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Related Concept Videos

Confidence Coefficient01:24

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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...
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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
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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.
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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.
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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
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A comment on sample size calculations for binomial confidence intervals.

Lai Wei1, Alan D Hutson1

  • 1Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA.

Journal of Applied Statistics
|March 19, 2016
PubMed
Summary
This summary is machine-generated.

New sample size calculations ensure desired confidence interval width for binomial proportions. This adjusted method maintains coverage probability with fewer participants, improving efficiency in statistical studies.

Keywords:
Agresti—Coull intervalWald intervalWilson Score intervalbinomial proportionexpected widthsample size calculation

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Inference

Background:

  • Accurate sample size calculation is crucial for reliable statistical inference.
  • Common methods for binomial proportions may not guarantee desired confidence interval width.
  • Existing methods often rely on fixed standard errors, which can be problematic with hypothesized proportions.

Purpose of the Study:

  • To evaluate sample size calculations for binomial proportions based on confidence interval width.
  • To introduce a new adjusted sample size calculation method.
  • To compare the performance of the new method against existing ones.

Main Methods:

  • Examination of sample size calculations for binomial proportions using Agresti-Coull, Wald, and Wilson Score intervals.
  • Development of an adjusted sample size calculation method based on the conditional expectation of the confidence interval width.
  • Comparison of coverage probability and efficiency with existing methods.

Main Results:

  • Commonly used sample size calculation methods may fail to ensure the desired confidence interval width.
  • The newly introduced adjusted method effectively guarantees the desired confidence interval width.
  • The adjusted method achieves nominal coverage probability with a reduced sample size.

Conclusions:

  • The proposed adjusted sample size calculation method offers an improvement over traditional approaches.
  • This method provides a more reliable way to determine sample sizes for binomial proportions.
  • The findings have implications for efficient study design in various scientific fields.