Online citations, reference lists, and bibliographies.
← Back to Search

Effect Size Measures For Mediation Models: Quantitative Strategies For Communicating Indirect Effects.

K. Preacher, K. Kelley
Published 2011 · Psychology, Medicine

Cite This
Download PDF
Analyze on Scholarcy
Share
The statistical analysis of mediation effects has become an indispensable tool for helping scientists investigate processes thought to be causal. Yet, in spite of many recent advances in the estimation and testing of mediation effects, little attention has been given to methods for communicating effect size and the practical importance of those effect sizes. Our goals in this article are to (a) outline some general desiderata for effect size measures, (b) describe current methods of expressing effect size and practical importance for mediation, (c) use the desiderata to evaluate these methods, and (d) develop new methods to communicate effect size in the context of mediation analysis. The first new effect size index we describe is a residual-based index that quantifies the amount of variance explained in both the mediator and the outcome. The second new effect size index quantifies the indirect effect as the proportion of the maximum possible indirect effect that could have been obtained, given the scales of the variables involved. We supplement our discussion by offering easy-to-use R tools for the numerical and visual communication of effect size for mediation effects.
This paper references
Multivariate analysis in education research
M M Tatsuoka (1973)
10.18637/JSS.V020.I08
Confidence Intervals for Standardized Effect Sizes: Theory, Application, and Implementation
K. Kelley (2007)
10.1037/0022-0167.51.4.473
How to Estimate and Interpret Various Effect Sizes
T. Vacha-Haase (2004)
10.4135/9781446212165
The Sage Handbook of Social Research Methods
Pertti Alasuutari (2008)
10.1002/(SICI)1097-0258(19990115)18:1<107::AID-SIM965>3.0.CO;2-P
Estimating the proportion of treatment effect explained by a surrogate marker.
P. Flandre (1999)
10.3758/BRM.41.2.425
Comparison of methods for constructing confidence intervals of standardized indirect effects
M. Cheung (2009)
10.4135/9781452272054.N2
Contemporary approaches to assessing mediation in communication research.
K. Preacher (2008)
10.1037/1082-989X.2.2.161
On the Logic and Purpose of Significance Testing
J. M. Cortina (1997)
NCES Statistical Standards.
E. Flemming (1992)
10.1146/ANNUREV.PSYCH.59.103006.093735
Sample size planning for statistical power and accuracy in parameter estimation.
S. Maxwell (2008)
10.1097/01.ede.0000147107.76079.07
The Mediation Proportion: A Structural Equation Approach for Estimating the Proportion of Exposure Effect on Outcome Explained by an Intermediate Variable
S. Ditlevsen (2005)
10.3758/BF03192993
Methods for the Behavioral, Educational, and Social Sciences: An R package
K. Kelley (2007)
10.1177/014662168000400309
Large Sample Estimators for Standard Errors of Functions of Correlation Coefficients
P. Bobko (1980)
10.1027/1614-1881.1.2.55
The Controversy over Null Hypothesis Significance Testing Revisited
N. Balluerka (2005)
10.1177/014920630302900106
Effect Size Estimation: Factors to Consider and Mistakes to Avoid
James A. Breaugh (2003)
Magnitudes of experimental effects
W. H. Yeaton (1982)
10.3758/BF03336685
Going beyond tests of significance: Is psychology ready?
D. Dooling (1975)
10.1198/tech.2005.s334
Introduction to Robust Estimation and Hypothesis Testing
J. Kastner (2005)
10.1016/S0378-3758(00)00330-X
Confidence intervals and statistical power of the ‘Validation’ ratio for surrogate or intermediate endpoints
L. Freedman (2001)
Effect size, confidence interval
S. 1136bmj.c869 Nakagawa (2007)
10.1080/10705510802339015
Comparison of Mediated Effects: A Correlation Structure Modeling Approach
T. Raykov (2008)
10.1177/004912418101000203
Standardization in Causal Analysis
Jae-on Kim (1981)
10.1037/1082-989X.7.1.83
A comparison of methods to test mediation and other intervening variable effects.
