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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...
Contaminants and Errors01:16

Contaminants and Errors

Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
Another key consideration is determining the appropriate number of samples required to...
Confidence Coefficient01:24

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...
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 Standard Deviation01:26

Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...

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Related Experiment Video

Updated: May 28, 2026

Sampling Soils in a Heterogeneous Research Plot
07:11

Sampling Soils in a Heterogeneous Research Plot

Published on: January 7, 2019

Sample size planning for composite reliability coefficients: accuracy in parameter estimation via narrow confidence

Leann Terry1, Ken Kelley

  • 1Pennsylvania State University, University Park, Pennsylvania, USA.

The British Journal of Mathematical and Statistical Psychology
|October 21, 2011
PubMed
Summary

Researchers can now plan sample size to achieve narrow confidence intervals for composite measure reliability. This ensures more precise estimates of reliability, crucial for psychological research and improving score interpretation.

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Area of Science:

  • Psychometrics
  • Psychology
  • Statistical Modeling

Background:

  • Composite measures are widely used in psychology but contain error.
  • Reliability of composite measures is essential for accurate interpretation.
  • Point estimates of reliability require confidence intervals due to fallibility.

Purpose of the Study:

  • To develop methods for planning sample size to obtain narrow confidence intervals for reliability coefficients.
  • To address the issue of wide confidence intervals and uncertainty in reliability estimates.
  • To provide researchers with tools for achieving accurate reliability estimates.

Main Methods:

  • Discussion of composite reliability coefficients and confidence interval formation.
  • Development of two sample size planning methods based on the accuracy in parameter estimation approach.
  • Verification of methods using Monte Carlo simulation studies.

Main Results:

  • Proposed methods effectively enable researchers to plan sample sizes for narrow confidence intervals.
  • The methods ensure desired precision in population reliability coefficient estimates.
  • Effectiveness validated through simulations, with accessible software provided.

Conclusions:

  • Accurate reliability estimation is vital in psychological research.
  • The developed methods offer practical solutions for sample size planning.
  • Researchers can now better control the precision of reliability estimates.