# Best metrics to use in comparing a proportion estimate vs. the true proportion?

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?

• +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
Commented Aug 27, 2022 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 $p$. Commented Aug 27, 2022 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. Commented Jul 20, 2023 at 21:27
• Possibly related
– Dave
Commented Jul 20, 2023 at 21:35