Statistics and uncertainty
| Location | Data structure | Test or analysis | N | Uncertainty [CI95%] |
|---|---|---|---|---|
| Extended Data Fig. 1-1D | Gaussian predictor Exponential response | Nonlinear regression (iterative optimization) | 64,620 64,620 64,620 64,620 | λ = 23.8 [23.5, 24.0] λ = 22.8 [22.7, 22.9] λ = 22.2 [22.1, 22.2] λ = 23.4 [23.3, 23.6] |
| Fig. 2A | Gaussian predictor Exponential response | Nonlinear regression (iterative optimization) | 16,110 | λ = 23.1 [22.8, 23.3] |
| Fig. 2B | Gaussian predictor Exponential response | Nonlinear regression (iterative optimization) | 16,110 | λ = 23.9 [23.7, 24.2] |
| Fig. 2C | Gaussian predictor Exponential response | Nonlinear regression (iterative optimization) | 32,400 | λ = 32.8 [32.5, 33.0] |
| Fig. 2D | Gaussian predictor Exponential response | Nonlinear regression (iterative optimization) | 64,620 | λ = 23.4 [23.3, 23.6] |
| Extended Data Fig. 2-2B | Gaussian predictor Gaussian response | Linear correlation | 1065 | r = −0.14 [−0.20, −0.08] |
| Fig. 3D | Gaussian predictor Exponential response | Nonlinear regression (iterative optimization) | 12,924 | λ = 27.8 [27.4, 28.2] |
| Fig. 3F | Gaussian predictor Gaussian response | Linear correlation | 1065 | r = 0.70 [0.67, 0.73] |
| Fig. 4C | Gaussian predictor Gaussian response | Linear correlation | 80 | r = 0.35 [0.14, 0.53] |
| Fig. 8A | Gaussian predictor Gaussian response | Linear correlation | 16,110 16,110 32,400 | r = −0.10 [−0.12, −0.09] r = −0.12 [−0.13, −0.10] r = −0.11 [−0.12, −0.10] |
| Fig. 8B | Gaussian predictor Gaussian response | Linear correlation | 351 351 66 91 231 231 28 780 780 10 | r = −0.17 [−0.27, −0.06] r = −0.13 [−0.23, −0.02] r = −0.41 [−0.60, −0.19] r = −0.26 [−0.44, −0.06] r = −0.30 [−0.42, −0.18] r = −0.30 [−0.40, −0.17] r = −0.56 [−0.77, −0.24] r = −0.12 [−0.19, −0.05] r = −0.17 [−0.24, −0.10] r = −0.74 [−0.93, −0.20] |
| Fig. 9B | Gaussian predictor Gaussian response | Linear correlation | 19,667 19,667 64,620 | r = 0.43 [0.42, 0.44] r = 0.23 [0.21, 0.24] r = 0.06 [0.05, 0.07] |
| Extended Data Fig. 9-1 | Gaussian predictor Gaussian response | Linear correlation | 8483 8483 16,110 8370 8370 16,110 | r = 0.42 [0.40, 0.44] r = 0.22 [0.20, 0.24] r = 0.06 [0.05, 0.07] r = 0.40 [0.38, 0.42] r = 0.22 [0.20, 0.24] r = 0.11 [0.10, 0.13] |
Where multiple uncertainties are listed for a figure panel, they correspond to the statistics read left-to-right, top-to-bottom in that panel. For Figure 8B, only uncertainties for significant correlations are listed. Uncertainties for Figures 6-8, 10 are not shown. Extended Data Figure 6-1 contains bootstrapped 95% confidence intervals for the 180 means shown in Figure 6, n = 179. Figure 7 shows bootstrapped 95% confidence intervals in gray; the values of these intervals for all distance bins are available in the figure source data at https://doi.org/10.5281/zenodo.4060485. For Figure 10, means across shuffled matrices are only necessary to account for arbitrary ordering among tied edge weights, and the bootstrapped 95% confidence intervals for these means are vanishingly small. The values of these intervals at all network densities are also included in the figure source data. For nonlinear regressions, confidence intervals are estimated using R−1, the inverse R factor from QR decomposition of the Jacobian, the degrees of freedom for error, and the root mean squared error. For linear correlations, the confidence intervals are based on an asymptotic normal distribution of 0.5*log((1+r)/(1–r)), with an approximate variance equal to 1/(N – 3). For descriptive statistics, e.g., means, empirical 95% confidence intervals are estimated by bootstrapping with 2000 iterations.