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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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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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Sample Size Planning for the Squared Multiple Correlation Coefficient: Accuracy in Parameter Estimation via Narrow

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This summary is machine-generated.

This study introduces new methods for sample size planning in multiple regression to ensure narrow confidence intervals for the squared multiple correlation coefficient. These techniques, implemented in the MBESS R package, help researchers achieve precise estimates with desired confidence.

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Area of Science:

  • Statistics
  • Quantitative Psychology
  • Health Services Research

Background:

  • Accurate sample size planning is crucial for reliable statistical inference.
  • Existing methods may not adequately address confidence interval precision for the squared multiple correlation coefficient with random regressors.
  • The accuracy in parameter approach offers a framework for sample size determination based on desired precision.

Purpose of the Study:

  • To develop and present methods for sample size planning in multiple regression.
  • To ensure sufficiently narrow confidence intervals for the population squared multiple correlation coefficient.
  • To provide methods that guarantee a desired level of assurance for interval width.

Main Methods:

  • Developed approximate and exact methods for sample size calculation.
  • Incorporated the accuracy in parameter approach.
  • Modified methods to achieve desired assurance levels for confidence interval width.
  • Utilized the MBESS R package for implementation.

Main Results:

  • Provided methods to determine sample sizes for achieving narrow confidence intervals for the squared multiple correlation coefficient.
  • Developed techniques to ensure a specified degree of assurance for confidence interval precision.
  • Demonstrated the application of methods with an empirical example.

Conclusions:

  • The developed methods offer robust approaches to sample size planning in multiple regression.
  • The MBESS R package facilitates the practical implementation of these advanced statistical techniques.
  • These methods enhance the precision and reliability of estimates for the squared multiple correlation coefficient in research.