Severely malnourished children with a low weight-for-height have a higher mortality than those with a low mid-upper-arm-circumference: I. Empirical data demonstrates Simpson’s paradox

Table 4 Effect of combining the diagnostic groups together to show Simpson’s paradox

Effect of combining diagnostic groups
Subgroups	Total	dead	CFR	comparisons	p
Subgroups	#	#	%	comparisons	p
All-muac v All-whz without oedeam
M-muac	7191	56	0.78	muac v whz	0.000
M-whz	16,530	332	2.01	muac v both	0.000
M-both	40,307	2000	4.96	whz v both	0.000
				Cramer’s V	0.044
M-All-muac	47,498	2056	4.33	χ² = 3.01	0.083
M-All-whz	56,837	2332	4.10	Cramer’s V	0.005
All-muac v All-whz with oedema
K-muac	1669	118	7.07	muac v whz	0.000
K-whz	1088	169	15.53	muac v both	0.000
K-both	4217	576	13.66	whz v both	0.411
				Cramer’s V	0.115
K-All-muac	5886	694	11.79	χ² = 9.75	0.002
K-All-whz	5305	745	14.04	Cramer’s V	0.028
All-muac v All-whz with and without oedema
M + K-muac	8860	174	1.96	muac v whz	0.000
M + K-whz	17,618	501	2.84	muac v both	0.000
M + K-both	44,524	2576	5.79	whz v both	0.000
				Cramer’s V	0.025
M + K - All-muac	53,384	2750	5.15	χ² = 2.16	0.141
M + K - All-whz	62,142	3077	4.95	Cramer’s V	0.004

The effect of grouping M-both and K-both with the single deficits to produce erroneous results due to mathematical coupling. All-muac is defined as M-muac + M-both or K-muac + K-both; All-whz is defined as M-whz + M-both or K-whz + K-both; Cramer’s V (a measure of the degree to which the two categories are associated, 0 = no association, 1 = identity) calculated for MUAC v WHZ only

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