I would like to compare the false positive rates (1 - specificity) from two different tests within the same sample. The false positive rate is calculated by comparing the test values against the actual prevalence of disease.
Test 1 has a false positive = 17.1% Test 2 has a false positive = 15.5%
I believe I am supposed to use the McNemar's test but I can't figure out how to set up the two by two table.
Thank you!
The false-positive rate is
$$\small \text{FPR}=\frac{\text{FP}}{\text{FP + TN}}$$
This would be some simulated data set of $187$ participants with the same percentages as in the OP:
> mat = as.table(rbind(c(23, 9), c(6, 149) ))
> colnames(mat) <- rownames(mat) <- c("False Positive", "True Negative")
> names(dimnames(mat)) = c("Test A", "Test B")
> mat
Test B
Test A False Positive True Negative
False Positive 23 9
True Negative 6 149
> addmargins(mat)
Test B
Test A False Positive True Negative Sum
False Positive 23 9 32
True Negative 6 149 155
Sum 29 158 187
> pr.mat = prop.table(mat)
> round(addmargins(pr.mat),3)
Test B
Test A False Positive True Negative Sum
False Positive 0.123 0.048 0.171
True Negative 0.032 0.797 0.829
Sum 0.155 0.845 1.000
> mcnemar.test(mat)
McNemar's Chi-squared test with continuity correction
data: mat
McNemar's chi-squared = 0.26667, df = 1, p-value = 0.6056
So you are really testing for the off-diagonal differences: the proportions of healthy individuals in which there was discrepancy with one of the tests being false positive, while the other was true negative. The idea is for the $2\times2$ contingency table to be populated with count data.
