Significance test of the regression pattern

To ascertain the significance of regression patterns, one essentially tests N local null hypothesis tests, where N is the number of grid points. However, assuming that each local null hypothesis is true can be misleading because of the many erroneous rejections that will invariably occur for real data. For this reason, climate scientists have raised concerns about the significance area of regression patterns that is often overstated because of a lack of rigorous significance testing (39, 40). Here, we further demonstrated that the statistics of the regression maps of SSTAs and Z500′ on tornado number anomalies over the SGP region in April (Fig. 1E) exceed the probability of being randomly significant, whereas those for May fail that test (fig. S4). For the test, we randomly shuffled the anomalous tornado number index 1000 times and calculated the regression fields between the random time series and the gridded data (SSTAs and Z500′). Figure S4 shows the histogram of the correlation coefficients between the time series and both global SSTA and Z500′ from each grid point within 20°N to 70°N and 0°E to 360°E. In April, the percentages of the number of grid points that exceed both the random mean (black line) and the 95% level of the two-tailed test (green lines) are more than 5.6% of the total grid points for Z500′ and 11.9% for SSTA. None of the grid points in May exceeds even 3% of the statistically significant grid points.

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