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Two-stage procedures are introduced to control the width and coverage (validity) of confidence intervals for the estimation of the mean, the between groups variance component and certain ratios of the variance components in one-way random effects models.
With interval width and coverage probability as evaluation measures, our method achieves a more than three times lower interval width than other methods while the coverage probability can be still guaranteed.
For a specific example of a three-stage drop-the-losers trial, we compare their performance against several alternative estimators in terms of bias, mean squared error, confidence interval width and coverage.
A question outside the scope of this paper is whether it is possible to develop Bayesian methods that would have performance comparable to the frequentist methods across all scenarios in terms of mean interval width and coverage probability.
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We only report 90%% CI widths and coverage as well as the actual power from the two methods in Tables 1, 2 and 3 and visualized the comparison of the corresponding CI widths, CI coverage, and bias in Figs. 1, 2, 3 and 4. Since the two methods yield same CIs in the first stage, we only present the CI width comparison for studies that are made to the 2nd stage in our simulation.
The cracks related to subsidence and vegetation had significant effects on soil hydraulic properties, especially BD; the crack width and vegetation coverage had a marked effect on BD.
The sound equipment was provided by Showco who used the PRISM system, which adapted the show for each venue according to its height, width and the coverage required.
From the 1000 nested case control samples, the average 95% confidence interval width and the coverage probability were estimated.
In each case, the relative bias of the optimal threshold estimate stemming from the mean, the median, and the mode of the posterior distribution were calculated, as well as the mean width, and the coverage probability of the 95% credible interval obtained with the quantile or the HPD method.
The performance of the proposed CIs are evaluated by simulation studies in terms of the empirical coverage probability, the empirical coverage width, and the ratio of the mesial non-coverage probability and non-coverage probability.
The proposed procedures were found to effectively control the width and probability of coverage of the resulting confidence intervals in all cases and were also found to be robust in the presence of missing observations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com