Table 4.

Power of closed testing procedures to reject $H_1:{\beta }_1^{(1)}=0,H_2:{\beta }_1^{(2)}=0,H_3:{\beta }_1^{(3)}=0$, at least one elementary hypothesis (any H_i), or all elementary hypotheses.

K	Statistic	Type	Approx.	Bias adj.	H 1	H 2	H 3	any Hi	all Hi
40	Wald	Quadratic	scaled F	yes	53.1	54.0	54.3	67.1	41.4
40	Wald	Maximum	MVT	yes	59.0	59.4	60.6	77.7	42.2
40	Wald	Maximum	t-Bonferroni	yes	57.4	57.9	58.9	75.5	41.5
40	Score	Quadratic	Chi-squared	no	57.7	53.8	64.0	71.7	46.0
40	Score	Maximum	MVN	no	63.0	58.1	69.2	80.7	46.6
100	Wald	Quadratic	Scaled F	yes	54.3	56.3	57.8	70.1	43.1
100	Wald	Maximum	MVT	yes	58.8	60.8	62.8	78.8	43.2
100	Wald	Maximum	t-Bonferroni	yes	57.5	59.4	61.4	76.9	42.7
100	Score	Quadratic	Chi-squared	no	56.3	56.1	61.5	71.5	45.0
100	Score	Maximum	MVN	no	60.6	60.2	66.1	79.7	45.1

Results are shown for the simulation scenario (a) with an effect in all endpoints. The results are based on 10⁵ simulation runs. MVN: multivariate normal; MVT: multivariate t.