Compare the sensitivities of Test 1 (T1) and Test 0 (T0) in a sample of patients, all of whom are D+ by the reference standard. Assumes a paired design in which all subjects receive both T0 and T1. Use McNemar's test to compare sensitivities.
For example, you believe T0 has 70% sensitivity and T1 has 80% sensitivity. Specify those sensitivities as S0 and S1 below. Your null hypothesisis will be S0 = S1 = 75% and your alternative hypothesis is S0 ≠ S1. The sample size will be higher if the two tests are independent (uncorrelated), so for a first analysis, treat the two tests as independent by setting P(T1+|T0+) to S1 = 80%. Then to get the minimum sample size, treat the two tests as perfectly correlated by setting P(T1+|T0+) to 100%.
Instructions: Enter parameters in the green cells. Answers will appear in the blue box below.
Compare
Since sensitivity and specificity are symmetrical, this calculator can be used for comparing tests of either type.
α (two-tailed) =
Threshold probability for rejecting the null hypothesis. Type I error rate.
β =
Probability of failing to reject the null hypothesis under the alternative hypothesis. Type II error rate.
S0
%
Assumed sensitivity of test T0, the lower sensitivity test.
S1
%
Assumed sensitivity of test T1, the higher sensitivity test.
P(T1+|T0+)
%
Probability that test T1 is positive given that test T0 is positive.
The standard normal deviate for α = Zα =
The standard normal deviate for β = Zβ =
Ψ = S0 + S1 - (2 * S0 * P(T1+|T0+) = . This is the probability that one test will be positive but not the other.
V0 = Ψ = . This is the variance (under the null hypothesis) of the difference between sample sensitivity in group 1 and in group 0.
VA = Ψ - (S1 - S0)2 = . This is the variance (under alternative hypothesis) of the difference between sample sensitivity in group 1 and in group 0.