Test			Student t-test	MEMA
				Gaussian		Laplacian
Results				TS	TKH	TS	TKH
Voxel 1	Group effect	Estimate	0.643	0.667		0.682
		t	4.542	5.006	5.153	5.942	5.443
		pa	0.0014	7.33e – 4	6.01e – 4	2.17e – 4	4.09e – 4
	Cross-subjects heterogeneity	t̂2b	0.200	0.0633		0.0296
		Qc	–	15.11 (0.0880)
		H, I2d	–	1.296, 0.406		1.149, 0.242
Voxel 2	Group effect	Estimate	0.508	0.381		0.364
		t	3.89	5.536	4.705	7.334	5.156
		pa	3.67e – 3	3.63e – 4	1.11e – 3	4.40e – 5	5.98e – 4
	Cross-subjects heterogeneity	t̂2b	0.171	0.0177		0.0004
		Qc	–	18.49 (0.0299)
		H, I2d	–	1.30, 0.409		1.009, 0.018
Voxel 3	Group effect	Estimate	− 0.319	−0.319		−0.323
		t	− 3.168	− 5.020	− 4.501	− 4.564	− 4.308
		pa	0.011	7.20e – 4	1.49e – 3	1.36e – 3	1.97e – 3
	Cross-subjects heterogeneity	t̂2b	0.101	0		0.007
		Qc	–	11.20(0.2622)
		H, I2d	–	1.0, 0.0001		1.081, 0.145
Voxel 4	Group effect	Estimate	− 0.193	− 0.138		− 0.138
		t	− 5.449	− 2.971	− 3.915	− 2.971	− 3.915
		pa	4.1e – 4	1.57e – 2	3.54e – 3	1.57e – 2	3.54e – 3
	Cross-subjects heterogeneity	t̂2b	0.0013	0		0
		Qc	–	5.18 (0.8183)
		H, I2d	–	1.0, 0.0		1.0, 0.0
Voxel 5	Group effect	Estimate	0.0496	0.0493		0.0493
		t	4.7152	0.8937	4.6376	0.8937	4.6376
		pa	0.0011	0.3947	0.0012	0.3947	0.0012
	Cross-subjects heterogeneity	t̂2b	1.1e-4	0		0
		Qc	–	0.3342 (1.0)
		H, I2d	–	1.0, 0.0		1.0, 0.0

Talairach coordinates (x, y, z) of the five voxels: (31, −91, −2) (Voxel 1), (−23, −89, 0) (Voxel 2), (−53, −17, 10) (Voxel 3), (−51, −11, 6) (Voxel 4), and (−5, 11, 0) (Voxel 5), where + x, y, z=RAS (neurological coordinates)

^ap-values for the t-statistics with 9 degrees of freedom are two-sided.

^bThe variance for the conventional approach (paired Student t-test) is the estimated τ²+σ² in the effect estimates, including both within- and inter-subject variances, assuming the within-subject variability being homogeneous in the group. The adjustment in T_KH relative to T_S does not involve the estimate of inter-subject variability τ², which remains the same between the two tests.

^cThe conventional approach assumes equal or no within-subject variance; thus, all the variability in the data is assumed to come between subjects. There is no way to test the significance of the inter-subject variability in the case of paired Student t-test under this assumption. The Q-statistic, defined in (8) for testing inter-subject variability (null hypothesis τ²=0), follows a χ²(9) distribution with the data at the five voxels (p-value shown within parentheses).

^dApproximate criteria for heterogeneity: H>1.5 (or I²>0.56), significant; 1.2<H<1.5 (or 0.31<I²<0.56), moderate; H<1.2 (or I²<0.31), negligible.