1
$\begingroup$

Wikipedia states

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and the population standard deviation is unknown.

And Britannica also states similarly

Student’s t-test, in statistics, a method of testing hypotheses about the mean of a small sample drawn from a normally distributed population when the population standard deviation is unknown.

Is the small sample size really a necessary condition for the distribution to be a t-distribution? Isn't a sample drawn from a normal population with unknown variance a necessary and sufficient criterion?

$\endgroup$
1
  • 1
    $\begingroup$ You’re right about necessary and sufficient. Their phrasing only describes a sufficient condition, though it would be nice if they didn’t make it sound necessary. $\endgroup$
    – Dave
    Jul 4 '20 at 14:57
2
$\begingroup$

The paragraph mentions that the Student's t-test is used when the sample size is small. It doesn't mean that the Student's t-distribution requires small sample size.

When the sample size is large, the Student's t-distribution is indistinguishable to the normal distribution. And Z-test would be good enough.

$\endgroup$
1
  • $\begingroup$ Strange enough, I don’t see people wanting to z-test when they have large sample sizes. I still see t-testing used. $\endgroup$
    – Dave
    Jul 4 '20 at 14:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.