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Confidence Intervals for Standardized Effect Sizes: Theory, Application, and Implementation

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  • Kelley, Ken

Abstract

The behavioral, educational, and social sciences are undergoing a paradigmatic shift in methodology, from disciplines that focus on the dichotomous outcome of null hypothesis significance tests to disciplines that report and interpret effect sizes and their corresponding confidence intervals. Due to the arbitrariness of many measurement instruments used in the behavioral, educational, and social sciences, some of the most widely reported effect sizes are standardized. Although forming confidence intervals for standardized effect sizes can be very beneficial, such confidence interval procedures are generally difficult to implement because they depend on noncentral t, F, and x2 distributions. At present, no main-stream statistical package provides exact confidence intervals for standardized effects without the use of specialized programming scripts. Methods for the Behavioral, Educational, and Social Sciences (MBESS) is an R package that has routines for calculating confidence intervals for noncentral t, F, and x2 distributions, which are then used in the calculation of exact confidence intervals for standardized effect sizes by using the confidence interval transformation and inversion principles. The present article discusses the way in which confidence intervals are formed for standardized effect sizes and illustrates how such confidence intervals can be easily formed using MBESS in R.

Suggested Citation

  • Kelley, Ken, 2007. "Confidence Intervals for Standardized Effect Sizes: Theory, Application, and Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i08).
    • Handle: RePEc:jss:jstsof:v:020:i08
    DOI: http://hdl.handle.net/10.18637/jss.v020.i08
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    References listed on IDEAS

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    1. Ding, Cherng G., 1996. "On the computation of the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 345-350, August.
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    Cited by:

    1. Paul Dudgeon, 2017. "Some Improvements in Confidence Intervals for Standardized Regression Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 928-951, December.
    2. repec:jss:jstsof:20:i01 is not listed on IDEAS
    3. Marko Hofmann & Silja Meyer-Nieberg, 2018. "Time to dispense with the p-value in OR?," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 193-214, March.
    4. Doll, Monika, 2017. "Relative efficiency of confidence interval methods around effect sizes," FAU Discussion Papers in Economics 22/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    5. Alan Agresti & Maria Kateri, 2017. "Ordinal probability effect measures for group comparisons in multinomial cumulative link models," Biometrics, The International Biometric Society, vol. 73(1), pages 214-219, March.
    6. Jeff Jones & Niels Waller, 2015. "The Normal-Theory and Asymptotic Distribution-Free (ADF) Covariance Matrix of Standardized Regression Coefficients: Theoretical Extensions and Finite Sample Behavior," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 365-378, June.

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