Trend in Proportions
Example: Time-ordered, retrospective data over cohorts
Most colleges and Universities have annual campaigns in which
they ask former graduates to contribute money. For the 1986 to
1987 Providence College fund-raising campaign, statistics were
recorded for the number of people contacted and the number of
doners categorized by their class year. Some of these data are
summarized in the rable below. (data from Providence College
Fund Year Report 1986-7).
Class
1961 1966 1971 1976 1981
Contributed 196 266 194 276 333
Did not Contribute 123 226 241 322 568
> giving = rbind(c(196, 266 , 194 , 276 , 333), c(123 , 226 , 241 , 322, 568))
> giving
[,1] [,2] [,3] [,4] [,5]
[1,] 196 266 194 276 333
[2,] 123 226 241 322 568
> # top row "Contributed"; could have use matrix and given names etc
> prop.table(giving,2)
[,1] [,2] [,3] [,4] [,5]
[1,] 0.6144201 0.5406504 0.445977 0.4615385 0.3695893
[2,] 0.3855799 0.4593496 0.554023 0.5384615 0.6304107
> chisq.test(giving) # is prob(giving) the same in all class years?
Pearson's Chi-squared test
data: giving
X-squared = 73.478, df = 4, p-value = 4.181e-15
> prop.trend.test(giving[1,], margin.table(giving, 2))
Chi-squared Test for Trend in Proportions
data: giving[1, ] out of margin.table(giving, 2) ,
using scores: 1 2 3 4 5
X-squared = 67.8656, df = 1, p-value < 2.2e-16
(matches SAS PROC FREQ)
> margin.table(giving, 2)
[1] 319 492 435 598 901
> prop.trend.test(giving[1,], margin.table(giving, 2), c(1961 , 1966 , 1971 , 1976 , 1981 ))
Chi-squared Test for Trend in Proportions
data: giving[1, ] out of margin.table(giving, 2) ,
using scores: 1961 1966 1971 1976 1981
X-squared = 67.8656, df = 1, p-value < 2.2e-16
> # equal spaced no difference; see stat141 ex for ordinal metric choices