standard error
The standard error(SE) is very similar to standard deviation. Both are measures of spread. The higher the number, the more spread out your data is. To put it simply, the two terms are essentially equal — but there is one important difference. While the standard error uses statistics (sample data) standard deviations use parameters (population data).
Pooled sample standard error
The standard error of a sample is another name for the standard deviation of a sample.There’s a slight difference between standard deviation and pooled sample standard error:
- When we are talking about a population, we talk about standard deviations.
- When we talk about a sample we call it a standard error.
\[SE_{pooled} = \sqrt{\frac{\left (n_{1}-1 \right )s_{1}^{2}+ \left (n_{2}-1 \right )s_{2}^{2}}{n_{1}+n_{2}-2}} \]
\[SE_{pooled} = \sqrt{\frac{\left (n_{1}-1 \right )s_{1}^{2}+ \left (n_{2}-1 \right )s_{2}^{2}+...+\left (n_{k}-1 \right )s_{k}^{2}}{n_{1}+n_{2}+...+n_{k}-k}} \]