D. MacKinnon (2002)
10.1002/9780470479216.CORPSY0812
Sample Size Planning
K. Kelley (2010)
An Introduction to the Bootstrap
M. Kenward (2007)
The Complex Nature of Unique and Shared Effects in Hierarchical Linear Regression : Implications for Developmental Psychology
R. Baltes (2001)
Criteria for the validation
M. 014920630302900106 Buyse (1998)
10.5860/choice.45-2315
Handbook of research methods in personality psychology
Richard W. Robins (2007)
10.1093/OXFORDJOURNALS.AJE.A114229
The fallacy of employing standardized regression coefficients and correlations as measures of effect.
S. Greenland (1986)
10.1177/1094428107303161
Meta-Analysis
Frank W. Schmidt (2008)
10.1111/j.1467-9280.2007.01881.x
Statistical Reform in Psychology
G. Cumming (2007)
10.1086/209469
Effect-Size Estimates: Issues and Problems in Interpretation
Edward F. Fern (1996)
Socialization of problem behavior
R. Press. Jessor (1991)
10.1037/0021-9010.69.2.307
Mediators, Moderators, and Tests for Mediation.
L. James (1984)
10.1037/1082-989X.8.4.406
Meta-analysis of raw mean differences.
C. Bond (2003)
PREACHER AND KELLEY
MBESS (Version 3.2.0) [Computer software
K. 108000273170802490632 Kelley (2010)
Variance Explained: Why Size Does Not (Always) Matter
M. Fichman (1999)
The nature of data, or how to choose a correlation
J. B. Carroll (1961)
10.2307/2533853
Criteria for the validation of surrogate endpoints in randomized experiments.
M. Buyse (1998)
10.1007/BF02289768
The nature of the data, or how to choose a correlation coefficient
J. Carroll (1961)
Measures of explained variance: Cautions
K. E. O’Grady (1982)
Confidence Intervals as an Alternative to Significance Testing
E. Brandstätter (1999)
10.1177/0193841X9301700202
Estimating Mediated Effects in Prevention Studies
D. MacKinnon (1993)
Statistical reform in psychology: Is anything changing?
G Cumming (2007)
10.1037/0033-2909.97.2.307
Correlation and the coefficient of determination
D. Ozer (1985)
10.2307/2111095
How Not to Lie with Statistics: Avoiding Common Mistakes in Quantitative Political Science
G. King (1986)
10.1177/0013164401614003
Computing Correct Confidence Intervals for Anova Fixed-and Random-Effects Effect Sizes
Fiona Fidler (2001)
10.1111/j.1469-185X.2007.00027.x
Effect size, confidence interval and statistical significance: a practical guide for biologists
S. Nakagawa (2007)
Mediation in experimental and non
P. E. 0193841X8200600501 Shrout (2002)
Introduction to Robust Estimation and Hypothesis Testing (2nd ed.)
Eric R. Ziegel (2005)
10.1080/00273170701341316
Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions
K. Preacher (2007)
10.2307/2277917
Methods of Correlation Analysis.
H. C. Carver (1931)
Asymptotic and resampling
Oaks (2008)
10.1111/J.0006-341X.2002.00803.X
A measure of the proportion of treatment effect explained by a surrogate marker.
Y. Wang (2002)
10.1207/s15327906mbr4103_1
Quantifying Parsimony in Structural Equation Modeling
K. Preacher (2006)
10.4324/9780203809556
Introduction to Statistical Mediation Analysis
D. MacKinnon (2008)
Contrasts in multiple mediator models.
D. MacKinnon (2000)
10.2307/j.ctvjsf6vm.14
The Fallacy of the
A. Keller (1945)
Analysis of mediating variables in prevention intervention studies Scientific methods for prevention intervention research
D P Mackinnon (1994)
10.1177/0959354300103006
Reporting Practices and APA Editorial Policies Regarding Statistical Significance and Effect Size
T. Vacha-Haase (2000)
Power and accuracy for omnibus
K. 989X.8.3.305 Kelley (2008)
Statistical methods in psychology journals
L Wilkinson (1999)
10.1080/00273170802490632
Sample Size Planning for the Squared Multiple Correlation Coefficient: Accuracy in Parameter Estimation via Narrow Confidence Intervals
K. Kelley (2008)
10.4135/9781506326139.n425
Mediation analysis.
