I ran an experiment looking if injuries affect the mortality of crabs over 50 days. How do I calculate the standard error for days when crabs died in relation to the percent mortality? Say I start with 24 crabs. On day 1, 11 crabs die. Day 2, 3 more crabs die. Day 5, 1 more crab dies. The rest survive until the end. That first day I'd have 45.8% mortality but how to I calculate the standard error?
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4$\begingroup$ Have you looked into survival analysis? What exactly do you want to find out? $\endgroup$– COOLSerdashJun 28, 2019 at 13:11
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It is a different story if you want to calculate the life expectancy and its standard error than if you want to calculate "percentage of individuals dead by day $n$" plus its standard error.
If I understood correctly, I should assume it is the latter case. Fortunatelly, when talking about proportions, you can estimate the standard error as $\sqrt{\frac{p(1-p)}{n}}$ where $p$ is the proportion of dead individuals (in a $[0,1]$ rannge, rather than percentage and $n$ is your sample size. The result you get must be multiplied by 100 if you want it as a percentage (see binomial distribution) for more details. What you are trying to estimate is nothing than the standard error of a binomial distribution divided by sample size in order to make it a proportion)
INTERESTING NOTE: You can certainly be sure that it will be lower than $\frac{1}{2\sqrt{n}}$, since $p(1-p)$ will be at most $0.25$
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$\begingroup$ Yes you are correct in assuming I'm after "percentage of individuals dead by day n". So, using that formula for day one: SE=sqrt(.458(1-.458)/24) * 100 = 10.17% What about calculating for day 2 when 2 more crabs die. So total of 13 dead. Should I pull out the 11 that already died from the sample size to calculate day 2 standard error? $\endgroup$ Jun 29, 2019 at 3:00
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$\begingroup$ That actually depends on what you exactly want to measure. You can calculate the proportion of individuals that die on day 2 from the overall population. Or maybe you want to calculate the chance of dying on day 2 among those who survied day 1. The only condition is that you have to be consistent (use the same data for both estimation of proportion and standard error) $\endgroup$– DavidJun 29, 2019 at 17:43