Binomial test for a single proportion - overview
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Binomial test for a single proportion |
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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:
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Example context | |
Is the proportion smokers amongst office workers different from $\pi_0 = .2$? | |
SPSS | |
Analyze > Nonparametric Tests > Legacy Dialogs > Binomial...
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Jamovi | |
Frequencies > 2 Outcomes - Binomial test
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Practice questions | |