CONFIDENCE INTERVALS FOR THE DIFFERENCE BETWEEN NORMAL MEANS WITH A KNOWN COEFFICIENT OF VARIATION

2016 ◽  
Vol 49 (1) ◽  
pp. 49-65
Author(s):  
Sa-aat Niwitpong
Keyword(s):  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Normal Means ◽  
The Difference

scholarly journals A Bayesian Approach for Estimation of Coefficients of Variation of Normal Distributions

2021 ◽  
Vol 50 (1) ◽  
pp. 261-278
Author(s):  
Warisa Thangjai ◽  
Sa-Aat Niwitpong ◽  
Suparat Niwitpong
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Coefficient Of Variation ◽  
Bayesian Approaches ◽  
Normal Distributions ◽  
Generalized Confidence Interval ◽  
Coefficients Of Variation ◽  
The Difference ◽  
Highest Posterior Density

The coefficient of variation is widely used as a measure of data precision. Confidence intervals for a single coefficient of variation when the data follow a normal distribution that is symmetrical and the difference between the coefficients of variation of two normal populations are considered in this paper. First, the confidence intervals for the coefficient of variation of a normal distribution are obtained with adjusted generalized confidence interval (adjusted GCI), computational, Bayesian, and two adjusted Bayesian approaches. These approaches are compared with existing ones comprising two approximately unbiased estimators, the method of variance estimates recovery (MOVER) and generalized confidence interval (GCI). Second, the confidence intervals for the difference between the coefficients of variation of two normal distributions are proposed using the same approaches, the performances of which are then compared with the existing approaches. The highest posterior density interval was used to estimate the Bayesian confidence interval. Monte Carlo simulation was used to assess the performance of the confidence intervals. The results of the simulation studies demonstrate that the Bayesian and two adjusted Bayesian approaches were more accurate and better than the others in terms of coverage probabilities and average lengths in both scenarios. Finally, the performances of all of the approaches for both scenarios are illustrated via an empirical study with two real-data examples.

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.

High Pressure Liquid Chromatographic Determination of Fensulfothion: Collaborative Study

1983 ◽  
Vol 66 (3) ◽  
pp. 801-803
Author(s):  
Margie E Owen ◽  
◽  
O O Bennett ◽  
L T Chenery ◽  
C J Cohen ◽  
...  
Keyword(s):  
Coefficient Of Variation ◽  
Collaborative Study ◽  
Internal Standard ◽  
Chromatographic Determination ◽  
Peak Height ◽  
Matched Pair ◽  
Standard Material ◽  
Liquid Chromatographic Determination ◽  
The Difference ◽  
Liquid Chromatographic

Abstract A method for analyzing fensulfothion was tested by 10 collaborators. Formulations were dissolved, or extracted from inerts, in methanol. Benzophenone was used as an internal standard. The solution was diromatographed on a Partisil-10 ODS-2, or equivalent, reverse phase column, and detected at 230 nm. A mobile phase of methanol-water-phosphoric acid was used. The ratio of fensulfothion peak height to benzophenone peak height was calculated from the UV response and compared to the standard material for quantitation. A 15% granular formulation was analyzed as a matched pair. The results of one collaborator were outliers by the Dixon test. The coefficient of variation for the granular formulation was 1.6%. A matched pair of 63% spray concentrate samples was analyzed by 10 collaborators. The difference in results was an outlier for one collaborator; the coefficient of variation for the other collaborators was 1.5%. The method has been adopted official first action.

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