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Related Concept Videos

Uncertainty: Confidence Intervals00:54

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...
Interpretation of Confidence Intervals01:19

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 Intervals01:21

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...
Confidence Interval for Estimating Population Mean01:25

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

Estimating Population Mean with Known Standard Deviation

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 + error bound)
The...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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 Guinness...

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Related Experiment Video

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A Two-interval Forced-choice Task for Multisensory Comparisons
07:13

A Two-interval Forced-choice Task for Multisensory Comparisons

Published on: November 9, 2018

Confidence intervals for two sample means: Calculation, interpretation, and a few simple rules.

Roland Pfister1, Markus Janczyk

  • 1Department of Psychology III, Julius Maximilians University of Würzburg, Germany.

Advances in Cognitive Psychology
|July 5, 2013
PubMed
Summary
This summary is machine-generated.

This study clarifies the use of confidence intervals (CIs) for psychological research, particularly for within-subjects designs. It provides practical guidance for researchers to confidently apply CIs in their statistical analyses and reporting.

Keywords:
between-subjects designsconfidence intervalsgraphical data presentationrepeated measureswithin-subjects designs

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Last Updated: May 10, 2026

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Area of Science:

  • Psychology
  • Statistics
  • Cognitive Science

Background:

  • Standard errors (SEs) and confidence intervals (CIs) are crucial statistical concepts.
  • Their application, especially for within-subjects designs in psychological literature, remains a point of confusion and debate.
  • Recent publications have offered solutions, but a clear introduction is still needed.

Purpose of the Study:

  • To provide a straightforward introduction to the principles of confidence interval (CI) construction.
  • To encourage the use of CIs in psychological reports and presentations.
  • To clarify the application of CIs for both between- and within-subjects designs.

Main Methods:

  • Focuses on the statistical inference of comparing two sample means.
  • Describes the construction of CIs for both between-subjects and within-subjects designs.
  • Provides hands-on examples for computing CIs.

Main Results:

  • Demonstrates how to calculate CIs for comparing two sample means.
  • Illustrates the relationship between CIs and classical t-tests.
  • Offers practical guidance for implementing CIs in cognitive psychology research.

Conclusions:

  • Confidence intervals (CIs) are valuable tools for statistical inference in psychology.
  • Understanding CI construction, especially for within-subjects designs, enhances research reporting.
  • This paper aims to demystify CIs and promote their consistent use among students and researchers.