Skip to main content
. Author manuscript; available in PMC: 2010 Jan 15.
Published in final edited form as: Comput Stat Data Anal. 2009 Jan 15;53(3):603–608. doi: 10.1016/j.csda.2008.06.010

Table 2.

Sample Size Required for Theoretical Statistical Power of 90% to Detect the Main Effect and the Interaction of Two Binary Fixed Effects in a Mixed-Effects Linear Regression Model with a Random Intercept

k=4 k=6 k=8
Main Effect Interaction Main Effect Interaction Main Effect Interaction
ICC
(ρ )		 Standardized
Effect (Δm)		 N(Δ1) Empirical
Power		 N(Δ3) Empirical
Power		 N(Δ1) Empirical
Power		 N(Δ3) Empirical
Power		 N(Δ1) Empirical
Power		 N(Δ3) Empirical
Power
0.20 .20 422 0.897 1688 0.890 352 0.900 1408 0.903 316 0.898 1264 0.903
.25 270 0.903 1080 0.902 226 0.897 904 0.896 202 0.895 808 0.898
.30 188 0.903 752 0.902 156 0.901 624 0.905 142 0.905 568 0.909
.35 138 0.897 552 0.902 116 0.901 464 0.905 104 0.904 416 0.902
.40 106 0.897 424 0.905 88 0.900 352 0.903 80 0.901 320 0.900
.45 84 0.902 336 0.900 70 0.897 280 0.902 64 0.911 256 0.913
.50 68 0.907 272 0.902 58 0.912 232 0.915 52 0.910 208 0.919
0.40 .20 578 0.897 2312 0.909 526 0.899 2104 0.902 500 0.902 2000 0.902
.25 370 0.894 1480 0.907 338 0.900 1352 0.899 320 0.905 1280 0.902
.30 258 0.896 1032 0.907 234 0.901 936 0.902 222 0.902 888 0.902
.35 190 0.907 760 0.897 172 0.900 688 0.899 164 0.894 656 0.900
.40 146 0.905 584 0.899 132 0.903 528 0.903 126 0.905 504 0.898
.45 116 0.904 464 0.907 104 0.902 416 0.904 100 0.906 400 0.900
.50 94 0.904 376 0.901 86 0.909 344 0.906 80 0.898 320 0.900
0.60 .20 736 0.901 2944 0.893 702 0.907 2808 0.907 684 0.899 2736 0.897
.25 472 0.903 1888 0.898 450 0.897 1800 0.914 438 0.901 1752 0.903
.30 328 0.895 1312 0.903 312 0.900 1248 0.900 304 0.895 1216 0.889
.35 242 0.905 968 0.902 230 0.901 920 0.904 224 0.901 896 0.902
.40 184 0.899 736 0.907 176 0.904 704 0.898 172 0.900 688 0.904
.45 146 0.902 584 0.899 140 0.908 560 0.906 136 0.905 544 0.907
.50 118 0.901 472 0.894 114 0.906 456 0.905 110 0.908 440 0.903

Notes:

1

k represents the number of observations per subject.

2

The sample sizes required to detect a main effect N(Δ1) or an interaction N(Δ3) represent the total sample size, based on equations (3) and (4), respectively and assume power of 90% and a two-tailed alpha-level of .05.

3

Empirical power is based on analyses of 6000 simulated data sets for each combination of parameter specifications.