Further, with computers to do the analysis, it is just as easy to use t as to use z.
So - always use t, never z.
And, yes, p values are better than critical values. (Unless you are stuck out in the desert without a computer....)
Alan
On Sunday, November 24, 2002, at 06:03 AM, Jay Warner wrote:
the "two question" question was beaten to death, but I can't help sticking myself
into this one. It's too old to ignore :)
when we compare two groups, i.e., one indep. categorical variable of two levels,
near continuous & interval or ratio scale response, we have a z or t test on our
hands.
the 'party line' is that if sigma is 'known' you can use the z, if not use t. And
often, to help 'simplify' things, the book will say that when the sample size is
over 30, you can use z anyway - the estimate of sigma is 'close enough.'
Please don't side track now on the population size - it is most often effectively
infinite.
What is meant by 'known sigma'? It means that you have measured a heck of a lot
of items (30 or more, if you believe the book) to estimate sigma of the
population, or you have been handed sigma from someone else who has made the
measurements. In a manufacturing environment, that someone is typically the QA
dept., if they follow this logic. In typical business-related analyses the
origins of 'known' sigmas may be less clear.
How good (accurate, precise, unbiased) is this estimate of sigma? When it comes
from someone else, we don't know, a nd often can't know. So we call it 'known'
and proceed. But the number we have is still an estimate of the population sigma,
which in principle we can never measure exactly (most cases). And often, we have
no way of assessing how well that number applies to the current situation. Did
the original sigma estimate come from the same defined population as the current
data? Did these samples use a different paint? Did this survey contact people
from the same part (statistically identical group of people) of town?
May I try a different dichotomy?
When I am given the estimated sigma from somewhere else, so that I can't assess
the validity of it, I call this an _external_ estimate of sigma. I accept it with
the usual reservations, and proceed to do the problem. The equation will be a z
test type.
When I am not handed sigma on a platter, but must estimate it from the sample
data, I call that an _internal_ estimate of sigma. The estimate definitely
applies to the population at hand, to be considered & evaluated as ever. the
equation will be a t test.
Notice: No n >= 30. As some mentioned recently, with machines we have p-values
for t tests, that were not feasible in the dark past without the machines.
therefore, there is no need to decide when n is 'close enough' to use a z test.
Using this method to split between the two test types, there is less confusion,
and we can retain a healthy skepticism about the validity of that external
estimate of sigma.
What are the holes in this approach?
Cheers,
Jay
"Robert J. MacG. Dawson" wrote:
Paul Bernhardt wrote:Now, if we can only get over the arbitrariness of the n<30 cut-off forHow about (at least for social & health sciences): use t when you don't
use of t vs z and teach: use z when you know sigma and t when you don't.
(Triola, as much as I like some of its choices, still retains this) <sigh>
know sigma, and speak to a statistician when you think you do?
-Robert Dawson
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