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## Exact binomial test using R

### Exact Binomial Test

Gives something like this:

 Exact binomial test data: c(1003, 1014) number of successes = 1003, number of trials = 2017, p-value = 0.4119 alternative hypothesis: true probability of success is less than 0.5 95 percent confidence interval: 0.0000000 0.5158274 sample estimates: probability of success 0.4972732

### Sign Test

R does not have a separate sign test, but it can be carried out by first eliminating ties and then using the exact binomial test.

Gives something like this:

 Exact binomial test data: c(7, 1) number of successes = 7, number of trials = 8, p-value = 0.03516 alternative hypothesis: true probability of success is greater than 0.5 95 percent confidence interval: 0.5293206 1.0000000 sample estimates: probability of success 0.875

### McNemar's test

Gives something like this:

 McNemar's Chi-squared test with continuity correction data: tab1 McNemar's chi-squared = 34.3, df = 1, p-value = 4.724e-09

### Cox & Stuart test for trend

Gives something like this:

 Exact binomial test data: c(4, 0) number of successes = 4, number of trials = 4, p-value = 0.125 alternative hypothesis: true probability of success is not equal to 0.5 95 percent confidence interval: 0.3976354 1.0000000 sample estimates: probability of success 1

There is as yet no provision in the package epitools in R for estimating the confidence interval to the difference between paired proportions.