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

From: 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

Effect of combining diagnostic groups
Subgroups Total dead CFR 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
  1. 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