# How to test the increase of proportions

Let say I've a contigency table as :

           score
<=2  [3-4]  >=5
no_event   248    796  288
event       71    419  285


I computed the percentage of events for each score category (<=2, [3-4] and >=5). Hereby the plot (top of each bar displays the number of events / (events+no_event) . I would like to test if the increase in proportion between >2 -> [3-4] -> >=5 is significative.

My first idea would be to use a chisq or fisher exact test.

 m <- matrix(c(248,71,796,419,288,285),ncol=3)
fisher.test(m)\$p.value
 9.640235e-17


However this test didn't take into account the order of the categories >2 -> [3-4] -> >=5

Any ideas ?

Thank you

One is to use a Cochran Armitage trend test. There is an implementation in R. I suppose you are interested in event vs non-event, so you need to flip your matrix:

library(DescTools)
m <- matrix(c(71,248,419,796,285,288),ncol=3)
CochranArmitageTest(m)

Cochran-Armitage test for trend

data:  m
Z = 8.5195, dim = 3, p-value < 2.2e-16
alternative hypothesis: two.sided


Since you have two groups, and you know the average score in event is higher, you can also test the difference of the scores using a wilcoxon:

event_scores =  rep(1:3,m[1,])
noevent_scores =  rep(1:3,m[2,])

wilcox.test(event_scores,noevent_scores)

Wilcoxon rank sum test with continuity correction

data:  event_scores and noevent_scores
W = 618058, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0