Simpson’s Paradox is suppression, but Lord’s Paradox is neither: clarification of and correction to Tu, Gunnell, and Gilthorpe (2008)

Table 4 Three 2 times 2 contingency tables for the data in Table 1

	Untreated	Treated
Association between treatment and status, disregarding sex
Alive	6	20
Dead	6	20
Total	12	40
Probability dead	.50	.50	Difference = 0	\(\phi = .00\)

	Male	Female
Association between sex and status, disregarding treatment
Alive	12	14
Dead	8	18
Total	20	32
Probability dead	.40	.56	Difference = .16	\(\phi = .16\)
Association between sex and treatment, disregarding status
Untreated	7	5
Treated	13	27
Total	20	32
Probability treated	.65	.84	Difference = .19	\(\phi = .22\)

Status coded 0 = alive, 1 = dead; treatment coded 0 = untreated, 1 = treated; sex coded 0 = male, 1 = female