D. MacKinnon (2007)
10.3758/BRM.40.3.879
Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models
K. Preacher (2008)
10.2307/2110737
Measuring Representation: Perils of the Correlation Coefficient
Christopher H. Achen (1977)
10.1080/00220970309600879
It's Not Effect Sizes So Much as Comments About Their Magnitude That Mislead Readers
D. Robinson (2003)
10.1177/0013164401614001
Confidence Intervals for Effect Sizes
X. Fan (2001)
10.15288/JSA.1978.39.948
Problem Behavior and Psychosocial Development; a Longitudinal Study of Youth
E. Labouvie (1978)
10.1177/0013164496056005002
Practical Significance: A Concept Whose Time Has Come
R. Kirk (1996)
10.1177/095935439992002
Defending the Statistical Status Quo
R. Frick (1999)
10.1348/000711008X331024
Covariances between regression coefficient estimates in a single mediator model.
Davood Tofighi (2009)
Reporting practices and APA editorial policies regarding REPORTING EFFECT SIZE FOR MEDIATION statistical significance and effect size
T Vacha-Haase (2000)
10.1037/0003-066X.54.8.594
Statistical Methods in Psychology Journals: Guidelines and Explanations
L. Wilkinson (1999)
10.1037/1082-989X.2.1.3
Optimal design in psychological research.
Gary H. McClelland (1997)
10.1136/bmj.c869
CONSORT 2010 Explanation and Elaboration: updated guidelines for reporting parallel group randomised trials
D. Moher (2010)
10.3102/0013189X035006033
Standards for Reporting on Empirical Social Science Research in AERA Publications
P. Moss (2006)
10.1080/01621459.1987.10478410
Better Bootstrap Confidence Intervals
B. Efron (1987)
Standardized or simple effect
T. Author. Baguley (2009)
10.1037/0022-3514.51.6.1173
The moderator-mediator variable distinction in social psychological research: conceptual, strategic, and statistical considerations.
R. M. Baron (1986)
Confidence intervals for standardized effect
httpwww.murray.harvard.edu (2007)
10.1093/HER/11.4.501
The law of maximum expected potential effect: constraints placed on program effectiveness by mediator relationships
W. Hansen (1996)
10.1177/001316447203200315
A Note on the Restriction of Range for Pearson Product-Moment Correlation Coefficients
L. Hubert (1972)
Evaluating effect size in personality research
R. W. Robins (2007)
Quantifying parsimony in structural equation
K. J. Guilford Press. Preacher (2006)
10.1037/1082-989X.12.1.23
Bias in cross-sectional analyses of longitudinal mediation.
S. Maxwell (2007)
10.1037/0021-9010.83.5.798
Determining relative importance of predictors with the observational design.
J. M. Cortina (1998)
10.1177/0011000005283558
Effect-Size Measures and Meta-Analytic Thinking in Counseling Psychology Research
Robin K Henson (2006)
10.3102/0013189X031003025
What Future Quantitative Social Science Research Could Look Like: Confidence Intervals for Effect Sizes
B. Thompson (2002)
Socialization of problem behavior in youth [Data file and code book
R Jessor (1991)
10.1057/JORS.1983.42
Sociological Methodology 1982
R. G. Stansfield (1983)
10.1007/3-540-45354-7_9
A Simulation Study to
Explore Configuring (2004)
10.1037/0033-2909.114.2.376
Statistical difficulties of detecting interactions and moderator effects.
G. Mcclelland (1993)
10.1037/1082-989X.8.3.305
Sample size for multiple regression: obtaining regression coefficients that are accurate, not simply significant.
K. Kelley (2003)
10.1177/00131640121971392
Correct Confidence Intervals for Various Regression Effect Sizes and Parameters: The Importance of Noncentral Distributions in Computing Intervals
M. Smithson (2001)
10.1002/EJSP.270
The burden of benevolent sexism: how it contributes to the maintenance of gender inequalities
M. Barreto (2005)
10.1002/SIM.1847
Statistical assessment of mediational effects for logistic mediational models.
B. Huang (2004)
10.1037/0021-843X.112.4.558
Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling.
D. Cole (2003)
10.1348/000712608X377117
Standardized or simple effect size: what should be reported?
Thom Baguley (2009)
10.2307/270723
Asymptotic Confidence Intervals for Indirect Effects in Structural Equation Models
M. Sobel (1982)
10.1207/S15327906MBR3001_3
A Simulation Study of Mediated Effect Measures.
