A binomial test uses sample data to determine if the population proportion of one level in a binary (or dichotomous) variable equals a specific claimed value. For example, a binomial test could be run to see if the proportion of leopards at a wildlife refuge that have a solid black coat color is equal to 0.35 (which is expected based on a genetic model).
The test calculates the probability of getting from a specific sample size, n, the number of the desired outcome (in this case, the number of leopards with a solid black coat color) as extreme or more extreme than what was observed if the true proportion actually equaled the claim (0.35). This is calculated using the binomial formula:
Note: There is no test statistic calculated in a binomial test, as is typically found in inferential tests. This is because the p-value is calculated directly using the binomial formula shown above.
Ho: The population proportion of one outcome equals some claimed value, or π = πo
HA: The population proportion of one outcome equals some claimed value, or π ≠ πo
- Random samples
- Independent observations
- The variable of interest is binary (only two possible outcomes).
- The number of trials, n, is fixed ahead of time.
Example 1: Hand calculation
In this video, a binomial test is run to see if the proportion of leopards with a solid black coat color equals 0.35.
Example 2: How to run in RStudio
This example tests if the percentage of female artists performing on ACL Live is different from 50%.
Sample conclusion: There is evidence to suggest that the percentage of female artists on ACL Live significantly differs from 50% (p < 0.05).