### Abstract

The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

Original language | English (US) |
---|---|

Pages (from-to) | 99-128 |

Number of pages | 30 |

Journal | Multivariate Behavioral Research |

Volume | 39 |

Issue number | 1 |

State | Published - 2004 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Statistics and Probability
- Social Sciences (miscellaneous)
- Psychology(all)
- Experimental and Cognitive Psychology

### Cite this

*Multivariate Behavioral Research*,

*39*(1), 99-128.

**Confidence limits for the indirect effect : Distribution of the product and resampling methods.** / Mackinnon, David; Lockwood, Chondra M.; Williams, Jason.

Research output: Contribution to journal › Article

*Multivariate Behavioral Research*, vol. 39, no. 1, pp. 99-128.

}

TY - JOUR

T1 - Confidence limits for the indirect effect

T2 - Distribution of the product and resampling methods

AU - Mackinnon, David

AU - Lockwood, Chondra M.

AU - Williams, Jason

PY - 2004

Y1 - 2004

N2 - The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

AB - The most commonly used method to test an indirect effect is to divide the estimate of the indirect effect by its standard error and compare the resulting z statistic with a critical value from the standard normal distribution. Confidence limits for the indirect effect are also typically based on critical values from the standard normal distribution. This article uses a simulation study to demonstrate that confidence limits are imbalanced because the distribution of the indirect effect is normal only in special cases. Two alternatives for improving the performance of confidence limits for the indirect effect are evaluated: (a) a method based on the distribution of the product of two normal random variables, and (b) resampling methods. In Study 1, confidence limits based on the distribution of the product are more accurate than methods based on an assumed normal distribution but confidence limits are still imbalanced. Study 2 demonstrates that more accurate confidence limits are obtained using resampling methods, with the bias-corrected bootstrap the best method overall.

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UR - http://www.scopus.com/inward/citedby.url?scp=3042811867&partnerID=8YFLogxK

M3 - Article

VL - 39

SP - 99

EP - 128

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

IS - 1

ER -