A quasi-exact method for the confidence intervals of the difference of two independent binomial proportions in small sample cases

2002 ◽  
Vol 21 (6) ◽  
pp. 943-956 ◽  
Author(s):  
Xun Chen
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Exact Method ◽  
Binomial Proportions ◽  
The Difference

Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions

2007 ◽  
Vol 51 (12) ◽  
pp. 5791-5799 ◽  
Author(s):  
Thomas J. Santner ◽  
Vivek Pradhan ◽  
Pralay Senchaudhuri ◽  
Cyrus R. Mehta ◽  
Ajit Tamhane
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Binomial Proportions ◽  
The Difference

Confidence intervals for a difference between lognormal means in cluster randomization trials

2014 ◽  
Vol 26 (2) ◽  
pp. 598-614 ◽  
Author(s):  
Julia Poirier ◽  
GY Zou ◽  
John Koval
Keyword(s):  
Confidence Intervals ◽  
Community Acquired Pneumonia ◽  
Small Sample ◽  
Cluster Randomization ◽  
Critical Pathway ◽  
Arithmetic Means ◽  
Multiple Parameters ◽  
The Difference ◽  
Using Data ◽  
Small Sample Sizes

Cluster randomization trials, in which intact social units are randomized to different interventions, have become popular in the last 25 years. Outcomes from these trials in many cases are positively skewed, following approximately lognormal distributions. When inference is focused on the difference between treatment arm arithmetic means, existent confidence interval procedures either make restricting assumptions or are complex to implement. We approach this problem by assuming log-transformed outcomes from each treatment arm follow a one-way random effects model. The treatment arm means are functions of multiple parameters for which separate confidence intervals are readily available, suggesting that the method of variance estimates recovery may be applied to obtain closed-form confidence intervals. A simulation study showed that this simple approach performs well in small sample sizes in terms of empirical coverage, relatively balanced tail errors, and interval widths as compared to existing methods. The methods are illustrated using data arising from a cluster randomization trial investigating a critical pathway for the treatment of community acquired pneumonia.

Confidence intervals for the Mann–Whitney test

2018 ◽  
Vol 28 (12) ◽  
pp. 3755-3768 ◽  
Author(s):  
Maja Pohar Perme ◽  
Damjan Manevski
Keyword(s):  
Confidence Intervals ◽  
Effect Size ◽  
Coverage Probability ◽  
Random Variable ◽  
Small Sample ◽  
Test Statistic ◽  
Whitney Test ◽  
Mann Whitney Test ◽  
Frequent Use ◽  
The Difference

The Mann–Whitney test is a commonly used non-parametric alternative of the two-sample t-test. Despite its frequent use, it is only rarely accompanied with confidence intervals of an effect size. If reported, the effect size is usually measured with the difference of medians or the shift of the two distribution locations. Neither of these two measures directly coincides with the test statistic of the Mann–Whitney test, so the interpretation of the test results and the confidence intervals may be importantly different. In this paper, we focus on the probability that random variable X is lower than random variable Y. This measure is often referred to as the degree of overlap or the probabilistic index; it is in one-to-one relationship with the Mann–Whitney test statistic. The measure equals the area under the ROC curve. Several methods have been proposed for the construction of the confidence interval for this measure, and we review the most promising ones and explain their ideas. We study the properties of different variance estimators and small sample problems of confidence intervals construction. We identify scenarios in which the existing approaches yield inadequate coverage probabilities. We conclude that the DeLong variance estimator is a reliable option regardless of the scenario, but confidence intervals should be constructed using the logit scale to avoid values above 1 or below 0 and the poor coverage probability that follows. A correction is needed for the case when all values from one sample are smaller than the values of the other. We propose a method that improves the coverage probability also in these cases.

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