The power to detect an association between mtDNA haplogroups and disease. In all situations, the number of disease cases is assumed to be equal to the number of control subjects. *A,* Monte Carlo simulation data for the European haplogroups H, I, J, K, and U. Data from the individual simulations, including those shown in , are shown on the same graph for different changes in the percentage level of a particular haplogroup at the α=.05 significance level. This demonstrates the scatter of the data points. *B,* These data collapse onto a simple sigmoid curve, with the *X*-axis scaling based on standard binomial theory. *N*_{c} is the number of disease cases (equal to the number of controls), *p*_{0} is the frequency of the haplogroup in the control population, and *p*_{1} is the frequency of the haplogroup in the cases. Data are shown for the significance level α=.05 (for α=.01 and α=.001, see ). Both the data and the theoretical curve describe the same sigmoidal shape, with the European haplogroup simulation data (with the 10 major European haplogroups plus “others” being equivalent to a 2×11 table) shifted to the right. *C,* Simulations (symbols) and theoretical 2×2 curve (*red line*) for populations with different numbers of mutually exclusive haplogroups. The simulated subdivisions could correspond to superhaplogroups, haplogroup clusters, or any mutually exclusive sequence variants in any population. All of the data collapse onto a single curve when the *X*-axis is normalized by the number of haplogroups, *N*_{H}, raised to the power 0.37 (). Data are shown for the significance level α=.05 (for α=.01 and α=.001, see ). *D,* Example showing the number of cases and controls required to generate 90% power at the .05 significance level for a study of the 10 major European haplogroups (*N*_{H}=11 to account for the <5% that do not fall into these 10 groups and are considered “others”). Haplogroup proportions in the control group are based on published values (haplogroup *H*=0.41 in controls [*black line*]; *I*=.02 in controls [*blue line*]; *J*=.11 in controls [*red line*]) (Torroni et al. ).

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