations Using Bonferroni-Type Inequalities

Abstract: The purpose of this paper is to examine the usability of Bonferroni-type combinatorial inequalities to estimation of support of itemsets as well as general Boolean expressions. Families of inequalities for various types of Boolean expressions are presented and evaluated experimentally.

A comprehensive method for genome scans

Abstract: In applications involving the use of genome scans the problem of correcting for multiple testing figures prominently. A frequently used approach is the Bonferroni adjustment, but this is known to be often severely conservative. As an alternative we use the method of importance sampling to accurately and efficiently obtain required exceedance probabilities. This method is comprehensive in the sense that it has application to exceedance probabilities for other classes of test statistics, such as those for linkage disequilibrium or Hardy-Weinberg equilibrium at multiple loci. We illustrate the importance sampling technique by focusing on affected sib pair tests done at a large number of fully informative markers. We demonstrate how our approach can be used to obtain exceedance probabilities for arbitrary marker spacings, and we compare our approach with that of Feingold et al. [1993], which uses the method of large deviations and does not provide the means for adjusting for unequal marker spacing.

Testing for candidate gene linkage disequilibrium using a dense array of single nucleotide polymorphisms in case-parents studies.

Abstract: The future of genetic studies of complex human diseases will rely more and more on the epidemiologic association paradigm, in particular the use of the transmission/disequilibrium test to detect linkage disequilibrium in a case-parents study. With the rapid progress in genomic studies, many single nucleotide polymorphisms will be identified and genotyped within a very short physical distance. Analyzing multiple single nucleotide polymorphisms within a candidate gene/region with Bonferroni correction for multiple transmission/disequilibrium tests will lead to a conservative test, and hence a power loss. I propose a new method, the "Adaptive PRIncipal COmponent Test" (APRICOT). The method has the following properties: (1) it does not need haplotype information; (2) it is nonparametric-it does not make specific assumptions about the population history or population structure; and (3) the calculation of the test statistic and the determination of its significance level are simple and straightforward. Monte-Carlo simulation reveals that adaptive principal component test maintains the nominal significance level under the null hypothesis of no linkage disequilibrium, even under complex situations of multiple ancestral haplotypes and structured populations. It provides a substantial power advantage over the conventional Bonferroni approach. The adaptive principal component test is a promising method for candidate gene testing using single nucleotide polymorphisms.

Poder de detecção de "Quantitative Trait Loci", da análise de marcas simples e da regressão linear múltipla

Abstract: In general terms, Quantitative Trait Loci (QTL) mapping differs from other research tools used in genetics since it is, basically, a multiple test procedure. The use of this technique leads to problems related to the genomewise significance level and, consequently, to the power of the test. Using computational data simulation the power of QTL mapping was obtained, carried out through multiple linear regression using stepwise procedures to select markers. Procedures based on single marker analisys, using both the False Discover Rate (FDR) and the Bonferroni criteria to determinate the genomewise significance level were also used. The procedure based on multiple regression, using the stepwise technique, was the most powerful in identifying markers associated to QTL's. However, in cases where its power was less intense, its advantage was the ability to detect only markers strongly associated to QTL's. In comparison to the Bonferroni method, the FDR criterion was in general more powerful, and should be adopted for interval mapping procedures.

Testing for conditional multiple marginal independence.

Abstract: Summary. Survey respondents are often prompted to pick any number of responses from a set of possible responses. Categorical variables that summarize this kind of data are called pick any/c variables. Counts from surveys that contain a pick any/c variable along with a group variable (r levels) and stratification variable (q levels) can be marginally summarized into an r×c×q contingency table. A question that may naturally arise from this setup is to determine if the group and pick any/c variable are marginally independent given the stratification variable. A test for conditional multiple marginal independence (CMMI) can be used to answer this question. Since subjects may pick any number out of c possible responses, the Cochran (1954, Biometrics10, 417–451) and Mantel and Haenszel (1959, Journal of the National Cancer Institute22, 719–748) tests cannot be used directly because they assume that units in the contingency table are independent of each other. Therefore, new testing methods are developed. Cochran's test statistic is extended to r×2×q tables, and a modified version of this statistic is proposed to test CMMI. Its sampling distribution can be approximated through bootstrapping. Other CMMI testing methods discussed are bootstrap p-value combination methods and Bonferroni adjustments. Simulation findings suggest that the proposed bootstrap procedures and the Bonferroni adjustments consistently hold the correct size and provide power against various alternatives.

Bonferroni in biomedical research

Abstract: The statistical methods for multiple comparisons are described in the paper. The pros and cons of Bonferroni correction versus more recent methods such as Holm correction are outlined. The lack of scientific consensus on the methods to be used in the different areas of biomedical research is shown by the disagreements, often quite harsh, between different statisticians. The papers presented at the meeting held in September 2001 in memory of Carlo Emilio Bonferroni, Rector of the Istituto Superiore di Scienze Economiche e Commerciali di Bari from 1925 to 1933 are summarized. In the meeting there was the historical reconstruction of the Bonferroni correction, from Boole (1850) to Olive Dunn (1959). In the meeting there was also a presentation concerning Bonferroni's ideas (he was a moderate frequentist) in the field of probability, appreciated even by a strong Bayesian such as de Finetti in his memorial talk given in 1961, one year after Bonferroni's death.

SMILEPLOT: Stata module to create plots for use with multiple significance tests

Abstract: This package contains the programs multproc, smileplot and smileplot7. multproc inputs a data set with 1 observation for each of a set of multiple significance tests and data on the P-values, and carries out a multiple test procedure chosen by the user to define a corrected overall critical P-value for accepting or rejecting the null hypotheses tested. These procedures may be one-step, step-up or step-down, and may control the familywise error rate (eg the Bonferroni, Sidak, Holm, Holland-Copenhaver, Hochberg and Rom procedures) or the false discovery rate (eg the Simes, Benjamini-Liu, Benjamini-Yekutieli and Benjamini-Krieger-Yekutieli procedures). smileplot, and its Stata 7 version smileplot7, work by calling multproc and then creating a smile plot, with data points corresponding to multiple estimated parameters, the P-values (on a reverse log scale) on the Y-axis, and the corresponding parameter estimates (or another variable) on the X-axis. There are Y-axis reference lines at the uncorrected and corrected overall critical P-values. The reference line at the corrected critical P-value, known as the parapet line, is interpreted informally as a boundary between data mining and data dredging. multproc, smileplot and smileplot7 are used on data sets with one observation per estimated parameter and data on estimates and their P-values, which may be created using parmby, parmest, statsby or postfile.