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My colleagues and I argued about the point estimate's accuracy. They said that

"The point estimate will tend to be accurate if the sample size exceeds 30."

While I am saying no,

"The point estimate is always a subject to error as we will never know the population value"

Which is the correct one?

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    $\begingroup$ What do you mean with 'accurate'? Unbiasedness? Since you come up with the 'n > 30', I guess you are thinking in the way of the Central Limit Theorem which says that the mean is unbiased. Now assuming your point estimate should represent this mean, there is still error. Unbiasedness means that if you repeat your experiment very often, calculate your point estimate and take the mean of all these point estimates, then it will be very close to the population value. However, if you just take one sample and calculate a point estimate, this value might not be even close to this population value. $\endgroup$
    – Mathemagician777
    Commented Dec 20, 2023 at 10:51
  • $\begingroup$ @Mathemagician777 Yes, that is what my colleagues think about. They believed it was because of the CLT. So, any large sample size will result in a very small sampling error without any conditions. $\endgroup$
    – Dr. Statistics
    Commented Dec 20, 2023 at 12:08
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    $\begingroup$ The question is too vague and depends a lot on what one considers as 'accurate'. It is also unclear what the actual discussion point is. The second statement has little to do with the first statement, or at least it is unclear why it should be a reason that the first is wrong. Potential related questions: stats.stackexchange.com/search?q=%22all+models+are+wrong%22 $\endgroup$
    – Sextus Empiricus
    Commented Dec 20, 2023 at 12:29
  • $\begingroup$ @SextusEmpiricus Thank you for your comment and the link. My colleague argues that the large sample size, without any conditions, reduces the sampling error. I don't see it this way, as there must be conditions, such as the sampling method. $\endgroup$
    – Dr. Statistics
    Commented Dec 20, 2023 at 12:58
  • $\begingroup$ @SextusEmpiricus The question is very clear about which statement is correct. I do respect your comment, but I think the question is should not be closed. $\endgroup$
    – Dr. Statistics
    Commented Dec 21, 2023 at 4:48

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Both, really, at least, in some conditions. But also neither, in some conditions.

Your statement is correct, unless we actually do know the population value. This can happen if the population is small and easily defined. E.g "what is the average age of full time professors in NYU's psychology department?" But usually, your statement is right, we have a sample and do not know the population value perfectly.

However, if you have a random sample, then the accuracy goes up as sample size increases, and, for some distributions, 30 is reasonably accurate (for some definition of "reasonably"). How much accuracy you need varies by application.

But it also depends what you are estimating. It's easier to estimate the mean than the 90th percentile (for most distributions, anyway).

EDIT On the other hand, if you do not have a random sample, it doesn't matter how big your sample is. The most infamous example of this is the Literary Digest poll of the 1936 presidential election. They polled tens of millions of people and got millions of response and confidently predicted that Dewey would beat FDR in a landslide. But, FDR actually won one of the biggest landslides of any presidential election. What went wrong? The magazine polled subscribers to the magazine, car owners, and phone owners. In 1936 this was a very biased sample.

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  • $\begingroup$ Great! Your help is fantastic. I appreciate it so much. However, do you know how about the sampling method? It affects the result, even if the sample size is large enough. For example, if I have a sample of 35 students with low grades, does that mean the average of the whole class (say 200 students) will be low? No, it is not. It depends on my sample. That is my point. $\endgroup$
    – Dr. Statistics
    Commented Dec 20, 2023 at 12:06
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    $\begingroup$ OK, I said "if your have a random sample" but I will add more about that. $\endgroup$
    – Peter Flom
    Commented Dec 20, 2023 at 12:14
  • $\begingroup$ Thank you so much. It is so much appreciated. $\endgroup$
    – Dr. Statistics
    Commented Dec 20, 2023 at 12:54

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