Confidence Intervals For Population Means: Part 1

2014 ◽  
Keyword(s):  
Confidence Intervals ◽  
Population Means

scholarly journals Estimating Forest Volume and Biomass and Their Changes Using Random Forests and Remotely Sensed Data

2019 ◽  
Vol 11 (16) ◽  
pp. 1944 ◽  
Author(s):  
Jessica Esteban ◽  
Ronald McRoberts ◽  
Alfredo Fernández-Landa ◽  
José Tomé ◽  
Erik Nӕsset
Keyword(s):  
Confidence Intervals ◽  
Random Forests ◽  
Remotely Sensed ◽  
Predictor Variables ◽  
Prediction Algorithm ◽  
Standard Errors ◽  
Original Structure ◽  
Remotely Sensed Data ◽  
Population Means ◽  
Model Based

Despite the popularity of random forests (RF) as a prediction algorithm, methods for constructing confidence intervals for population means using this technique are still only sparsely reported. For two regional study areas (Spain and Norway) RF was used to predict forest volume or aboveground biomass using remotely sensed auxiliary data obtained from multiple sensors. Additionally, the changes per unit area of these forest attributes were estimated using indirect and direct methods. Multiple inferential frameworks have attracted increased recent attention for estimating the variances required for confidence intervals. For this study, three different statistical frameworks, design-based expansion, model-assisted and model-based estimators, were used for estimating population parameters and their variances. Pairs and wild bootstrapping approaches at different levels were compared for estimating the variances of the model-based estimates of the population means, as well as for mapping the uncertainty of the change predictions. The RF models accurately represented the relationship between the response and remotely sensed predictor variables, resulting in increased precision for estimates of the population means relative to design-based expansion estimates. Standard errors based on pairs bootstrapping within or internal to RF were considerably larger than standard errors based on both pairs and wild external bootstrapping of the entire RF algorithm. Pairs and wild external bootstrapping produced similar standard errors, but wild bootstrapping better mimicked the original structure of the sample data and better preserved the ranges of the predictor variables.

Confidence intervals for population means of partially paired observations

2015 ◽  
Vol 58 (1) ◽  
pp. 35-51 ◽  
Author(s):  
Nicole Fuchs ◽  
Werner Pölz ◽  
Arne C. Bathke
Keyword(s):  
Confidence Intervals ◽  
Population Means

Simultaneous confidence intervals for two linear functions of population means when population variances are not equal

1970 ◽  
Vol 67 (2) ◽  
pp. 365-370 ◽  
Author(s):  
Saibal Banerjee
Keyword(s):  
Confidence Intervals ◽  
Linear Functions ◽  
Simultaneous Confidence Intervals ◽  
Population Means

AbstractIt is shown that given k samples of nj units from it is possible to construct simultaneous confidence intervals for two given linear functions of population means, (where cij are known constants), when population variances are not equal.

Confidence Intervals for Ratios of Means and Medians

2020 ◽  
Vol 45 (6) ◽  
pp. 750-770
Author(s):  
Douglas G. Bonett ◽  
Robert M. Price
Keyword(s):  
Confidence Intervals ◽  
Meta Analysis ◽  
T Test ◽  
Interval Methods ◽  
Population Means ◽  
Paired Samples ◽  
Special Cases ◽  
Standardized Measure ◽  
Propensity Score Stratification ◽  
R Functions

In studies where the response variable is measured on a ratio scale, a ratio of means or medians provides a standardized measure of effect size that is an alternative to the popular standardized mean difference. Confidence intervals for ratios of population means and medians in independent-samples designs and paired-samples designs are proposed as supplements to the independent-samples t test and paired-samples t test. The performance of the proposed confidence intervals are evaluated in a simulation study. The proposed confidence interval methods are extended to the case of a 2 × m factorial design that includes propensity score stratification and meta-analysis as special cases. R functions that implement the recommended confidence intervals are provided in the Supplemental Material file, available in the online version of this article, and are illustrated with several examples.

Forestry Applications of Saddle-Point Approximations to Construct Confidence Intervals for Population Means

Biometrics ◽  
1995 ◽  
Vol 51 (1) ◽  
pp. 61
Author(s):  
Jufang Li ◽  
Mei-Ching Chen ◽  
Hans T. Schreuder ◽  
Tim G. Gregoire
Keyword(s):  
Saddle Point ◽  
Confidence Intervals ◽  
Population Means ◽  
Saddle Point Approximations

Reducing the width of confidence intervals for the difference between two population means by inverting adaptive tests

2016 ◽  
Vol 27 (5) ◽  
pp. 1422-1436 ◽  
Author(s):  
Thomas W O’Gorman
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Stochastic Search ◽  
Adaptive Tests ◽  
P Values ◽  
Population Means ◽  
Testing Method ◽  
Tests Of Significance ◽  
The Difference ◽  
Adaptive Confidence Intervals

In the last decade, it has been shown that an adaptive testing method could be used, along with the Robbins–Monro search procedure, to obtain confidence intervals that are often narrower than traditional confidence intervals. However, these confidence interval limits require a great deal of computation and some familiarity with stochastic search methods. We propose a method for estimating the limits of confidence intervals that uses only a few tests of significance. We compare these limits to those obtained by a lengthy Robbins–Monro stochastic search and find that the proposed method is nearly as accurate as the Robbins–Monro search. Adaptive confidence intervals that are produced by the proposed method are often narrower than traditional confidence intervals when the distributions are long-tailed, skewed, or bimodal. Moreover, the proposed method of estimating confidence interval limits is easy to understand, because it is based solely on the p-values from a few tests of significance.

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