Binomialtest
A binomial test is a statistical test in which the test statistic is a binomial distribution. It is used to test hypotheses about features that can take just two values ( dichotomous variables ).
Hypotheses and test statistic
With the binomial test the following hypothesis pairs for the unknown probability of a characteristic in the population to be tested:
The test statistic indicates how often the feature has occurred in a random sample of size. Under the null hypothesis, the statistical test is distributed, that is,
Significance level and critical values
Since the test statistic is distributed discretely, the predetermined significance level usually can not be met. Therefore, it is required to choose the critical values so that applies to the largest possible exact significance level.
Therefore be determined as critical values the largest and the smallest for the two-sided test, applies to the
- And
- .
The exact significance level is obtained as. For the two one-sided tests procedure is analogous.
Approximation of the distribution of the test statistic
The binomial distributed test statistic can be approximated with a different distribution. The necessary Approximationsbedingungen may vary depending on the literature source.
In the case of the approximation of the normal distribution can be considered instead of the test statistic also equal to the test statistic.