Figure 2From: Comprehensive analysis of correlation coefficients estimated from pooling heterogeneous microarray dataMean differences across a pool of N groups causes Simpson’s paradox. (a) r xy was obtained from combining N groups of simulated data; simulation parameter ρ xy is the true correlation of the pair xy within each group i = 1,N for . All other simulation parameters are as follows: μxy,i = (i,N−(i−1)), −0.9 ≤ ρ xy ≤ 0.9, n i = 10, λ i = λ, 0.01 ≤ λ ≤ 0.1, for i = 1,N, and 10 ≤ N ≤ 100. (b) Scatterplot of a pair xy obtained with the simulation parameters: μxy,i = (i,(11−i)), ρ xy = 0.9 and n i = 50 for i = 1,10 groups. This plot shows clearly that even though there is a positive trend within each of the 10 groups, the trend across the pool of 10 groups is negative (Simpson’s paradox).Back to article page