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Related Concept Videos

Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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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...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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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...
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Confidence Intervals01:21

Confidence Intervals

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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...
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Estimating Population Mean with Unknown Standard Deviation01:22

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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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...
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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Confidence intervals for a difference between lognormal means in cluster randomization trials.

Julia Poirier1, G Y Zou1,2, John Koval1

  • 11 Department of Epidemiology & Biostatistics, Schulich School of Medicine & Dentistry, Western University, London ON, Canada.

Statistical Methods in Medical Research
|October 1, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical method for analyzing cluster randomization trials with skewed outcome data. The approach provides accurate confidence intervals, improving statistical inference for complex trial designs.

Keywords:
asymmetrycluster randomization trialgeneralized confidence intervallognormal meanmethod of variance estimates recovery

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Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Epidemiology

Background:

  • Cluster randomization trials (CRTs) are increasingly used in public health and medical research.
  • Outcome data in CRTs often exhibit positive skewness, commonly following lognormal distributions.
  • Existing methods for confidence intervals of arithmetic means in CRTs with skewed data have limitations, including restrictive assumptions or implementation complexity.

Purpose of the Study:

  • To develop a straightforward and effective method for constructing confidence intervals for treatment arm arithmetic means in cluster randomization trials with lognormal outcomes.
  • To address the limitations of current statistical procedures for analyzing skewed data in CRTs.

Main Methods:

  • The proposed method models log-transformed outcomes within each treatment arm using a one-way random effects model.
  • It leverages the 'method of variance estimates recovery' to derive closed-form confidence intervals.
  • A simulation study was conducted to evaluate the performance of the new method against existing approaches, assessing empirical coverage, tail error balance, and interval width.

Main Results:

  • The simulation study demonstrated that the proposed method performs well, particularly in small sample sizes.
  • The method achieved favorable empirical coverage probabilities, balanced tail errors, and competitive interval widths compared to existing procedures.
  • The approach proved to be simpler to implement than some alternative methods.

Conclusions:

  • The developed statistical approach offers a practical and reliable solution for calculating confidence intervals in cluster randomization trials with skewed outcome data.
  • This method enhances statistical inference for treatment effects in such trials, offering advantages in simplicity and performance.
  • The utility of the method was illustrated using data from a clinical trial for community-acquired pneumonia.