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I have a sample of data with n=200 and I would like to predict my descriptive statistics such as mean, Std Dev and 95% CI when I have specific sample size for example n=10 based on the current study. I assumed my population follows the Normal distribution and I applied t test to calculate CI. What I have done, I applied random sampling with replacement with n=10 from the original sample and repeated the process 100 times and calculated the mean of each 100 samples then calculate the mean(100 means), sd(100 means) then 95%CI(100 means) to get a good prediction of descriptive statistics for any random sample with size n=10. I was wondering if this approach is correct or not? Or the other solution could be to get the mean(100 means) and Pooled.Sd(100 sd) then calculate 95%CI. Could you please give me advise?

Thanks in advance for your help.

Ati
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  • Ordinarily, when we estimate something it is a property of a postulated underlying distribution. A "descriptive statistic" is something else altogether: it's a mathematical function of data. It appears you are trying to determine something about statistics of smaller samples, but even then the question is ambiguous: are you trying to ask about how those statistics vary among all possible samples or only how they vary among all possible subsamples of the data? Regardless, the applicability of a CI here is unclear, so please spell out what you mean by that. – whuber May 08 '23 at 14:50
  • Thanks for your reply. My main question is what would be the best estimation of mean and Std Dev and 95% CI for any new sample with size n (=10) based on the current study and data (N=200? – Ati May 08 '23 at 15:11
  • The best estimate to use for any future sample is the best estimate for the population. The CI is not estimated, because it is not a property of the population: as a property of a new sample, it is a prediction. Maybe it would be helpful to review this distinction: see https://stats.stackexchange.com/questions/16493 for instance. If you really do want to predict a CI, then the answer depends on what specific procedure to compute a CI you are using as well as the assumptions you make about the population, so please include that information in your post. – whuber May 08 '23 at 15:29
  • Yes, I want to predict CI for new sample size (n=10), and as I assumed the population follows the normal distribution and I used t.test for calculating new CI. – Ati May 08 '23 at 15:36
  • Good--that's clear now. Please edit your post to reflect those details. – whuber May 08 '23 at 15:39
  • Thanks, I have added... – Ati May 08 '23 at 15:55

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