Figure 1: Displayed are rejection rates for omnibus null hypotheses in the simulation studies of section 6. Methods CCS1, CCS2, and CCS3, refer to our proposed testing procedure from Section 5 with (δ,ε)=(1/2, 1/10), (δ, ε)=(0.051/2,0.051/2), and (δ,ε)=(1/10, 1/2), respectively. Method CB refers to a modified likelihood ratio test applied to p-values, and treated as arising from the contaminated beta model defined in section 6 [10].