Table 1.

Influence of intra-individual variation in behavior and number of replicates on attenuation, bias in observed relative risks, and on statistical power

Intra- individual varation	Replicates	Attenuation (λ)	Nai̇ve relative risks			Statistical Power (α=0.01)
			Large effect (RR=4.0)	Medium effect (RR=2.5)	Small effect (RR=1.5)	Large effect (RR=4.0)	Medium effect (RR=2.5)	Small effect (RR=1.5)
80%	1	0.20	1.32	1.20	1.08	0.39	0.16	0.03
	2	0.33	1.58	1.35	1.14	0.65	0.29	0.05
	3	0.43	1.82	1.48	1.19	0.79	0.39	0.06
	4	0.50	2.00	1.58	1.22	0.86	0.46	0.07
	5	0.56	2.17	1.67	1.25	0.90	0.52	0.08
	6	0.60	2.30	1.73	1.28	0.92	0.56	0.09
70%	1	0.30	1.52	1.32	1.13	0.60	0.26	0.04
	2	0.46	1.89	1.52	1.21	0.82	0.42	0.07
	3	0.56	2.17	1.67	1.25	0.90	0.52	0.08
	4	0.63	2.39	1.78	1.29	0.93	0.58	0.09
	5	0.68	2.57	1.86	1.32	0.95	0.63	0.10
	6	0.72	2.71	1.93	1.34	0.96	0.66	0.11
60%	1	0.40	1.74	1.44	1.18	0.75	0.36	0.06
	2	0.57	2.20	1.69	1.26	0.91	0.53	0.08
	3	0.67	2.53	1.85	1.31	0.95	0.61	0.10
	4	0.73	2.75	1.95	1.34	0.97	0.66	0.11
	5	0.77	2.91	2.02	1.37	0.97	0.69	0.12
	6	0.80	3.03	2.08	1.38	0.98	0.71	0.12

λ = 1/1 + (σ_ε²/n/σ_T²), adaptation of Equation 2 where n is the number of replicates

Attenuated relative risks calculated as: True RR^λ.

Thus, a true RR of 4.0 with an attenuation factor of 0.5 = 4.0^0.5=2.0.

Statistical power is calculated for N=100 subjects for each effect size and α = 0.01