Created
February 28, 2017 11:40
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Simpson's paradox demo inspired by the kidney-stone example on Wikipedia. You can play with proportions and n.
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| # data from | |
| # https://en.wikipedia.org/wiki/Simpson's_paradox#Kidney_stone_treatment | |
| # in all tabs: row 1 successful, row 2 failed treatment | |
| # small stones | |
| mk = matrix(c(81, 87-81, 234, 270-234), ncol=2) | |
| chisq.test(mk) | |
| # large stones | |
| vk = matrix(c(192, 263-192, 55, 80-55), ncol=2) | |
| chisq.test(vk) | |
| # all cases | |
| tot = matrix(c(273, 350-273, 289, 350-289), ncol=2) | |
| chisq.test(tot) | |
| # demo | |
| mkap = 0.95; mkan = 100 # small stones, A treatment | |
| mkbp = 0.85; mkbn = 1000 # small stones, B treatment | |
| vkap = 0.15; vkan = 1000 # large stones, A treatment | |
| vkbp = 0.05; vkbn = 100 # large stones, B treatment | |
| tab_mk = matrix(c(mkap * mkan, (1-mkap) * mkan, mkbp * mkbn, (1-mkbp) * mkbn), ncol=2) | |
| prop.table(tab_mk, 2) | |
| tab_vk = matrix(c(vkap * vkan, (1-vkap) * vkan, vkbp * vkbn, (1-vkbp) * vkbn), ncol=2) | |
| prop.table(tab_vk, 2) | |
| tab_all = tab_mk + tab_vk | |
| prop.table(tab_all, 2) | |
| chisq.test(tab_mk)$p.value | |
| chisq.test(tab_vk)$p.value | |
| chisq.test(tab_all)$p.value | |
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It might be a nice shiny app one day ;-)