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Related Concept Videos

Sample Size Calculation01:19

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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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The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except for one difference— experimental manipulation. The experimental group gets the experimental manipulation—that is, the treatment or variable being tested—and the control group does not. Since experimental manipulation is the only difference between the experimental and control groups, we can be sure that any differences between...
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Generalized SAMPLE SIZE Determination Formulas for Investigating Contextual Effects by a Three-Level Random Intercept

Satoshi Usami1

  • 1University of Tsukuba, Tsukuba, Japan. usamis@human.tsukuba.ac.jp.

Psychometrika
|November 3, 2016
PubMed
Summary

Researchers can now determine necessary sample sizes for studying contextual effects using generalized formulas. These formulas, based on a three-level model, help achieve desired statistical power and confidence interval width for behavioral and psychological research.

Keywords:
confidence intervalcontextual effectsmultilevel modelsample size determinationstatistical power

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Area of Science:

  • Behavioral and psychological sciences
  • Multilevel modeling
  • Statistical power analysis

Background:

  • Contextual effects, the influence of combined individual- and group-level predictors on outcomes, are of significant interest in behavioral and psychological research.
  • Accurate sample size determination is crucial for reliable investigation of these effects.

Purpose of the Study:

  • To provide generalized formulas for calculating sample size in multilevel contextual effects research.
  • To simplify sample size determination by investigating the influence of various indices on standard errors.

Main Methods:

  • Derivation of sample size formulas within a three-level random intercept model.
  • Inclusion of one predictor/contextual variable at each level to encompass diverse contextual effects.
  • Investigation of the relative influence of formula indices on standard errors.

Main Results:

  • Simulation studies revealed that calculated statistical power can exhibit bias.
  • Sample size estimates can be positively or negatively biased due to unreliability, multicollinearity, and assumption violations.
  • The derived formulas offer a method for sample size calculation in multilevel contextual effects studies.

Conclusions:

  • The developed formulas provide a framework for sample size estimation in multilevel contextual effects research.
  • Researchers should consider potential biases in sample size estimates by evaluating various index specifications.
  • Careful consideration of model assumptions and variable characteristics is essential for accurate sample size planning.