standard error
1. sampling distribution
- Pick a statistic that can be calculated over a sample (like the sample mean)
- A simple consists of \(n\) observations \(x_1, x_2, ... x_n\)
- Then, over repeated samplings, we can build a distribution of the sample statistic
- This distribution has its own mean and variance
2. standard error
- Let \(\bar{x}\) be the random variable that corresponds with the sample mean over the samples that can be drawn
- Then, the standard deviation of this random variable is \(\sigma_{\bar{x}} = \sigma/\sqrt{n}\) where \(\sigma\) is the population standard deviation.