CONFIDENCE INTERVALS FOR THE DIFFERENCE BETWEEN INVERSE OF NORMAL MEANS

2016 ◽  
Vol 48 (5) ◽  
pp. 337-347
Author(s):  
Suparat Niwitpong ◽  
Arunee Wongkhao
Keyword(s):  
Confidence Intervals ◽  
Normal Means ◽  
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.

scholarly journals Comment on "Quantitative performance metrics for stratospheric-resolving chemistry-climate models" by Waugh and Eyring (2008)

2009 ◽  
Vol 9 (23) ◽  
pp. 9101-9110 ◽  
Author(s):  
V. Grewe ◽  
R. Sausen
Keyword(s):  
Observational Data ◽  
Confidence Intervals ◽  
Climate Models ◽  
Performance Metrics ◽  
Statistical Tests ◽  
Low Grade ◽  
Perfect Model ◽  
Special Cases ◽  
Quantitative Performance ◽  
The Difference

Abstract. This comment focuses on the statistical limitations of a model grading, as applied by D. Waugh and V. Eyring (2008) (WE08). The grade g is calculated for a specific diagnostic, which basically relates the difference of means of model and observational data to the standard deviation in the observational dataset. We performed Monte Carlo simulations, which show that this method has the potential to lead to large 95%-confidence intervals for the grade. Moreover, the difference between two model grades often has to be very large to become statistically significant. Since the confidence intervals were not considered in detail for all diagnostics, the grading in WE08 cannot be interpreted, without further analysis. The results of the statistical tests performed in WE08 agree with our findings. However, most of those tests are based on special cases, which implicitely assume that observations are available without any errors and that the interannual variability of the observational data and the model data are equal. Without these assumptions, the 95%-confidence intervals become even larger. Hence, the case, where we assumed perfect observations (ignored errors), provides a good estimate for an upper boundary of the threshold, below that a grade becomes statistically significant. Examples have shown that the 95%-confidence interval may even span the whole grading interval [0, 1]. Without considering confidence intervals, the grades presented in WE08 do not allow to decide whether a model result significantly deviates from reality. Neither in WE08 nor in our comment it is pointed out, which of the grades presented in WE08 inhibits such kind of significant deviation. However, our analysis of the grading method demonstrates the unacceptably high potential for these grades to be insignificant. This implies that the grades given by WE08 can not be interpreted by the reader. We further show that the inclusion of confidence intervals into the grading approach is necessary, since otherwise even a perfect model may get a low grade.

Uncertainty and Inference for Verification Measures

2007 ◽  
Vol 22 (3) ◽  
pp. 637-650 ◽  
Author(s):  
Ian T. Jolliffe
Keyword(s):  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Multiple Testing ◽  
Prediction Intervals ◽  
Hypothesis Tests ◽  
Statistical Inferences ◽  
The Difference ◽  
Main Ideas

Abstract When a forecast is assessed, a single value for a verification measure is often quoted. This is of limited use, as it needs to be complemented by some idea of the uncertainty associated with the value. If this uncertainty can be quantified, it is then possible to make statistical inferences based on the value observed. There are two main types of inference: confidence intervals can be constructed for an underlying “population” value of the measure, or hypotheses can be tested regarding the underlying value. This paper will review the main ideas of confidence intervals and hypothesis tests, together with the less well known “prediction intervals,” concentrating on aspects that are often poorly understood. Comparisons will be made between different methods of constructing confidence intervals—exact, asymptotic, bootstrap, and Bayesian—and the difference between prediction intervals and confidence intervals will be explained. For hypothesis testing, multiple testing will be briefly discussed, together with connections between hypothesis testing, prediction intervals, and confidence intervals.

scholarly journals Hacer estimaciones estadísticas

2017 ◽  
Vol 5 (10) ◽  
Author(s):  
M. H Badii
Keyword(s):  
Confidence Intervals ◽  
Statistical Estimation ◽  
Good Estimator ◽  
The Mean ◽  
The Difference

Keywords: Estimations, sampling, statisticsAbstract. The notion of statistical estimation both in terms of point and interval is described. The criteria of a good estimator are noted. The procedures to calculate the intervals for the mean, proportions and the difference among two means as well as the confidence intervals for the probable errors in statistics are provided.Palabras clave: Estadística, estimación, muestreoResumen. En la presente investigación se describen la noción de la estimación estadística, tanto de tipo puntual con de forma de intervalo. Se presentan los criterios que debe reunir un estimador bueno. Se notan con ejemplos, la forma de calcular la estimación del intervalo para la media, la proporción y de la diferencia entre dos medias y los intervalos de confianza para los errores probables.

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