Simulate 100 coin tosses
heads <- rbinom(1, size = 100, prob = 0.5)Test whether about 50% heads came up in these coin tosses. This uses the normal approximation to the binomial distribution with or without the continuity correction
prop.test(heads, 100) # continuity correction TRUE by default##
## 1-sample proportions test with continuity correction
##
## data: heads out of 100, null probability 0.5
## X-squared = 0.25, df = 1, p-value = 0.6171
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.4280 0.6296
## sample estimates:
## p
## 0.53
prop.test(heads, 100, correct = FALSE) # without continuity correction##
## 1-sample proportions test without continuity correction
##
## data: heads out of 100, null probability 0.5
## X-squared = 0.36, df = 1, p-value = 0.5485
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.4329 0.6249
## sample estimates:
## p
## 0.53
prop.test(heads, 100, conf.level = 0.95) # confidence level of 0.95 is the default##
## 1-sample proportions test with continuity correction
##
## data: heads out of 100, null probability 0.5
## X-squared = 0.25, df = 1, p-value = 0.6171
## alternative hypothesis: true p is not equal to 0.5
## 95 percent confidence interval:
## 0.4280 0.6296
## sample estimates:
## p
## 0.53
The exact test is based on binomial probabilities:
binom.test(heads, 100)##
## Exact binomial test
##
## data: heads and 100
## number of successes = 53, number of trials = 100, p-value = 0.6173
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
## 0.4276 0.6306
## sample estimates:
## probability of success
## 0.53
Save the output in an object named temp.
temp <- prop.test(heads, 100)names(temp) shows us what output is generated and the names of the output objects.
Confidence interval for the proportion of heads
temp$conf.int## [1] 0.4280 0.6296
## attr(,"conf.level")
## [1] 0.95
Estimated proportion
temp$estimate## p
## 0.53
Pvalue for the hypothesis test
temp$p.value## [1] 0.6171