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Research ArticleOriginal Research

What Is an Intracluster Correlation Coefficient? Crucial Concepts for Primary Care Researchers

Shersten Killip, Ziyad Mahfoud and Kevin Pearce
The Annals of Family Medicine May 2004, 2 (3) 204-208; DOI: https://doi.org/10.1370/afm.141
Shersten Killip
MD, MPH
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Ziyad Mahfoud
PhD
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Kevin Pearce
MD, MPH
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Figures

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  • Figure 1.
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    Figure 1.

    Two-level nesting, or clustering.

  • Figure 2.
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    Figure 2.

    Three-level nesting.

Tables

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    Table 1.

    Effective Sample Size and Power Holding mk Constant

    Number of PhysiciansNumber of PatientsTotal Numberρ= 0.017Power
    km(mk)DEESStTest*
    *Power to detect a minimum effect size of 0.5 when one half the clusters is randomly assigned to treatment and the other half to placebo, and mean responses are compared using a 2-sample t test made at the .05 level of significance.
    m = number of subjects in a cluster; k= number of clusters; mk = total number of subjects in a clustered study; DE = design effect; and ESS = effective sample size.
    4321281.5278461
    8161281.25510270
    1681281.11911475
    3241281.05112278
    6421281.01712679
    12811281.00012880
    • View popup
    Table 2.

    Effective Sample Size and Power Holding k Constant

    Number of PhysiciansNumber of PatientsTotal Numberρ= 0.017Power
    km(mk)DEESStTest*
    *Power to detect a minimum effect size of 0.5 when one half the clusters is randomly assigned to treatment and the other half to placebo, and mean responses are compared using a 2-sample t test made at the .05 level of significance.
    m = number of subjects in a cluster; k= number of clusters; mk = total number of subjects in a clustered study; DE = design effect; and ESS = effective sample size.
    410401.1533429
    420801.3236047
    4401601.6639667
    4803202.34313682
    • View popup
    Table 3.

    Effective Sample Size and Power Holding m Constant

    Number of PhysiciansNumber of PatientsTotal Numberρ= 0.017Power
    km(mk)DEESStTest*
    *Power to detect a minimum effect size of 0.5 when one half the clusters is randomly assigned to treatment and the other half to placebo, and mean responses are compared using a 2-sample t test made at the .05 level of significance.
    m = number of subjects in a cluster; k= number of clusters; mk = total number of subjects in a clustered study; DE = design effect; and ESS = effective sample size.
    210201.1531816
    410401.1533630
    810801.1537050
    16101601.15313883

Additional Files

  • Figures
  • Tables
  • Supplemental Appendix

    Basic Statistical Ideas

    Files in this Data Supplement:

    • Supplemental data: Appendix - PDF file, 1 page, .44 MB.
  • The Article in Brief

    A primary care research study can involve data at both group and individual levels. It is important for researchers to recognize and understand the ways in which this "clustering" can affect their analyses of data.

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The Annals of Family Medicine: 2 (3)
The Annals of Family Medicine: 2 (3)
Vol. 2, Issue 3
1 May 2004
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What Is an Intracluster Correlation Coefficient? Crucial Concepts for Primary Care Researchers
Shersten Killip, Ziyad Mahfoud, Kevin Pearce
The Annals of Family Medicine May 2004, 2 (3) 204-208; DOI: 10.1370/afm.141

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What Is an Intracluster Correlation Coefficient? Crucial Concepts for Primary Care Researchers
Shersten Killip, Ziyad Mahfoud, Kevin Pearce
The Annals of Family Medicine May 2004, 2 (3) 204-208; DOI: 10.1370/afm.141
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  • Article
    • Abstract
    • INTRODUCTION
    • DEFINITION AND EXPLANATION OF CLUSTERED DESIGNS
    • ADVANTAGES AND DISADVANTAGES OF CLUSTERED DESIGNS
    • THE INTRACLUSTER CORRELATION COEFFICIENT, OR ρ
    • EFFECTIVE SAMPLE SIZE AND THE DESIGN EFFECT
    • THE EFFECT OF ρ AND THE DESIGN EFFECT ON POWER AND SAMPLE SIZE CALCULATIONS
    • SUMMARY
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