Jarad - 1 year ago 87
R Question

# R: prop.test returns different values based on whether matrix or vectors are passed to it

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`

``````> 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`:

``````x    a 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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