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Suppose I have a proportion estimate defined as the proportion of times some event occurs out of $N$ trials. I call this proportion the sample proportion $\hat{p}$, while I call a second as the true population proportion $p$. Suppose I have something akin to a bootstrap over different inputs, where I can generate many such pairs, and I would like to compare these two values as my evaluation criteria. Generally, I am thinking of just taking the difference as a metric in comparing how different they are:

$$ \hat{p}-p $$

However, are there better metrics for comparing these? Would the ratio be better in certain cases?

kjetil b halvorsen
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user321627
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  • +1 for the interesting q, but how do you know the population value $p_2?$ $\text{//}$ It would be more common to refer to your $p_2$ parameter as $p$ and your $p_1$ estimate of $p_2$ as $\hat p$. – Dave Aug 27 '22 at 11:10
  • @Dave Thanks, I have changed it. I am assuming that the population value is known. For example, I have the actual value and I want to evaluate how well a model gets $\hat{p}$ to the true value $p$. – user321627 Aug 27 '22 at 11:52
  • If both $p$ and $\hat{p}$ would tend to be small, the difference would also be small, so the ratio would be better, I think. – kjetil b halvorsen Jul 20 '23 at 21:27
  • Possibly related – Dave Jul 20 '23 at 21:35

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