this post was submitted on 29 Jul 2024
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whatβ½ how is the student t distribution more important than the normal distribution?? you can't even use the t unless you've confirmed that you've got a normal! ππ
Correct me if I'm wrong but isn't the student t distribution a set of distributions that includes the normal distribution?
Because if so, it feels a little like saying "you can't even call something red unless you've confirmed that it's crimson"
The t-distribution approaches the normal distribution with increasing degrees of freedom. It is certainly more relevant in for example hypothesis testing, since t-Tests (variance is estimated from the data) is much more common than z-tests (variance is treated as fixed and coming from a normal distribution).
In all of statistics or probability theory, the normal theory is however way more influential.
Nonetheless, it's a cool bit of history where modern statistics got its roots. As a lover of both statistics and guinness, i approve!π»
The t-student goes to the normal when your degrees of freedom get close to infinitum (in practice with 30 df they're practically the same).
I argue that is more important because in practice you usually don't have enough samples (or can't resample) to use the normal distribution.