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. 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 3.

Sample Size Required for Theoretical Statistical Power of 95% 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 .20 520 0.953 2080 0.944 434 0.952 1736 0.948 390 0.947 1560 0.950
.25 334 0.948 1336 0.953 278 0.953 1112 0.949 250 0.947 1000 0.953
.30 232 0.951 928 0.954 194 0.955 776 0.949 174 0.951 696 0.953
.35 170 0.954 680 0.951 142 0.954 568 0.949 128 0.949 512 0.949
.40 130 0.954 520 0.950 110 0.956 440 0.948 98 0.950 392 0.953
.45 104 0.952 416 0.956 86 0.954 344 0.951 78 0.955 312 0.954
.50 84 0.951 336 0.947 70 0.945 280 0.955 64 0.957 256 0.957
0.40 .20 716 0.952 2864 0.950 650 0.956 2600 0.952 618 0.946 2472 0.950
.25 458 0.952 1832 0.947 416 0.948 1664 0.952 396 0.948 1584 0.953
.30 318 0.947 1272 0.951 290 0.954 1160 0.949 276 0.946 1104 0.949
.35 234 0.952 936 0.952 214 0.954 856 0.950 202 0.952 808 0.952
.40 180 0.948 720 0.948 164 0.951 656 0.952 156 0.955 624 0.954
.45 142 0.949 568 0.952 130 0.950 520 0.950 122 0.950 488 0.952
.50 116 0.952 464 0.952 104 0.955 416 0.956 100 0.956 400 0.952
0.60 .20 910 0.942 3640 0.953 868 0.950 3472 0.953 846 0.953 3384 0.952
.25 584 0.950 2336 0.952 556 0.949 2224 0.946 542 0.952 2168 0.952
.30 406 0.956 1624 0.951 386 0.950 1544 0.946 376 0.948 1504 0.950
.35 298 0.953 1192 0.942 284 0.957 1136 0.960 276 0.946 1104 0.951
.40 228 0.950 912 0.952 218 0.951 872 0.952 212 0.953 848 0.948
.45 180 0.951 720 0.946 172 0.948 688 0.949 168 0.949 672 0.955
.50 146 0.948 584 0.952 140 0.952 560 0.953 136 0.952 544 0.955

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 95% 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.