Search code examples
rstatisticscontingencystatistical-test

McNemar exact test

I have the following data:

> Performance = as.table(rbind(c(794,150),c(86,570))
> Performance
    A   B
A 794 150
B  86 570

I perform an Exact McNemar test in R, obtaining the following result:

> library(exact2x2)
> mcnemar.exact(Performance)

    Exact McNemar test (with central confidence intervals)

data:  Performance
b = 150, c = 86, p-value = 3.716e-05
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 1.329228 2.300979
sample estimates:
odds ratio 
  1.744186

I understand the results, nevertheless, someone could explain to me how the confidence interval is computed?

Solution

  • You can read it more in this vignette and also check out the code. Using this wiki picture for illustration:

    enter image description here

    The odds ratio is b / c, which in your case works out to be 150/86 = 1.744186. You can construct a binomial confidence interval around the proportion of successes, treating b as success and number of trials to be b + c.

    In the code, they used this bit of code to calculate:

    library(exactci)
CI = binom.exact(150,86+150,tsmethod = "central")
CI

data:  150 and 86 + 150
number of successes = 150, number of trials = 236, p-value = 3.716e-05
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
 0.5706732 0.6970596
sample estimates:
probability of success 
             0.6355932

    You have the upper and lower bound of b, then odds ratio is p / 1- p :

    CI$conf.int/(1-CI$conf.int)
[1] 1.329228 2.300979

    The vignette for binom.exact states:

    The 'central' method gives the Clopper-Pearson intervals, and the 'minlike' method gives confidence intervals proposed by Stern (1954) (see Blaker, 2000).

    So this is one of the many methods of estimating a binomial confidence interval.