Approximate Confidence Intervals for Standardized Effect Sizes in the Two-Independent and Two-Dependent Samples Design

2007 ◽  
Vol 32 (1) ◽  
pp. 39-60 ◽  
Author(s):  
Wolfgang Viechtbauer
Keyword(s):  
Monte Carlo ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Effect Sizes ◽  
Iterative Estimation ◽  
Exact Confidence Intervals ◽  
Standardized Effect Sizes ◽  
Approximate Confidence Intervals ◽  
Exact Confidence Interval ◽  
Dependent Samples

Standardized effect sizes and confidence intervals thereof are extremely useful devices for comparing results across different studies using scales with incommensurable units. However, exact confidence intervals for standardized effect sizes can usually be obtained only via iterative estimation procedures. The present article summarizes several closed-form approximations to the exact confidence interval bounds in the two-independent and two-dependent samples design. Monte Carlo simulations were conducted to determine the accuracy of the various approximations under a wide variety of conditions. All methods except one provided accurate results for moderately large sample sizes and converged to the exact confidence interval bounds as sample size increased.

Confidence Intervals

2009 ◽  
Vol 217 (1) ◽  
pp. 15-26 ◽  
Author(s):  
Geoff Cumming ◽  
Fiona Fidler
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Null Hypothesis ◽  
Prediction Intervals ◽  
Effect Sizes ◽  
Significance Testing ◽  
Null Hypothesis Significance Testing ◽  
P Values ◽  
Standardized Effect Sizes ◽  
Mainstream Science

Most questions across science call for quantitative answers, ideally, a single best estimate plus information about the precision of that estimate. A confidence interval (CI) expresses both efficiently. Early experimental psychologists sought quantitative answers, but for the last half century psychology has been dominated by the nonquantitative, dichotomous thinking of null hypothesis significance testing (NHST). The authors argue that psychology should rejoin mainstream science by asking better questions – those that demand quantitative answers – and using CIs to answer them. They explain CIs and a range of ways to think about them and use them to interpret data, especially by considering CIs as prediction intervals, which provide information about replication. They explain how to calculate CIs on means, proportions, correlations, and standardized effect sizes, and illustrate symmetric and asymmetric CIs. They also argue that information provided by CIs is more useful than that provided by p values, or by values of Killeen’s prep, the probability of replication.

Confidence Intervals for Ages of Marsupials Determined from Body Measurements

1981 ◽  
Vol 8 (2) ◽  
pp. 269 ◽  
Author(s):  
JT Wood ◽  
SM Carpenter ◽  
WE Poole
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Growth Curves ◽  
Head Length ◽  
Body Measurements ◽  
Approximate Confidence Intervals ◽  
Using Data

Fitted growth curves for several individual animals for a measurement such as head length will often differ significantly from each other, even though the curves all have the same general form. For construction of a confidence interval for the age of an animal of unknown age with a particular head length, account should be taken of between-animal variation as well as within-animal variation. This paper gives methods for estimating the components of the variation from observations on animals of known age, and for combining them to give approximate confidence intervals for the age of animals of unknown age. The methods are illustrated using data from grey kangaroos.

A new procedure to construct confidence intervals for genotypic variance and expected response to selection

Genome ◽  
1989 ◽  
Vol 32 (2) ◽  
pp. 307-308 ◽  
Author(s):  
G. C. C. Tai
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Progeny Test ◽  
Variance Ratio ◽  
Confidence Limits ◽  
Response To Selection ◽  
Genotypic Variance ◽  
Exact Confidence Intervals

This paper describes a procedure to construct confidence intervals for genotypic variance and expected response to selection estimated from progeny test experiments. It involves the introduction of parameters into the confidence limits of existing exact confidence intervals for variance and variance ratio. The parameters in the limits of the derived intervals are estimated by comparing the limits of different potential intervals covering the same parameter, i.e., genotypic variance or expected response to selection. This leads to the construction of a confidence interval for the concerned parameter.Key words: confidence intervals, genotypic variance, expected response to selection.

ESTIMATING THE SHAPE PARAMETER OF THE LOG-LOGISTIC DISTRIBUTION

2006 ◽  
Vol 13 (03) ◽  
pp. 257-266 ◽  
Author(s):  
ZHENMIN CHEN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Confidence Intervals ◽  
Shape Parameter ◽  
Interval Estimation ◽  
Maximum Likelihood Estimators ◽  
Logistic Distribution ◽  
Pivotal Quantity ◽  
Estimation Problems ◽  
Exact Confidence Intervals

The log-logistic distribution is a useful distribution in survival analysis. Parameter estimation problems have been discussed by many authors. This paper focuses on the interval estimation for the shape parameter of the log-logistic distribution. Bain and Engelhardt3 gave confidence intervals for the parameters of a logistic distribution based on pivotal quantities formed by maximum likelihood estimators. Chen10 proposed another method for obtaining exact confidence intervals of the shape parameter of the log-logistic distribution. Compared with the existing methods for constructing confidence intervals for the parameters of the log-logistic distribution, the method given in Chen10 is easier to use. In the present paper, the pivotal quantity used in Chen10 is adjusted to improve the performance of statistical analysis. Monte Carlo simulation is conducted to compare the performance of different pivotal quantities. The simulation result shows that the adjusted pivotal quantity has better performance, and then should be recommended to the statistics users.

scholarly journals Assessing the Accuracy of Approximate Confidence Intervals Proposed for the Mean of Poisson Distribution

2020 ◽  
Vol 18 (1) ◽  
pp. 2-13
Author(s):  
Alireza Shirvani ◽  
Malek Fathizadeh
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Count Data ◽  
Coverage Probability ◽  
Discrete Distribution ◽  
Interval Length ◽  
Average Confidence ◽  
The Mean ◽  
Approximate Confidence Intervals

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

Confidence Intervals After Variance Stabilization May Go Head-to-Head with Exact Confidence Intervals: A New Class of Illustrations

2021 ◽  
pp. 000806832110511
Author(s):  
Nitis Mukhopadhyay
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Large Sample ◽  
New Class ◽  
Variance Stabilization ◽  
Subject Classifications ◽  
Coverage Probabilities ◽  
Exact Confidence Intervals ◽  
Exact Calculations ◽  
Better Than

We begin with an overview on variance stabilizing transformations (VST) along with three classical examples for completeness: the arcsine, square-root and Fisher's z-transformations (Examples 1–3). Then, we construct three new examples (Examples 4–6) of VST-based and central limit theorem (CLT)’based large-sample confidence interval methodologies. These are special examples in the sense that in each situation, we also have an exact confidence interval procedure for the parameter of interest. Tables 1–3 obtained exclusively under Examples 4–6 via exact calculations show that the VST-based (a) large-sample confidence interval methodology wins over the CLT-based large-sample confidence interval methodology, (b) confidence intervals’ exact coverage probabilities are better than or nearly same as those associated with the exact confidence intervals and (c) intervals are never wider (in the log-scale) than the CLT-based intervals across the board. A possibility of such a surprising behaviour of the VST-based confidence intervals over the exact intervals was not on our radar when we began this investigation. Indeed the VST-based inference methodologies may do extremely well, much more so than the existing literature reveals as evidenced by the new Examples 4–6. AMS subject classifications: 62E20; 62F25; 62F12

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