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# Tests on proportions

In this chapter we present tests for the parameter of a binomial distribution. We first treat a test on the population proportion in the one-sample case. We further cover tests for the difference of two proportions using the pooled as well as the unpooled variances. The last test in this chapter deals with the equality of proportions for the multi-sample case. Not all tests are covered by a SAS procedure or R function. We give the appropriate sample code to perform all discussed tests.

# 4.1 One-sample tests

In this section we deal with the question, if a population proportion differs from a predefined value between 0 and 1.

## 4.1.1 Binomial test

 Description: Tests if a population proportion differs from a value . Assumptions: Data are randomly sampled from a large population with two possible outcomes. Let be denoted as “success” and as “failure”. The parameter of interest is given by the proportion of successes in the population. The number of successes ...

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