Confidence Intervals for Proportions A binomial proportion has counts for two levels of a nominal variable. 6, and the proportion of males are 8/20 or 0.4. ˆ. It is the most direct confidence interval … The "exact" method uses the F distribution to compute exact (based on the binomial cdf) intervals; the "wilson" interval is score-test-based; and the "asymptotic" is the text-book, asymptotic normal interval. We use a 95% confidence level and wish to find the confidence interval. Wald interval relies a lot on normal approximation assumption of binomial distribution and there are no modifications or corrections that are applied. The result is the Wilson Score confidence interval for a proportion: (5) 1 4 ˆ ˆ 2 ˆ 2 An example would be counts of students of only two sexes, male and female. Following Agresti and Coull, the Wilson interval is to be preferred and so is the default. confidence interval formula for a proportion: pˆ. The result is more involved algebra (which involves solving a quadratic equation), and a more complicated solution. Calculate 95% confidence interval in R CI (mydata$Sepal.Length, ci=0.95) You will observe that the 95% confidence interval is between 5.709732 and 5.976934. Interpreting it in an intuitive manner tells us that we are 95% certain that the population mean falls in the range between values mentioned above. ˆ ˆ ˆ / (4) = ± α / 2 p p z pq n. The Wilson Score method does not make the approximation in equation 3. The range described above is called a confidence interval. include.x q. Alternatively, the shortest (narrowest) such interval is sometimes desired. If there are 20 students in a class, and 12 are female, then the proportion of females are 12/20, or 0. 1 Most often cited is the central confidence interval for which the probability of being wrong is divided equally into a range of proportions below the interval and another range (usually of different size) above the interval. The Wald interval is the most basic confidence interval for proportions. The commands to find the confidence interval in R are the following: > a <- 5 > s <- 2 > n <- 20 > error <- qt (0.975, df = n -1)* s /sqrt( n) > left <- a - error > right <- a + error > left  4.063971 > right  5.936029.