# Why do they call it "sampling distribution of the sample mean"?

Ok, I understand that there is a true population mean and one that I get from the sample. It is different for every sample and, thus, I can build the distribution of the sample means. I arrive at a distribution of sample means. But why is it a sampling distribution? Is the whole point that the moniker must be longer than necessary? What do I lose if I omit the extra qualifier and get away with distribution of sample mean alone?

• You lose channel capacity in information transmission between you and any other people when discussing statistics. This CV post has some info: stats.stackexchange.com/questions/10810/… Oct 30, 2013 at 19:43
• I seriously doubt the point of the term is to make one longer than necessary. Oct 30, 2013 at 21:22

Within a particular setting where the type of distribution is known or implied, "distribution of the sample mean" works just fine. But in general would the "distribution of the sample mean" be its sampling distribution, a bootstrap distribution, a permutation distribution, or perhaps something else?

The existence of different kinds of distribution of a sample statistic requires some linguistic method of disambiguation. Without that, you lose precision and perhaps miscommunicate with your audience.

For a given data set, the sample mean provides a single estimate of the population mean. This estimate is a constant and thus its distribution is rather boring.

In contrast, the sampling distribution of the mean refers to the frequentist approach of considering the distribution of the sample means between many hypothesized samples drawn from the same population.

So it kind of makes sense to use a 'new' word.

You can have a sampling distribution of other statistics than the mean, such as the estimated median, or estimated variance.

Sometimes "sampling distribution" might be a loose term referring to the estimated mean and estimated variance of the sample taken together (with the unspoken assumption that the distribution of sample means is approximately normal).

• I have not encountered sampling distribution as implying mean and variance. If there are usages such as you report, I would go so far as calling them incorrect. A distribution is a set of values, not a summary of them. Oct 31, 2013 at 0:59