I was reading a post where the author was conducting hypothesis testing on the incidence of COVID-19 by conducting a poll on their Instagram. She found that while the world prevalence for COVID-19 was 0.5%, the prevalence in the sample was 6%.
I'm curious how the author found the t-statistic to get the p-values in categorical data. Isn't standard deviation required to get the t-statistic? What would be the standard deviation in this data where the responses are either a "yes" or a "no"?
Since the variable is a proportion, the standard deviation is contained in the proportion.
Proportion variables are Bernoulli variables. For a Bernoulli variable with parameter $p$, the expected value is $p$ and variance is $1-p$.
Now you have the standard deviation that you can use in a hypothesis test.
Do note, however, that a t-test would not be ideal. The basic way of testing a proportion is a proportion z-test. My favorite proportion test at the moment is called the G-test. Other popular ways include the chi-squared test and Fisher’s exact test.
The reason a t-test is not ideal is because it is designed for normal distributions. While it has some nice robustness to deviations from normality, there are specialized tests for proportions (given above) that have better ability to reject a false null hypothesis (power) without having excessive rejections of true null hypotheses.
