Table 1 .

Empirical type I error rate for common correlation structure when ${\beta }_1=1$ and all other ${\beta }_j=0$ $\left(j\ne 1\right),$ based on multivariate normal distribution

Sample size	No. traits	Trait correlation	Nominal type I error rate
			0.05	0.01
100	4	0.2	0.072	0.020
		0.5	0.070	0.016
		0.8	0.066	0.014
	10	0.2	0.105	0.036
		0.5	0.092	0.032
		0.8	0.094	0.029
500	4	0.2	0.056	0.017
		0.5	0.058	0.011
		0.8	0.058	0.009
	10	0.2	0.061	0.010
		0.5	0.056	0.011
		0.8	0.068	0.019
1000	4	0.2	0.052	0.012
		0.5	0.058	0.008
		0.8	0.051	0.010
	10	0.2	0.057	0.012
		0.5	0.052	0.010
		0.8	0.046	0.007

Underlined values are for when empirical type I error exceeds the upper 95% C.I.