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This suggested edit was approved and applied to the post over 1 year ago by Peter Taylor‭.

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What is the formula for sample standard deviation of a small sample size?
  • The formula for sample standard deviation is given by:
  • s=i=1i=N(xix¯)2N1
  • **Am I right that when the sample size is small (N<30), the formula for sample standard deviation becomes:**
  • s=tN1,confidencei=1i=N(xix¯)2N1        ?
  • Here, tN1,confidence is the Student's t coefficient obtained from the tables (the tables are given, for instance, [here](https://www.scribbr.com/statistics/students-t-table/)).
  • -----------------
  • The reason I am asking is the following. I had no doubts whatsoever that I must multiply standard deviation by the Student's t coefficient for a small sample size. And I have been doing it all the time. I used it in a draft for an article. When I was checking the draft, I decided to check this formula. First, I could not remember where I got it from. Second, I searched the books and the Internet only to find out that people use Student's t coefficient to calculate confidence interval, not standard deviation. I tried to derive my formula from the formula for confidence interval and failed. I talked to a fellow student who also thinks standard deviation must be multiplied by Student's t coefficient and also does not remember why.
  • The formula for sample standard deviation is given by:
  • s=i=1i=N(xix¯)2N1
  • **Am I right that when the sample size is small (N<30), the formula for sample standard deviation becomes:**
  • s=tN1,confidencei=1i=N(xix¯)2N1        ?
  • Here, $t_{N-1, \text{confidence}}istheStudentst$ coefficient obtained from the tables (the tables are given, for instance, [here](https://www.scribbr.com/statistics/students-t-table/)).
  • -----------------
  • The reason I am asking is the following. I had no doubts whatsoever that I must multiply standard deviation by the Student's t coefficient for a small sample size. And I have been doing it all the time. I used it in a draft for an article. When I was checking the draft, I decided to check this formula. First, I could not remember where I got it from. Second, I searched the books and the Internet only to find out that people use Student's t coefficient to calculate confidence interval, not standard deviation. I tried to derive my formula from the formula for confidence interval and failed. I talked to a fellow student who also thinks standard deviation must be multiplied by Student's t coefficient and also does not remember why.

Suggested over 1 year ago by samcarter‭