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Interpretation of Confidence Intervals

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...

Confidence Intervals

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...

Confidence Interval for Estimating Population Mean

Confidence Interval for Estimating Population Mean

A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...

Confidence Coefficient

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...

Margin of Error

Margin of Error

The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.

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Related Experiment Video

Updated: Jul 6, 2026

The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials

The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials

Published on: April 19, 2024

Confidence intervals for the overall effect size in random-effects meta-analysis.

Julio Sánchez-Meca¹, Fulgencio Marín-Martínez

¹Department of Basic Psychology and Methodology, Faculty of Psychology, Espinardo Campus, University of Murcia, Murcia, Spain. jsmeca@um.es

Psychological Methods

|March 12, 2008

Summary

Standard confidence intervals (CIs) in meta-analysis are often too narrow. This study found the weighted variance CI provides more accurate coverage, outperforming other methods for estimating overall effect sizes.

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The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials

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Meta-analysis of Voxel-Based Neuroimaging Studies using Seed-based d Mapping with Permutation of Subject Images (SDM-PSI)

Meta-analysis of Voxel-Based Neuroimaging Studies using Seed-based d Mapping with Permutation of Subject Images (SDM-PSI)

Published on: November 27, 2019

Area of Science:

Biostatistics
Medical Research Methodology

Background:

Meta-analysis aims to estimate overall effect size using confidence intervals (CIs).
Standard CI methods often underestimate variance by not accounting for heterogeneity (tau2) and within-study variance estimation uncertainty.
This leads to CIs with lower actual coverage probability than the nominal confidence level.

Purpose of the Study:

To evaluate the performance of three alternative confidence interval (CI) methods for meta-analysis.
To compare these methods against the standard CI procedure under a random-effects model.
To assess the impact of different heterogeneity variance (tau2) estimators on CI performance.

Main Methods:

A random-effects meta-analysis model was employed.
Eight different tau2 estimators were used to derive study weights.
Performance was evaluated using Monte Carlo simulations comparing the t distribution CI, weighted variance CI, and quantile approximation method.

Main Results:

The weighted variance CI demonstrated superior performance across all tested scenarios.
Outperformance was consistent regardless of the tau2 estimator, tau2 value, number of studies, or sample size.
The weighted variance CI provided more accurate coverage probabilities compared to the standard method and alternatives.

Conclusions:

The weighted variance CI is recommended for meta-analysis to achieve more reliable confidence intervals for effect size estimation.
Standard CI methods may lead to overconfidence due to underestimated variance.
Accurate estimation of heterogeneity variance is crucial for robust meta-analysis CIs.