Why is the standard error of the mean also called the standard deviation of the sampling distribution of the mean, when the two values co…

Answer by Joe Blitzstein:

Q: What's the difference between a standard deviation and a standard error?

A: Hard to say what the difference is, but the ratio is the square root of the sample size.

By definition, the standard error of a statistic is its standard deviation (which, again by definition, is the standard deviation of its sampling distribution). The reason for having separate terminology is to reduce the risk of confusion with the population standard deviation. The statement "the latter is calculated by the variance in the sample distribution" is not correct.

Specifically, let [math]y_1,\dots,y_n[/math] be independent random variables, with [math]E(y_j)=\mu, Var(y_j)=\sigma^2.[/math] Let [math]\bar{y}[/math] be their sample mean, which is the natural estimator for [math]\mu[/math].

Then the standard deviation of [math]\bar{y}[/math] is [math]\sigma/\sqrt{n}[/math]. This is known as the standard error of the sample mean, to avoid confusion with the population standard deviation [math]\sigma[/math].

Why is the standard error of the mean also called the standard deviation of the sampling distribution of the mean, when the two values co…

Advertisements

Leave a comment

Filed under Life

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s