Timeline for What is the standard error of a binomial process with a false-positive rate
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| Jan 31 at 14:38 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| Jan 31 at 14:08 | comment | added | cambridgecircus | @GaryS no worries, if this answer has helped, please mark it as answered. Regarding your follow-on comment, yes it's possible to have $T$ and $F$ as RVs themselves. However I'm not too sure what yo mean by $Tp$ and $F(1-p)$ being negatively correlated, and the algebra simplyfing. Also I'm not sure what you mean by treating $T$,$F$ as RVs but parameters elsewhere; the point is that $\hat{p}$ will be a compound probability distribution parameterised by $T$ and $F$, which are RVs themselves. | |
| Jan 30 at 19:00 | comment | added | Gary S | The comments on the original post raise an interesting question. Suppose $T$ and $F$ as random variables with known probabilities, such as $T=p(Y=1|X=1)$, where $X$ is the patient's true state, disease or not. The $Var(Y_i)$ is the variance of the sum of two (negatively) correlated terms: $Tp$ and $F(1-p)$. The algebra simplifies nicely. However, can we treat $T$ and $F$ as random variables when addressing the variance of $Y_i$ but treat them as parameters elsewhere in the equation for $\hat{p}$? | |
| Jan 30 at 18:46 | comment | added | Gary S | Thanks, cambridgecircus for you clear and most helpful answer, which has helped me learn. | |
| Jan 29 at 1:40 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| Jan 28 at 15:30 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| Jan 28 at 15:21 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| Jan 28 at 15:14 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| Jan 28 at 15:05 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| Jan 28 at 14:53 | review | First answers | |||
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| Jan 28 at 14:51 | history | edited | cambridgecircus | CC BY-SA 4.0 |
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| S Jan 28 at 14:39 | review | First answers | |||
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| S Jan 28 at 14:39 | history | answered | cambridgecircus | CC BY-SA 4.0 |