Testing for Main Random Effects in Two-Way Random and Mixed Effects Models: Modifying the 𝐹 Statistic

Table 1

Comparison of achieved type I error rates and power for 𝑆_𝐵,mixed, 𝑆_𝐵,rand, and 𝐹 with 𝑁=1000 tests for the random and mixed effects models.

	Random effects model								Mixed effects model
	Balanced				Unbalanced				Balanced				Unbalanced
	𝛼=.05		𝛼=.10		𝛼=.05		𝛼=.10		𝛼=.05		𝛼=.10		𝛼=.05		𝛼=.10
	𝑆𝐵	𝐹	𝑆𝐵	𝐹	𝑆𝐵	𝐹	𝑆𝐵	𝐹	𝑆𝐵	𝐹	𝑆𝐵	𝐹	𝑆𝐵	𝐹	𝑆𝐵	𝐹
Homo.
𝐻0	.054	.220	.111	.247	.049	.167	.092	.198	.065	.047	.112	.099	.063	.045	.109	.086
𝐴1	.053	.229	.123	.265	.069	NA	.140	NA	.227	.187	.318	.296	.184	.138	.260	.228
𝐴2	.125	.337	.221	.367	.113	NA	.201	NA	.761	.719	.820	.804	.542	.489	.634	.638
𝐴3	.236	.532	.369	.563	.234	NA	.360	NA	.975	.963	.982	.982	.888	.863	.920	.917
Hetero.
𝐻0	.045	.150	.089	.182	.015	.230	.042	.303	.070	.056	.106	.100	.062	.935	.107	.952
𝐴1	.045	.160	.088	.199	.021	NA	.053	NA	.077	.060	.129	.121	.074	NA	.124	NA
𝐴2	.114	.273	.190	.316	.047	NA	.094	NA	.151	.129	.221	.215	.104	NA	.152	NA
𝐴3	.195	.430	.318	.467	.117	NA	.215	NA	.270	.235	.353	.341	.131	NA	.189	NA