Showing papers on "Bonferroni correction published in 1986"
TL;DR: In this article, a modification of the Bonferroni procedure for testing multiple hypotheses is presented, based on the ordered p-values of the individual tests, which is less conservative than the classical BFP but is still simple to apply.
Abstract: SUMMARY A modification of the Bonferroni procedure for testing multiple hypotheses is presented. The method, based on the ordered p-values of the individual tests, is less conservative than the classical Bonferroni procedure but is still simple to apply. A simulation study shows that the probability of a type I error of the procedure does not exceed the nominal significance level, a, for a variety of multivariate normal and multivariate gamma test statistics. For independent tests the procedure has type I error probability equal to a. The method appears particularly advantageous over the classical Bonferroni procedure when several highly-correlated test statistics are involved.
2,220 citations
TL;DR: In this article, a modified Bonferroni procedure with greater power than the B procedure was introduced, and the criterion continues to be modified in a stagewise manner, with the denominator of α′ reduced by 1 each time a hypothesis is rejected, so that tests can be conducted at successively higher significance levels.
Abstract: Suppose that n hypotheses H 1, H 2, …, H n with associated test statistics T 1, T 2, …, T n are to be tested by a procedure with experimentwise significance level (the probability of rejecting one or more true hypotheses) smaller than or equal to some specified value α. A commonly used procedure satisfying this condition is the Bonferroni (B) procedure, which consists of rejecting H i , for any i, iff the associated test statistic T i is significant at the level α′ = α/n. Holm (1979) introduced a modified Bonferroni procedure with greater power than the B procedure. Under Holm's sequentially rejective Bonferroni (SRB) procedure, if any hypothesis is rejected at the level α′ = α/n, the denominator of α′ for the next test is n − 1, and the criterion continues to be modified in a stagewise manner, with the denominator of α′ reduced by 1 each time a hypothesis is rejected, so that tests can be conducted at successively higher significance levels. Holm proved that the experimentwise significance level...
753 citations
TL;DR: The present program is written in an elementary subset of BASIC and will perform Kruskal-Wallis test followed by multiple comparisons between the groups on practically any computer programmable in BASIC.
329 citations
01 Dec 1986
TL;DR: Simulation results show that the Bonferroni procedure is more efficient than Dudewicz and Dalal's procedure when the percentage of variance reduction is high.
Abstract: This paper presents a Bonferroni procedure for selecting the alternative with the largest mean when the variances are unknown and unequal and correlation is induced among the observations for each alternative by common random numbers. Simulation results show that the Bonferroni procedure is more efficient than Dudewicz and Dalal's procedure when the percentage of variance reduction is high.
45 citations
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TL;DR: The relationships between two events in time can also be absolute or relative: to ensure unwrinkled clothes remove them within an hour of the dryer finishing, or to ensure that one task must follow another.
Abstract: The relationships between two events in time can also be absolute or relative. Some relationships epecify an exact amount of time that must come between the two events: ten minutes after the plastic has been poured, remove the widgets from their molds. More common are the simple relative relationships which just specify that one task must follow another. In between are tasks that are related by some interval: to ensure unwrinkled clothes remove them within an hour of the dryer finishing.
39 citations
TL;DR: It is shown that this combinatorial structure is a natural tool for obtaining Bonferroni type inequalities which are equalities for some families of sets.
38 citations
TL;DR: The loss of statistical power associated with the use of the Bonferroni procedure is demonstrated in this article, and two options for alleviating the problem are explored, such as setting a less stringent significance level for the set of tests is shown to be less effective than increasing the sample size.
Abstract: The Bonferroni procedure controls the risk of rejecting one or more true null hypotheses no matter how many significance tests are performed, but permits the risk of failing to reject false null hypotheses to grow with the number of tests. The loss of statistical power associated with the use of this procedure is demonstrated, and two options for alleviating the problem are explored. Setting a less stringent significance level for the set of tests is shown to be less effective than increasing the sample size.
