Jarad - 4 months ago 13

R Question

Why would *r*'s

`prop.test`

`matrix`

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.

Answer

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`