D. MacKinnon (1995)
Confidence intervals and statistical power
L. S. Freedman (2001)
10.1080/00220973.1993.10806594
Evaluating Results Using Corrected and Uncorrected Effect Size Estimates
P. Snyder (1993)
Estimating mediated effects
Mahwah (1993)
10.1037//1082-989x.7.4.422
Mediation in experimental and nonexperimental studies: new procedures and recommendations.
P. Shrout (2002)
10.1177/0013164402062002001
Confidence Intervals for Effect Sizes in Analysis of Variance
K. Bird (2002)
10.4324/9781410601155
Statistics As Principled Argument
R. Abelson (1995)
10.1177/0193841X8200600501
Magnitudes of Experimental Effects in Social Science Research
L. Sechrest (1982)
10.2307/2529115
Statistical Power Analysis for the Behavioral Sciences
J. Cohen (1969)
10.1002/PITS.20234
Effect sizes, confidence intervals, and confidence intervals for effect sizes
B. Thompson (2007)
10.1037/0033-2909.92.3.766
Measures of explained variance: Cautions and limitations.
K. E. O’grady (1982)
10.1037/1082-989X.12.1.1
Methods for integrating moderation and mediation: a general analytical framework using moderated path analysis.
J. Edwards (2007)
Analysis of mediating variables in prevention intervention studies
D. P. MacKinnon (1994)
Standards for Reporting on Empirical Social Science Research in AERA Publications American Educational Research Association
B. Schneider (2006)
Multivariate analysis in education research
B. Thompson (1973)
10.3109/07380577.2011.629024
Publication Manual of the American Psychological Association
Kate E Decleene (2012)
10.1002/SIM.3016
Mediation analysis via potential outcomes models.
J. Albert (2008)
Effect sizes for research: A broad practical approach.
Robert J. Grissom (2005)
10.2307/2094445
The Decomposition of Effects in Path Analysis
D. Alwin (1975)
10.3758/BRM.41.2.486
R2 effect-size measures for mediation analysis
Amanda J Fairchild (2009)
10.1037/e495892006-009
Analysis of mediating variables in prevention and intervention research.
D. MacKinnon (1994)
10.2466/pr0.2002.91.3.955
Least Sum of Euclidean Regression Residuals: Estimation of Effect Size
K. Berry (2002)
Publication manual of the
(2010)
10.2307/2290095
Statistical Power Analysis for the Behavioral Sciences (2nd ed.)
P. Lachenbruch (1989)
10.3200/JEXE.75.2.109-125
Is the Pearson r 2 Biased, and if So, What Is the Best Correction Formula?
Zhongmiao Wang (2007)
10.4135/9781452272054
The Sage sourcebook of advanced data analysis methods for communication research
A. Hayes (2008)
Evaluating effect size in personality research
D J Ozer (2007)
The controversy over null
N. 000712608X377117 Balluerka (2005)
10.1177/0013164401614002
A Primer on the Understanding, Use, and Calculation of Confidence Intervals that are Based on Central and Noncentral Distributions
G. Cumming (2001)
10.1002/JOB.406
Clarifying conditions and decision points for mediational type inferences in Organizational Behavior
J. Mathieu (2006)



This paper is referenced by
“I Don’t Care About Politics, I Just Like That Guy!” Affective Disposition and Political Attributes in Information Processing of Political Talk Shows
C. Weinmann (2017)
10.1177/0361684316630965
STEM Stereotypic Attribution Bias Among Women in an Unwelcoming Science Setting
J. LaCosse (2016)
10.1016/J.PAID.2015.03.016
How forgiveness affects processing time: Mediation by rumination about the transgression
Ramzi Fatfouta (2015)
10.1080/10810730.2015.1061071
Health Literacy and Patient-Reported Outcomes: A Cross-Sectional Study of Underserved English- and Spanish-Speaking Patients With Type 2 Diabetes
E. Hahn (2015)
10.1016/J.LEARNINSTRUC.2016.12.001
Autonomy and competence frustration in young adolescent classrooms: Different associations with active and passive disengagement
Stephen R. Earl (2017)
10.1007/s10865-017-9891-6
Bidirectional mediation of depression and pain intensity on their associations with upper extremity physical function
M. Talaei-Khoei (2017)
10.1007/S10826-017-0789-2
The Relationship between Cultural Identification, Family Socialization and Adolescent Alcohol Use among Native American Families
Zhyldyz Urbaeva (2017)
10.1017/BEC.2018.13
The Mediating Relationship between Maladaptive Behaviours, Cognitive Factors, and Generalised Anxiety Disorder Symptoms
A. Mahoney (2018)
10.1177/1359104517712041
Interpersonal rejection sensitivity mediates the associations between peer victimization and two high-risk outcomes
Caitlin A. Williams (2017)
10.1038/ncomms15193
A peripheral epigenetic signature of immune system genes is linked to neocortical thickness and memory
V. Freytag (2017)
10.1037/tra0000259
Posttraumatic Stress Symptoms and Marital Adjustment Among Israeli Combat Veterans: The Role of Loneliness and Attachment
Liat Itzhaky (2017)
10.5993/AJHB.38.4.8
Emotion dysregulation and coping drinking motives in college women.
