# Computing statistical significance from experimental data

As described in my previous question, I am currently conducting an epidemiological study in a health institution where we investigate the prevalence of Corona virus infections by measuring the existence of antibodies.

We now have the results of our study and are looking at 424 participants in a population of 785 individuals and a prevalence of 2.8% (12 individuals). As posted in my question before, I used the formula from Niang 1 to calculate the necessary sample size for a 95% confidence interval and arrived at 618.

Now to my question: Since we only have 424 participants, I guess that we will not be able to extrapolate this data for the whole population? Or is there a way to do so, after all? Thank you for your guidance!

1 NAING, L., WINN, T. & RUSLI, B. 2006. Practical issues in calculating the sample size for prevalence studies. Archives of orofacial Sciences, 1, 9-14.

• Is your question about testing or about extrapolation? I would note that extrapolation is heavily related to questions about the sampling strategy, which you have not said anything about here. For example, if you put out a call on facebook and say you'll give free tests to anyone who volunteers, you will get a biased sample that would make extrapolation heavily flawed.
– mkt
Commented Aug 13, 2020 at 9:37
• A minimum sample size is necessary to achieve a desired level of precision in your estimate of population prevalence. If your sample's smaller than that minimum the consequence is that the confidence interval's wider than you'd like - but not invalid (provided it's calculated by a method appropriate to the sampling scheme, as @mkt points out). Commented Aug 13, 2020 at 9:57
• Thank you for the feedback. @mkt-ReinstateMonica What I want to have as my endpoint is to say: "3.2% of the participants in my sample were antibody-positive, so 3.2% of people in the hospital are presumed to be positive" - I thought that was called extrapolation? Commented Aug 13, 2020 at 10:06
• @Scortchi-ReinstateMonica thanks for the clarification. Our sampling scheme was actually quite crude - we had planned to test the whole population in the hospital. Since we used the formula in the linked question, we got 960 participants for an assumed prevalence of .4%, which we first assumed. Could you give me pointers as for how I would calculate the confidence interval in this case? Thanks a lot! Commented Aug 13, 2020 at 10:08
• Though your initial guesses as to the hospital population & prevalence of COVID-19 infection don't matter now you have data, your sample size calculation does assume simple random sampling (without replacement): if that assumption remains valid, you can calculate confidence intervals as planned from the true population size & no. cases observed. Commented Aug 13, 2020 at 12:19