# Tag Info

### Correlation between proportion variable and categorical variable

If you want to test a correlation you could construct a linear regression that codes for the categorical variable. You do this by splitting the categorical variable into binary predictors. Your model ...

### Chi-square test or Z-test for comparing two proportions?

The tests are equivalent. They both test the same null hypothesis $H_0: p_1 = p_2$, versus $H_1: p_1 \ne p_2$ (for the two-sided case). In the two-sample binomial test, we assume a Normal ...
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### How to estimate the confidence interval of a very small proportion?

I think this is precisely what Beta distribution is for. If $r\sim Beta\left(\alpha,\,\beta\right)$ then $r$ is the rate of success given that you have observed $\alpha-1$ successes and $\beta-1$ ...
• 698
1 vote

### How to estimate the confidence interval of a very small proportion?

i would suggest the jeffreys interval see here for this and alternatives https://en.m.wikipedia.org/wiki/Binomial_proportion_confidence_interval jeffreys interval is a simple formula that just uses ...
• 7,065
It seems to me that you can reduce your data to a simple 2 $\times$ 2 contingency table and run a $\chi^2$ test on it. If you just want to compare the groups, the time variable is irrelevant. You can ...