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Related Concept Videos

Uncertainty: Confidence Intervals00:54

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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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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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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.
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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.
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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.
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Absolute precision confidence intervals for unstandardized mean differences using sequential stopping rules.

Douglas A Fitts1

  • 1University of Washington, Snohomish, WA, 98290, USA. dfitts@uw.edu.

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|June 29, 2022
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Summary

Sequential stopping rules (SSR) offer a cost-effective way to achieve precise confidence intervals (CIs) for effect sizes in psychology research. SSRs ensure desired CI width, unlike fixed-sample rules, while maintaining accurate statistical coverage.

Keywords:
Effect sizeMean differencesOptional stoppingPoint and interval estimation

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Area of Science:

  • Psychology
  • Statistical Methods

Background:

  • Psychology journals advocate for confidence intervals (CIs) on effect sizes.
  • Achieving maximum CI precision with minimal cost is a key research objective.

Purpose of the Study:

  • To compare fixed-sample rule (FSR) methods with sequential stopping rules (SSR) for calculating confidence intervals.
  • To evaluate the efficiency and accuracy of SSRs in achieving desired confidence interval widths and coverage.

Main Methods:

  • Focus on unstandardized widths for confidence intervals of mean differences.
  • Investigated sequential stopping rules (SSR) and their impact on CI coverage.
  • Utilized simulations to assess SSR methods with manipulated sample sizes, desired widths, and confidence coefficients.

Main Results:

  • Sequential stopping rules (SSR) can consistently produce confidence intervals (CIs) of a desired width.
  • SSRs demonstrate comparable average sample size to FSR without assurance, but with guaranteed width.
  • Improper SSR use can degrade CI coverage, but specific SSR methods ensure nominal or near-nominal coverage.

Conclusions:

  • Sequential stopping rules (SSR) provide a more efficient and reliable approach to obtaining precise confidence intervals (CIs) in psychological research compared to fixed-sample rules.
  • Careful implementation of SSR methods is crucial to maintain accurate statistical coverage and ensure the validity of research findings.