R：prop.test 根据传递给它的矩阵或向量返回不同的值

Question

为什么 r 的 prop.test 函数 (documentation here) 会根据我传递的是 matrix 还是向量返回不同的结果？

我在这里传递向量：

> 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 

在这里我创建了一个matrix 并将其传入：

> 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 

为什么我会得到不同的结果？我希望两种方案都返回相同的结果。

Answer 1

当x 和n 作为单独的向量输入时，它们分别被视为成功次数和试验总数。但是当您输入一个矩阵时，第一列被视为成功次数，第二列被视为失败次数。来自prop.test的帮助：

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.

因此，要使用矩阵获得相同的结果，您需要将矩阵的第二列转换为失败次数（假设在您的示例中，x 是成功次数，n 是次数试验）。

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