Post History
#6: Post edited
by
samcarter
·
2023-09-13T22:46:05Z (8 months ago)
see previous edit summary
What is the formula for sample standard deviation of a small sample size?
- The formula for sample standard deviation is given by:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
- $$s = t_{N-1, \text{confidence}} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
Here, $t_{N-1, confidence}$ 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:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
- $$s = t_{N-1, \text{confidence}} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
- Here, $t_{N-1, \text{confidence}}$ 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.
#5: Post edited
by
samcarter
·
2023-09-13T19:17:25Z (8 months ago)
don't set whole words in math mode, this completely destroys the kerning
What is the formula for sample standard deviation of a small sample size?
- The formula for sample standard deviation is given by:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
$$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$- Here, $t_{N-1, confidence}$ 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:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
- $$s = t_{N-1, \text{confidence}} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
- Here, $t_{N-1, confidence}$ 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.
#4: Post edited
by
Ivan Nepomnyashchikh
·
2023-09-11T20:21:42Z (8 months ago)
- The formula for sample standard deviation is given by:
$$s = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}}$$- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
$$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$- Here, $t_{N-1, confidence}$ 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:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
- $$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
- Here, $t_{N-1, confidence}$ 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.
#3: Post edited
by
Flomic
·
2023-09-11T16:50:56Z (8 months ago)
Minor edit of equation format (for correctness)
What is the formula for sample standard deviation of a small sample size?
- The formula for sample standard deviation is given by:
$$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
$$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$- Here, $t_{N-1, confidence}$ 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:
- $$s = \sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
- $$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
- Here, $t_{N-1, confidence}$ 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.
#2: Post edited
by
Ivan Nepomnyashchikh
·
2023-09-08T17:02:37Z (8 months ago)
- The formula for sample standard deviation is given by:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
**Am I write that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**- $$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
- Here, $t_{N-1, confidence}$ 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:
- $$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
- **Am I right that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
- $$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
- Here, $t_{N-1, confidence}$ 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.
#1: Initial revision
by
Ivan Nepomnyashchikh
·
2023-09-08T17:01:40Z (8 months ago)
What is the formula for sample standard deviation of a small sample size?
The formula for sample standard deviation is given by:
$$s = \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}}$$
**Am I write that when the sample size is small ($N<30$), the formula for sample standard deviation becomes:**
$$s = t_{N-1, confidence} \sqrt{\frac{\sum_{i=1}^{i=N} (x_i - \bar{x})^2}{N-1}} \ \ \ \ \ \ \ \ ?$$
Here, $t_{N-1, confidence}$ 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.