# t vs Z, distributions and testing

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#### Dason

##### Ambassador to the humans
You aren't even defining exactly what you mean by those terms. I've said it before and I'll say it again - you aren't particularly great at expressing yourself mathematically. This is another partial reason why I want to know your background.

But I will guarantee that you can't just do a simple multiplication to turn a T distribution into a Z distribution.

One could multiply the critical t value by some constant to turn it into the corresponding critical Z value for a Z test and then we could pretend we are doing the Z test - which seems to be what you're trying to do but your approach doesn't actually work. But really what is the point of that? It actually creates more work. And if your goal is to get to that point where you're talking about type-II error rates it does absolutely nothing for you because you haven't actually modified the test statistic in any meaningful way such that you change the underlying distribution.

#### joeb33050

##### Member
I can help you through this. In ANY case, with X1, X2, n, and sigma or s, the rms estimate of sigma ;is P (t </= t test) = P (Z </= Z test)?
Think about it, about expected values. Think about going to a Normal distribution, picking n samples, calculating x - mu n times and calculating the mean, x bar - mu. Dividing that by sigma or s rms/ sqrt n. Make a pdf. With infinite n, how many pdfs / n are there? Is it 1?

"But I will guarantee that you can't just do a simple multiplication to turn a T distribution into a Z distribution."
No need to multiply, it's already done. For ANY set of inputs, P (t </= t test) = P (Z </= Z test) on average. Want my workbook?

#### Dason

##### Ambassador to the humans
Nope. You failed. I asked you to explain the terms you're using and you haven't done that. You really like making wild claims without giving *valid* mathematical proof that the claims you're making actually are true.

So for the last time - either give proper mathematical justification for literally anything you're doing (which just so you're aware - you haven't done this at all yet) or respond and let me know what kind of background you have. Otherwise I'm literally done with this thread. I won't respond. And as a mod I will lock the thread and if you attempt to make another thread about this random nonsense without providing any of the feedback I ask for - I will ban you for a month.

Take some time to think over your next post.

#### joeb33050

##### Member
Comparing P (z</= Z test) and P (t</= t test), n 2 through 10, randomy inputs, shows P Z / P t = 1.0088, I think that this is rounding/estimating error.
x1, x2, n the same, sigma to Z, S RMS / sigma to t calcs.
P (z</= Z test) very close to P (t</= t test)

#### Dason

##### Ambassador to the humans
Thread closed. Send me a pm if you think it should be reopened but you better have a good reason. Basically you are unwilling to listen to anybody and it doesn't make sense to allow you to continue to rant your nonsense anymore until you actually show you're willing to listen to people that know more than you do.

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