How to calculate a suitable sample size for reducing the standard error by a factor of 4? For instance if I have sample size of 1000 how much would I increase it to have a standard error reduced by 4?
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$\begingroup$ What do you think? $\endgroup$– user2974951Commented Feb 20, 2023 at 12:35
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$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotCommented Feb 20, 2023 at 12:36
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$\begingroup$ Welcome to Cross Validated! How are you calculating the standard error? If you have an equation, perhaps that can suggest a solution. $\endgroup$– DaveCommented Feb 20, 2023 at 12:40
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$\begingroup$ I don't have more data. Standard error of the estimate mean should be equal to σ / √n $\endgroup$– SamCommented Feb 20, 2023 at 12:46
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1$\begingroup$ So if you want $\sigma/\sqrt n$ to be a quarter of its previous size, what do you have to do to $n?$ $\endgroup$– DaveCommented Feb 20, 2023 at 12:56
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$$ SE_1 =\dfrac{\sigma}{\sqrt n_1}\\ SE_2 =\dfrac{\sigma}{\sqrt n_2} $$
You want $SE_1/SE_2=4$. Therefore, $ 4=SE_1/SE_2=\dfrac{ \sigma/\sqrt{n_1} }{ \sigma/\sqrt{n_2} } $. Now just do some algebra to get $n_2$ in terms of $n_1$.
