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 1.

Sample Size Required for Theoretical Statistical Power of 80% 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 .20 314 0.808 1256 0.796 262 0.808 1048 0.803 236 0.803 944 0.798
.25 202 0.796 808 0.804 168 0.806 672 0.801 152 0.809 608 0.799
.30 140 0.806 560 0.801 118 0.802 472 0.814 106 0.813 424 0.815
.35 104 0.813 416 0.815 86 0.811 344 0.795 78 0.810 312 0.803
.40 80 0.796 320 0.800 66 0.791 264 0.800 60 0.801 240 0.811
.45 64 0.811 256 0.810 52 0.799 208 0.811 48 0.815 192 0.814
.50 52 0.817 208 0.809 42 0.798 168 0.804 38 0.798 152 0.799
0.40 .20 432 0.798 1728 0.795 394 0.788 1576 0.795 374 0.807 1496 0.799
.25 278 0.805 1112 0.812 252 0.805 1008 0.803 240 0.803 960 0.808
.30 192 0.797 768 0.801 176 0.805 704 0.803 166 0.806 664 0.798
.35 142 0.796 568 0.803 130 0.804 520 0.811 122 0.801 488 0.811
.40 108 0.808 432 0.798 100 0.808 400 0.816 94 0.808 376 0.799
.45 86 0.808 344 0.808 78 0.807 312 0.799 74 0.805 296 0.797
.50 70 0.804 280 0.808 64 0.810 256 0.806 60 0.794 240 0.805
0.60 .20 550 0.796 2200 0.797 524 0.817 2096 0.796 512 0.810 2048 0.798
.25 352 0.798 1408 0.793 336 0.797 1344 0.802 328 0.800 1312 0.802
.30 246 0.799 984 0.808 234 0.804 936 0.808 228 0.801 912 0.803
.35 180 0.799 720 0.803 172 0.800 688 0.800 168 0.803 672 0.806
.40 138 0.798 552 0.807 132 0.801 528 0.801 128 0.794 512 0.800
.45 110 0.811 440 0.806 104 0.800 416 0.812 102 0.801 408 0.803
.50 88 0.809 352 0.797 84 0.801 336 0.801 82 0.809 328 0.808

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 80% 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.