Why would r 's prop.test
function ( documentation here ) return different results based on whether I pass it a matrix
or vectors?
Here I pass it vectors:
> prop.test(x = c(135, 47), n = c(1781, 1443))
2-sample test for equality of proportions with
continuity correction
data: c(135, 47) out of c(1781, 1443)
X-squared = 27.161, df = 1, p-value = 1.872e-07
alternative hypothesis: two.sided
95 percent confidence interval:
0.02727260 0.05918556
sample estimates:
prop 1 prop 2
0.07580011 0.03257103
Here I create a matrix
and pass it in instead:
> table <- matrix(c(135, 47, 1781, 1443), ncol=2)
> prop.test(table)
2-sample test for equality of proportions with
continuity correction
data: table
X-squared = 24.333, df = 1, p-value = 8.105e-07
alternative hypothesis: two.sided
95 percent confidence interval:
0.02382527 0.05400606
sample estimates:
prop 1 prop 2
0.07045929 0.03154362
Why do I get different results? I expect the same results for both scenarios to be returned.
When x
and n
are entered as separate vectors, they are treated, respectively, as the number of successes and the total number of trials. But when you enter a matrix, the first column is treated as the number of successes and the second as the number of failures. From the help for prop.test
:
xa vector of counts of successes, a one-dimensional table with two entries, or a two-dimensional table (or matrix) with 2 columns, giving the counts of successes and failures, respectively.
So, to get the same result with a matrix, you need to convert the second column of the matrix to the number of failures (assuming that in your example x
is the number of successes and n
is the number of trials).
x = c(135, 47)
n = c(1781, 1443)
prop.test(x, n) # x = successes; n = total trials
2-sample test for equality of proportions with continuity correction data: x out of n X-squared = 27.161, df = 1, p-value = 1.872e-07 alternative hypothesis: two.sided 95 percent confidence interval: 0.02727260 0.05918556 sample estimates: prop 1 prop 2 0.07580011 0.03257103
prop.test(cbind(x, n - x)) # x = successes; convert n to number of failures
2-sample test for equality of proportions with continuity correction data: cbind(x, n - x) X-squared = 27.161, df = 1, p-value = 1.872e-07 alternative hypothesis: two.sided 95 percent confidence interval: 0.02727260 0.05918556 sample estimates: prop 1 prop 2 0.07580011 0.03257103
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