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Table 3.

Two-tailed p values for relative homology obtained from the empirical Mahalanobis distance or χ2 test.

(a)
Relative homology – χ2 (empirical) – Separate Variance
North South
Res FWHM b0 b1 ECrel b0 b1 ECrel
Threshold = 0.90
1024 10′ 0.4083 0.0733 0.1483 0.9917 0.7617 0.8867
512 20′ 0.4633 0.0850 0.1650 0.9933 0.8183 0.9933
256 40′ 0.0600 0.3350 0.4767 0.3500 0.8167 0.7283
128 80′ 0.0367 0.0367 0.0350 0.6617 0.9017 0.9150
64 160′ 0.0433 0.0583 0.0733 0.2833 0.7217 0.8500
32 320′ 0.0200 0.2150 0.1017 0.5967 0.1033 0.1717
16 640′ 0.5600 0.2900 0.4700 0.4283 0.1783 0.2683
Summary N/A 0.0233 0.0533 0.0167 0.5767 0.8767 0.9250
(b)
Relative homology – χ2 (empirical) – Gloabal Variance
North South
Res FWHM b0 b1 ECrel b0 b1 ECrel
Threshold = 0.90
1024 10′ 0.4600 0.1467 0.2750 0.5167 0.2567 0.3150
512 20′ 0.1917 0.1450 0.1250 0.3783 0.1117 0.1733
256 40′ 0.1817 0.3400 0.5217 0.4533 0.0833 0.3233
128 80′ 0.0750 0.2383 0.3567 0.1217 0.0400 0.1367
64 160′ 0.3383 0.1250 0.2867 0.5150 0.1583 0.5817
32 320′ 0.0383 0.2967 0.2617 0.0650 0.0017 0.0000
16 640′ 0.8800 0.9617 0.9000 0.3317 0.0167 0.0150
Summary N/A 0.1667 0.6383 0.5283 0.0783 0.0183 0.0000

Notes.

The table was computed from the sample covariance matrices, for different resolutions and smoothing scales for the NPIPE dataset. Panel (a) presents the p values for experiments in which the variance was computed for each hemisphere separately, and panel (b) presents results for experiments in which the hemispheres were assigned the variance of the full sky. The last entry is the p value for the summary statistic computed across all resolutions. Marked in boldface are p values of 0.05 or smaller.

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