Pairwise Comparisons with Binary Responses: Multiplicity-Adjusted P-Values and Simultaneous Confidence Intervals

ABSTRACT There are several linear and nonlinear models for analyzing repeated measurements. The mean response for an individual depends on the regression parameters specific to that individual. One of the simple forms is the sum of vectors of fixed parameters and random effects. When the models with mixed effects for several groups are parallel, pairwise comparisons of level differences are considered. For the comparisons, approximate simultaneous confidence intervals are given.

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Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

Journal of Probability and Statistics ◽

10.1155/2011/484272 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10

Author(s):

Xin Yan ◽

Xiaogang Su

Keyword(s):

Confidence Intervals ◽

Error Rate ◽

Pairwise Comparisons ◽

Simultaneous Inference ◽

Familywise Error Rate ◽

Linear Combinations ◽

Simultaneous Confidence Intervals ◽

Nominal Level ◽

Equal Variance ◽

Heteroscedastic Errors

We proposed a statistical method to construct simultaneous confidence intervals on all linear combinations of means without assuming equal variance where the classical Scheffé's simultaneous confidence intervals no longer preserve the familywise error rate (FWER). The proposed method is useful when the number of comparisons on linear combinations of means is extremely large. The FWERs for proposed simultaneous confidence intervals under various configurations of mean variances are assessed through simulations and are found to preserve the predefined nominal level very well. An example of pairwise comparisons on heteroscedastic means is given to illustrate the proposed method.

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Exact Simultaneous Confidence Intervals for Pairwise Comparisons of Three Normal Means

Journal of the American Statistical Association ◽

10.1080/01621459.1985.10478137 ◽

1985 ◽

Vol 80 (390) ◽

pp. 438-442 ◽

Cited By ~ 13

Author(s):

John D. Spurrier ◽

Steven P. Isham

Keyword(s):

Confidence Intervals ◽

Pairwise Comparisons ◽

Simultaneous Confidence Intervals ◽

Normal Means

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Simultaneous confidence intervals for all pairwise comparisons of the means of delta-lognormal distributions with application to rainfall data

PLoS ONE ◽

10.1371/journal.pone.0253935 ◽

2021 ◽

Vol 16 (7) ◽

pp. e0253935

Author(s):

Patcharee Maneerat ◽

Sa-Aat Niwitpong ◽

Suparat Niwitpong

Keyword(s):

Confidence Intervals ◽

Rainy Season ◽

Direct Action ◽

Parametric Bootstrap ◽

Rainfall Data ◽

Pairwise Comparisons ◽

Simultaneous Confidence Intervals ◽

Lognormal Distributions ◽

Natural Rainfall ◽

Fiducial Generalized Confidence Interval

Natural disasters such as flooding and landslides are important unexpected events during the rainy season in Thailand, and how to direct action to avoid their impacts is the motivation behind this study. The differences between the means of natural rainfall datasets in different areas can be estimated using simultaneous confidence intervals (SCIs) for pairwise comparisons of the means of delta-lognormal distributions. Our proposed methods are based on a parametric bootstrap (PB), a fiducial generalized confidence interval (FGCI), the method of variance estimates recovery (MOVER), and Bayesian credible intervals based on mixed (BCI-M) and uniform (BCI-U) priors. Their coverage probabilities, lower and upper error probabilities, and relative average lengths were used to evaluate and compare their SCI performances through Monte Carlo simulation. The results show that BCI-U and PB work well in different situations, even with large differences in variances σ j 2. All of the methods were applied to estimate pairwise differences between the means of natural rainfall data from five areas in Thailand during the rainy season to determine their abilities to predict occurrences of flooding and landslides.

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