Required sample size and power for SEM

MacCallum et al. (1996, 1997, 2006) and Kim (2005) propose methods to calculate the required sample size (given a desired power) or the achieved power (given a sample size) to assess the fit of structural equation models based upon different fit indices (e.g. RMSEA or AGFI). The code on this page implements these routines in R and SPSS.

Instructions: Choose the calculation of interest below, fill in the necessary information and press the download button. To run the code, copy and paste it in your R or SPSS syntax window on your computer.

Calculate required sample size

  • For RMSEA (1)

  • For RMSEA (2)

  • For GFI

  • For AGFI

  • For Steigers γ

  • For McDonalds MC

  • For test of no difference between nested models (RMSEA)

  • For test of small difference between nested models (RMSEA)


Calculate power

  • For RMSEA

  • For GFI

  • For AGFI

  • For test of no difference between nested models (RMSEA)

  • For test of small difference between nested models (RMSEA)



Apparently Preacher and Coffman (2006) have already published similar R routines a while ago. You can run their code online, without having to install R on your computer. Check it out.

Some of these routines are also provided in the semTools package in R.

Additionally Friendly (2000) wrote a SAS Macro to conduct these power estimations.


  • Friendly, M. (2000, June).The csmpower macro - Power estimation for Covariance Structure Models [Computer software]. Available from (2008-08-30).
  • Kim, K. H. (2005). The Relation Among Fit Indexes, Power, and Sample Size in Structural Equation Modeling. Structural Equation Modeling, 12, 368-390. doi: 10.1207/s15328007sem1203_2.
  • MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. Psychological Methods, 11, 19-35. doi: 10.1037/1082-989X.11.1.19.
  • MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1, 130-149. doi: 10.1037/1082-989X.1.2.130.
  • MacCallum, R. C. & Hong, S. (1997). Power Analysis in Covariance Structure Modeling Using GFI and AGFI. Multivariate Behavioral Research, 32, 193-210. doi: 10.1207/s15327906mbr3202_5 .
  • Preacher, K. J. & Coffman, D. L. (2006, May). Computing power and minimum sample size for RMSEA [Computer software]. Available from (2012-03-13).


Zuletzt geändert: 2013-08-28 18:09:59
Timo Gnambs

PD Dr. Timo Gnambs

Leibniz Institute for Educational Trajectories
Wilhelmsplatz 3
96047 Bamberg
Germany / Europe

Email: timo@gn[REMOVE THIS PART]


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