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Table 4.

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

(a)
Relative homology – χ2 (empirical) – Separate Variance
Quad 1 Quad 2
Res FWHM b0 b1 ECrel b0 b1 ECrel
Threshold = 0.90
512 20′ 0.1800 0.3433 0.2917 0.5617 0.0283 0.0567
256 40′ 0.0250 0.3650 0.2233 0.5483 0.5533 0.7467
128 80′ 0.4117 0.3267 0.5183 0.4350 0.4767 0.5667
64 160′ 0.0050 0.0150 0.0033 0.2867 0.4700 0.6450
32 320′ 0.4283 0.1517 0.4067 0.1817 0.4083 0.6050
Summary N/A 0.0017 0.0383 0.0100 0.2767 0.3200 0.2183
(b)
Relative homology – χ2 (empirical) – Separate Variance
Quad 3 Quad 4
Res FWHM b0 b1 ECrel b0 b1 ECrel
Threshold = 0.90
512 20′ 0.9767 0.6133 0.8833 0.9283 0.6967 0.9700
256 40′ 0.8100 0.5233 0.7183 0.2333 0.7300 0.6200
128 80′ 0.7983 0.6400 0.8350 0.7683 0.6383 0.7500
64 160′ 0.5533 0.4483 0.7083 0.5933 0.6100 0.6267
32 320′ 0.1233 0.5200 0.1433 0.2100 0.3617 0.3517
Summary N/A 0.7433 0.6200 0.4683 0.4717 0.6917 0.5533

Notes.

The values were computed from the sample covariance matrices, for different resolutions and smoothing scales for the maps in different quadrants of the sphere 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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