Binomial test for a single proportion  overview
This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the righthand column. To practice with a specific method click the button at the bottom row of the table
Binomial test for a single proportion 


Independent variable  
None  
Dependent variable  
One categorical with 2 independent groups  
Null hypothesis  
$\pi = \pi_0$
$\pi$ is the population proportion of "successes"; $\pi_0$ is the population proportion of successes according to the null hypothesis  
Alternative hypothesis  
Two sided: $\pi \neq \pi_0$ Right sided: $\pi > \pi_0$ Left sided: $\pi < \pi_0$  
Assumptions  
Sample is a simple random sample from the population. That is, observations are independent of one another  
Test statistic  
$X$ = number of successes in the sample  
Sampling distribution of $X$ if H0 were true  
Binomial($n$, $p$) distribution
Here $n = N$ (total sample size), and $p = \pi_0$ (population proportion according to the null hypothesis)  
Significant?  
Two sided:
 
Example context  
Is the proportion smokers amongst office workers different from $\pi_0 = .2$?  
SPSS  
Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
 
Jamovi  
Frequencies > 2 Outcomes  Binomial test
 
Practice questions  