"Bliese, Paul D LTC USAMH" <paul.bliese at us.army.mil> writes:
> Does anyone know of another version of the Mcnemar test that provides:
>
>
>
> 1. Odds Ratios
>
> 2. 95% Confidence intervals of the Odds Ratios
>
> 3. Sample probability
>
> 4. 95% Confidence intervals of the sample probability
>
>
>
> Obviously the Odds Ratios and Sample probabilities are easy to calculate
> from the contingency table, but I would appreciate any help on how to
> calculate the confidence intervals.
>
>
>
> Below is a simple example of the test, and the corresponding output with
> the function mcnemar.test.
>
>
>
> > xtabs(~PLC50.T1+PLC50.T2,data=LANCET.DAT)
>
> PLC50.T2
>
> PLC50.T1 0 1
>
> 0 464 22
>
> 1 6 1
>
> > mcnemar.test(xtabs(~PLC50.T1+PLC50.T2,data=LANCET.DAT))
>
>
>
> McNemar's Chi-squared test with continuity correction
>
>
>
> data: xtabs(~PLC50.T1 + PLC50.T2, data = LANCET.DAT)
>
> McNemar's chi-squared = 8.0357, df = 1, p-value = 0.004586
What is the "sample probability" in this context? The odds ratio is a
simple functional of the off-diagonal elements, and the conditional
distribution of those given their sum is just a binomial, so you can
use prop.test or binom.test to get estimate and confidence intervals
for the probability parameter and convert that to odds.
E.g.
> prop.test(6,28)
1-sample proportions test with continuity correction
data: 6 out of 28, null probability 0.5
X-squared = 8.0357, df = 1, p-value = 0.004586
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
0.09027927 0.41462210
sample estimates:
p
0.2142857
> ci.p <- prop.test(22,28)$conf
> ci.odds <- ci.p/(1-ci.p)
> ci.odds
[1] 1.411835 10.076740
attr(,"conf.level")
[1] 0.95> ci.p <- binom.test(22,28)$conf
> ci.odds <- ci.p/(1-ci.p)
> ci.odds
[1] 1.441817 11.053913
attr(,"conf.level")
[1] 0.95
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907