19 citations
01 Dec 1986
TL;DR: In conventional discrete event simulation svstems, the flow of simulated time is controlled by-a data structure that is variously called the event set, the pending eventSet, the future-event chain, or the sequencing-set.
Abstract: In conventional discrete event simulation svstems, the flow of simulated time is controlled by-a data structure that is variously called the event set, the pending event set, the future-event chain, or the sequencing-set. At any instant, this structure contains records of those events, processes or activities that are to be simulated at some future time as a result of events that have already been simulated.
11 citations
TL;DR: In this paper, improved Bonferroni type inequalities for the union of a set of nonexchangeable events are presented, which are stronger than or equivalent with the bounds proposed by KOUNIAS (1968), HUNTER (1976), MARGOLIN & MAURER (1976, GALAMBOS (1977), and by Mǎrgǎkritescu (1983).
Abstract: In this note we present improved Bonferroni type inequalities for the union of a set of nonexchangeable events. These new bounds are stronger than or equivalent with the bounds proposed by KOUNIAS (1968), HUNTER (1976), MARGOLIN & MAURER (1976), GALAMBOS (1977) and by Mǎrgǎkritescu (1983). In the particular case of the exchangeable events, the bounds given by SOBEL & UPPULURI (1972) can be derived. A generalization in terms of a partition of {1, 2, …, n} is also established.
8 citations
TL;DR: A computer program is described that performssucha protection procedure for multiple correlation tests (the Bonferroni multistage procedure), and thereby maintains the specified Type I error rate (alpha level) across a set (family) of correlations.
Abstract: When researchers perform several bivariate correlations on a data set, they need to know which of these correlationcoefficients are statistically significant. However, this assessment is not straightforward. The probability estimates thatare output by computerized statistical packages and shown in statistical tables are calculated on the assumption that only one test has been performed, and the probability of making at leastone Type 1error increases withthe number of testsperformed (Larzelere & Mulaik, 1977). This problem is analogous to that posed by performing multiple t tests on a data set. Although several procedures are readily available (and routinely performed) to provideprotection for multiple comparisons of means (seeKeppel, 1982, chap. 8), noprocedure is readily available to protect researchers from unacceptable levels of Type I error when multiple correlation tests are performed. The present paper describes a computerprogram that performssucha protection procedurefor multiple correlation tests (the Bonferroni multistage procedure), and therebymaintains the specified Type I error rate (alpha level) across a set (family) of correlations.
5 citations
TL;DR: A BASIC computer program is described that computes power for any combination of effect size, degrees of freedom for hypothesis, degreesof freedom for error, and a level.
Abstract: Statistical power analysis is becoming an increasingly routine procedure when planning experiments and assessing the validity of tests of hypotheses following statistical analysis. For those situations where Type I error rate is not set to .10, .05, or .01 the task is impeded by the unavailability of tables for computation. A BASIC computer program is described that computes power for any combination of effect size, degrees of freedom for hypothesis, degrees of freedom for error. and a level. As a consequence of the algorithm an approximation to the critical value of the Bonferroni F-test is also computed.
TL;DR: Bonferroni adjusted F-tables are given for α=0.10 and α = 0.001 with degrees of freedom following classical tables of Fisher and Yates in this article.
Abstract: Bonferroni adjusted F-tables are given for α=0.10 and α = 0.001 with degrees of freedom following classical tables of Fisher and Yates. The tables may be used in simultaneous analysis of variances or in evaluating binomial tests by means of F-tables in configural frequency testing.
TL;DR: In this paper, a method for constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model is presented, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient.
Abstract: This paper demonstrates a method, derived byKhuri (1981), of constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model. The method may be applied to obtain confidence intervals for the variance components and other linear functions of the expected mean squares used in generalizability theory, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient. The Khuri intervals are compared with the approximate intervals obtained by usingSatterthwaite’s (1941, 1946) method in conjunction with Bonferroni’s inequality.