Table 1.

Comparison of local and global correlations. Listed are positive rates for Cases 1, 8 to 12, and correlation measurement (with estimated p-value) for Cases 2 to 7. For Case 1 the (false) positive rate is type-I error. For Cases 8 through 12 the (correct) positive rate is statistical power.

Case	M	MI	C	Sp
positive rates
1	3 %	1%	3 %	3 %
8	100 %	100 %	96 %	3 %
9	100 %	100 %	22 %	11 %
10	100 %	100 %	100 %	99 %
11	100 %	99 %	100 %	98 %
12	100 %	100 %	98 %	100 %
Correlation measurement (p-values)
2	1.60 (< ε)	3.32 (< ε)	1.00 (< ε)	1.00 (< ε)
3	1.55 (< ε)	2.01 (< ε)	0.76 (< ε)	0.82 (< ε)
4	1.47 (< ε)	2.14 (< ε)	−0.40 (< ε)	−0.59 (< ε)
5	0.08 (< ε)	2.39 (< ε)	0.97 (< ε)	1.00 (< ε)
6	0.19 (0.0005)	2.60 (< ε)	0.97 (< ε)	1.00 (< ε)
7	1.60 (< ε)	1.67 (< ε)	−0.37 (< ε)	−0.40 (< ε)

ε = 2.50 · 10^–4. For the cases with stochastic components, i.e., Cases 1, and 8 to 12, the estimated positive rate is listed based on 100 simulations for each case. M: maximum local correlation; MI: mutual information; C: Pearson correlation; Sp: Spearman correlation.