**R**: Check assumptions, then use the functionprop.test(x, n, alternative, conf.level)

To explain the parameters:

`x`

is a vector of the number of successes seen in the two categories`n`

is a vector of the two sample sizes`alternative`

is a string of text that specifies the alternative hypothesis (i.e., "two.sided", "less", or "greater", for $p_1 \neq p_2, p_1 \lt p_2, \textrm{ and } p_1 \gt p_2$, respectively.`conf.level`

is associated with the significance level for the test.`correct`

is a logical value (i.e.,`TRUE`

or`FALSE`

) that indicates is a "Yates Continuity Correction" should be used. There is a large body of research that suggests this correction is too strict. To perform an uncorrected $z$-test of a proportion (which pools the proportions), specify`correct = FALSE`

to override the default.

As an example of its use, suppose we have two samples of 500 individuals. Everyone in the first sample has lung cancer, while everyone in the second sample is healthy. There are 490 smokers in the first group, while only 400 in the second.

Perform the test in R with:

results = prop.test(x = c(490, 400), n = c(500,500)) results

which results in:2-sample test for equality of proportions with continuity correction data: c(490, 400) out of c(500, 500) X-squared = 80.909, df = 1, p-value < 2.2e-16 alternative hypothesis: two.sided 95 percent confidence interval: 0.1408536 0.2191464 sample estimates: prop 1 prop 2 0.98 0.80

Note, after running the above, you can access the $p$-value of the test with

`results$p.value`

, and the related confidence interval with`results$conf.int`

.