Showing papers on "Bonferroni correction published in 1992"
TL;DR: In this article, the authors proposed that results from simultaneous tests be reported as adjusted P-values such that, if the adjusted p-value for an individual hypothesis is less than the chosen significance level of a, then the hypothesis is rejected with an experimentwise error rate of no more than ax.
Abstract: This paper proposes that results from simultaneous tests be reported as adjusted P-values such that, if the adjusted P-value for an individual hypothesis is less than the chosen significance level of a, then the hypothesis is rejected with an experimentwise error rate of no more than ax. Examples are given of adjusted P-values for multiple comparisons in the analysis of variance and of adjusted P-values based on the Bonferroni procedure and modifications of that procedure by Holm (1979, Scandinavian Journal of Statistics 6, 65-70), Hochberg (1988, Biometrika 75, 800-802), and Hommel (1988, Biometrika 75, 383-386). The modified Bonferroni-based procedures are much more powerful than the original Bonferroni procedure, and they deserve wider use. In addition to the above, a procedure is outlined for obtaining adjusted P-values for any closed test procedure.
975 citations
TL;DR: Several empirical estimates are discussed for the published BXD marker set of 142 mapped loci and the newer unpublished marker set (October 1991) comprised of 352 marker loci, which appear to be roughly 40 and 65 for these two marker sets, respectively.
Abstract: Most chromosome mapping efforts with the BXD recombinant inbred (RI) strains involve comparisons between a trait of interest and each of a large number of marker loci for evidence of linkage. Such multiple tests or comparisons greatly increase the Type I error rate compared to the single-test situation. Perhaps the most direct way to obtain multiple-test error rates is to employ a Bonferroni correction, where the single-test alpha is multiplied by the number of independent (nonredundant) comparisons (k) to yield a multiple-test alpha that protects against even one fortuitous association with any of the markers. Several empirical estimates ofk are discussed for the published BXD marker set of 142 mapped loci and the newer unpublished marker set (October 1991) comprised of 352 marker loci. Reasonable estimates ofk appear to be roughly 40 and 65 for these two marker sets, respectively.
52 citations
TL;DR: In this article, the upper and lower bounds of P(Vm⩾1, Un ⩾ 1) are obtained by means of the bivariate binomial moments.
Abstract: LetA1,A2, ⋯,Am,C1,C2, ⋯,Cn be events on a given probability speace. LetVm andUn, respectively, be the numbers among theAi's andCj's which occur.Upper and lower bounds ofP(Vm⩾1, Un⩾1) are obtained by means of the bivariate binomial moments. These extend recent univariate optimal Bonferroni-type inequalities.
13 citations
01 Jan 1992
TL;DR: When the estimation of this distribution is in terms of linear combinations of the binomial moments of m n(A), we speak of Bonferroni-type inequalities as discussed by the authors.
Abstract: Several problems of probability theory lead to the need of estimating the distribution of the number m n = m n (A) of occurrences in a sequence A 1,A 2,…,A n of events. When the estimation of this distribution is in terms of linear combinations of the binomial moments of m n(A), we speak of Bonferroni-type inequalities. That is, let (1.1).
10 citations
01 Jan 1992
TL;DR: For a sequence A 1,A 2,A 3,A 4,A 5,A n of events, the binomial moments of m n(A) are denoted by S k = S k,n(A), that is, (1) as discussed by the authors.
Abstract: For a sequence A 1,A 2,… ,A n of events, we denote by m n(A) the number of those which occur. The binomial moments of m n(A) are denoted by S k = S k,n(A), that is, (1).
6 citations
01 Jan 1992
TL;DR: In this paper, the explicit forms of sharp Bonferroni-type inequalities on p{nm} and q m using or, l≤k, are obtained, and a general method to obtain sharp inequalites using, l ≥ k, is shown.
Abstract: Let p m ( or gm) be the probability that exactly (or at least) m out of n events, A 1,…,A n, occur. Let The explicit forms of sharp Bonferroni-type inequalities on p{nm} and q m using or, l≤k, are obtained. These inequalities extend some of the known inequalities, including, for example, the classical Bonferroni inequalities of three terms. A general method to obtain sharp inequalites using,l≤k, is shown.
4 citations
01 Jan 1992
TL;DR: The resulting code computes Ordinary Least Squares estimates on a CYBER 205 in 2% of the time needed on a Vax 8700 if the regression model is small; for large models the CYBER runs much faster.
Abstract: Part I covers vector computers, in the context of Monte Carlo experiments with regression models. These computers should exploit a specific dimension of the Monte Carlo experiment, namely its replicates. The resulting code computes Ordinary Least Squares (OLS) estimates on a CYBER 205 in 2% of the time needed on a Vax 8700. For Generalized Least Squares, however, the code runs slower on the CTBER 205 if the regression model is small; for large models the CYBER runs much faster. Part II covers regression models with correlated errors. To test the validity of the specified regression model, Rao (1959) generalized the F statistic for lack of fit, whereas Kleijnen (1983) proposed cross-validation using Student’s t statistic and Bonferroni’s inequality. A large Monte Carlo experiment compares these two methods, for normal and non-normal errors. Under normality, cross-validation is conservative, whereas Rao’s test realizes its nominal type I error and has high power. Several confidence interval procedures for regression parameters are also compared. Under lognormality, only cross-validation with OLS works.
3 citations
TL;DR: In this article, seven procedures of multiple comparisons: Tukey, Scheffe, Bonferroni, Studentized Maximum Modulus, Duncan, Newman-Keuls and F are compared with respect to the probability of the correct decision.
Abstract: Seven procedures of multiple comparisons: Tukey, Scheffe, Bonferroni, Studentized Maximum Modulus, Duncan, Newman-Keuls and F are compared with respect to the probability of the correct decision. Monte Carlo simulation shows that there is no the best procedure.
AMS 1985 Subject Classification: 62 J 15.
2 citations
TL;DR: When multiple tests are conducted simultaneously in educational and psychological research, the criterion a level for each individual hypothesis test must be adjusted in order to control the overall Type I error.
Abstract: When multiple tests are conducted simultaneously in educational and psychological research, the criterion a level for each individual hypothesis test must be adjusted in order to control the overall Type I error. The Bonferroni procedure is the most commonly used technique for this purpose. Several modified Bonferroni procedures have been suggested in an effort to increase statistical power. However, in exchange for the increase in power, the newer approaches are more complex and are difficult
1 citations