Table 1. Type 1 error rates for a few parameter combinations.

N = sample size; ES (r) = correlations of predictor with covariate and covariate with outcome; reliability = reliability of predictor and covariate. These error rates are determined using the methods described in the next section, and described in more detail in the S1 Appendix.

N	ES (r)	reliability	Type I error rate
30	0.6	0.4	0.12
30	0.6	0.8	0.07
120	0.5	0.4	0.2
120	0.5	0.8	0.09
300	0.4	0.4	0.19
300	0.4	0.8	0.09
3000	0.3	0.4	0.48
3000	0.3	0.8	0.16
30000	0.2	0.4	0.76
30000	0.2	0.8	0.25