T. Messman‐Moore (2014)
10.1037/a0036672
Observed parental responsiveness/warmth and children's coping: cross-sectional and prospective relations in a family depression preventive intervention.
Kelly H. Watson (2014)
10.1108/JMP-03-2016-0085
Older workers’ representation and age-based stereotype threats in the workplace
Eduardo André da Silva Oliveira (2017)
10.1002/smi.2689
Grin and Bear It?: Employees' Use of Surface Acting During Co‐worker Conflict
A. Nixon (2017)
10.1007/S10826-016-0495-5
Do Children’s Attributions Mediate the Link Between Parental Conditional Regard and Child Depression and Emotion?
Laura Perrone (2016)
10.1590/1806-9282.64.05.420
Functionality, comorbidity, complication & surgery of hip fracture in older adults by age distribution.
Sonia Jiménez-Mola (2018)
10.1007/s12529-016-9562-y
Negative Stress Beliefs Predict Somatic Symptoms in Students Under Academic Stress
S. Fischer (2016)
10.1080/10496491.2020.1829772
Toward a Psychosocial Model of Employees’ Participation in Corporate Social Responsibility. Evidence from Italian Small and Medium-Sized Enterprises
Gianvito D'Aprile (2020)
10.1016/j.jpsychires.2020.10.017
Salivary markers of stress system activation and social withdrawal in humans.
S. Bauduin (2020)
10.1371/journal.pone.0238020
The effect of religiosity on violence: Results from a Brazilian population-based representative survey of 4,607 individuals
J. P. B. Gonçalves (2020)
10.1177/0018720815582261
The Role of Trust as a Mediator Between System Characteristics and Response Behaviors
Eric T. Chancey (2015)
10.1177/0033294118787496
Self-Efficacy as a Mechanism Linking Daily Stress to Mental Health in Students: A Three-Wave Cross-Lagged Study
P. Schönfeld (2018)
10.1007/s12144-019-00485-6
Perceived autonomy-supportive parenting and internet addiction: respiratory sinus arrhythmia moderated the mediating effect of basic psychological need satisfaction
D. Liu (2019)
10.1016/j.jad.2020.07.088
Role of anxiety, depression and neurocognition for cognitive behavioural therapy pre-therapy skills in people living with dementia, older and younger adults✰.
J. Stott (2020)
10.1037/spq0000301
Religious Head Covering, Being Perceived as Foreigners, Victimization, and Adjustment Among Sikh American Adolescents
K. Atwal (2019)
10.1007/s11251-019-09490-5
Examining Chinese kindergarten children’s psychological needs satisfaction in problem solving: A self-determination theory perspective
Heyi Zhang (2019)
10.1016/J.CHILDYOUTH.2018.10.021
The relationship between parental conflict and preschool children's behavior problems: A moderated mediation model of parenting stress and child emotionality
X. Xuan (2018)
10.1016/J.JSR.2019.04.002
How do organizational practices relate to perceived system safety effectiveness? Perceptions of safety climate and co-worker commitment to safety as workplace safety signals.
Madelynn R D Stackhouse (2019)
10.15703/KJC.16.3.201506.253
The Influence of Internalized Shame on the Drinking Problems Among College Students: The Mediating Effects of Dysfunctional Anger Expression
김누리 (2015)
10.1371/journal.pone.0154140
Direct and Indirect Effects of Five Factor Personality and Gender on Depressive Symptoms Mediated by Perceived Stress
S. Kim (2016)
10.1016/J.JVB.2018.10.011
Applying career construction model of adaptation to career transition in adolescence: A two-study paper
Iva Šverko (2019)
See more
Semantic Scholar Logo Some data provided by SemanticScholar