Table 1.

Power analyses and exact p values

	Reference	test	Sample size	Observed power (α = 0.05)	p value
a	Text	ANOVA	a.m: 53 p.m: 52	0.15	0.65
b	Fig. 4C	KW	Pre: 347 Post: 311 Back: 340	1.0	3.3e-78
		MW U	See previous	Pre vs post: 1.0 Pre vs back: 1.0 Post vs back: 1.0	Pre vs post: 4.2e-08 Pre vs back: 1.8e-81 Post vs back: 4.9e-29
c	Fig. 4E, left	KW	See previous	1.0	2.5e-34
		MW U	See previous	Pre vs post: 0.75 Pre vs back: 1.0 Post vs back: 1.0	Pre vs post: 8.9e-04 Pre vs back: 2.1e-38 Post vs back: 3.3e-11
d	Fig. 4E, right	KW	See previous	1.0	1.6e-40
		MW U	See previous	Pre vs post: 1.0 Pre vs back: 1.0 Post vs back: 1.0	Pre vs post: 7.1e-08 Pre vs back: 1.2e-44 Post vs back: 3.3e-10
e	Text	WSR	340	1.0	6.1e-43
f	Fig. 5C	t-test	18	0.57	7.8e-03
g	Fig. 5F	t-test	18	0.68	3.1e-03
h	Fig. 6B	t-test	17	0.98	2.8e-05
i	Fig. 6E	t-test	17	0.54	1.0e-02
j	Extended Data Fig. 6-1B	χ²	2631	1.0	1

Lower case letters in first column are used as superscripts in text and figure captions. KW, Kruskal–Wallis test; MW U, Mann–Whitney U test; WSR, Wilcoxon signed-rank test; t test, one-sampled t test against zero-mean distribution; p values in rows b–d were corrected using the Bonferroni method.