Extended Data Fig. 5: Relationship of δD_ice and δAr/N₂ of the trapped air in the Allan Hills ice and the robustness given analytical uncertainties.

Panels (a-c) are conceptually very similar to Fig. 2 in the main text, but here δAr/N₂ provides additional evidence to the observed negative correlation between δD_ice and δO₂/N₂ in samples dating back to 1.5 and 2.0 Ma. Error bars represent the pooled standard error of the δAr/N₂ measurements (± 1.47 ‰). Dashed lines represent 95% confidence interval. δAr/N₂ is only significantly (two-tailed p < 0.05) correlated in the 1.5 and 2.0 Ma samples (sample N = 29, r² = 0.28), and not significantly correlated in the 810 ka (N = 34, r² = 0.07) or the 400 ka samples (N = 29, r² = 0.10). However, the 95^th percentile of r value between the 29 δAr/N₂ and δD_ice data pairs dating back to 1.5 and 2.0 Ma is –0.272 in a 10⁶-iteration Monte Carlo simulation (panel d). Given the sample size (N = 29), the critical r value at 0.05 significance level (one-tailed) is –0.311 (dashed vertical line), meaning that there is a greater than 5% chance that the analytical uncertainties in δAr/N₂ lead to insignificant correlation. The negative δAr/N₂-δD_ice relationship is thus not considered robust. Histogram bin size is 0.01.

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