I am asking this questions for clarifications on the terms between "null distribution" and "sampling distribution". I find that when some one says null distribution, actually they mean the same thing as when others say sampling distribution.
In this hypothesis testing article , you can see the following description of an example
We are considering a random variable Y which is normally distributed. (This is one of the model assumptions.)
Our null hypothesis is: The population mean µ of the random variable Y is a certain value µ0. For simplicity, we will discuss a one-sided alternative hypothesis: The population mean µ of the random variable Y is greater than µ0. (i.e., µ > µ0)
Another model assumption says that samples are simple random samples. We have data in the form of a simple random sample of size n.
To understand the idea behind the hypothesis test, we need to put our sample of data on hold for a while and consider all possible simple random samples of the same size n from the random variable Y.
For any such sample, we could calculate its sample mean ȳ and its sample standard deviation s. We could then use ȳ and s to calculate the t-statistic t = (ȳ - µ0)/(s/√n)
Doing this for all possible simple random samples of size n from Y gives us a new random variable, Tn. Its distribution is called a sampling distribution.
The mathematical theorem associated with this inference procedure (one-sided t-test for population mean) tells us that if the null hypothesis is true, then the sampling distribution has what is called the t-distribution with n degrees of freedom.
I have no problem with understanding the content, my main concern is about the term "sampling distribution". Here the so-called sampling distribution refers to the test statistic distribution, given the null hypothesis is true. It is a theoretical distribution. According to wikipedia , null hypothesis seems to mean the same thing. I have read many lectures notes on statistics, I find both terms coexist. But if you search for sampling distribution, you get many more results.
Could someone clarify my doubts-- Do null distribution and sampling distribution mean the same thing?