Re: Student's t vs. z tests

[Paul Swank]

I agree. I normally start inference by using the binomial and then then the normal approximation to the binomial for large n. It might be best to begin all graduate students with nonparametric statistics followed by linear models. Then we could get them to where they can do something interesting without taking four courses.


At 01:28 PM 4/19/01 -0500, you wrote:
>Why not introduce hypothesis testing in a binomial setting where there are
>no nuisance parameters and p-values, power, alpha, beta,... may be obtained
>easily and exactly from the Binomial distribution?
>
>Jon Cryer
>
>At 01:48 AM 4/20/01 -0400, you wrote:
>>At 11:47 AM 4/19/01 -0500, Christopher J. Mecklin wrote:
>>>As a reply to Dennis' comments:
>>>
>>>If we deleted the z-test and went right to t-test, I believe that
>>>students' understanding of p-value would be even worse...
>>
>>
>>i don't follow the logic here ... are you saying that instead of their
>>understanding being "bad" .... it will be worse? if so, not sure that this
>>is a decrement other than trivial
>>
>>what makes using a normal model ... and say zs of +/- 1.96 ... any "more
>>meaningful" to understand p values ... ? is it that they only learn ONE
>>critical value? and that is simpler to keep neatly arranged in their mind?
>>
>>as i see it, until we talk to students about the normal distribution ...
>>being some probability distribution where, you can find subpart areas at
>>various baseline values and out (or inbetween) ... there is nothing
>>inherently sensible about a normal distribution either ... and certainly i
>>don't see anything that makes this discussion based on a normal
>>distribution more inherently understandable than using a probability
>>distribution based on t ... you still have to look for subpart areas ...
>>beyond some baseline values ... or between baseline values ...
>>
>>since t distributions and unit normal distributions look very similar ...
>>except when df is really small (and even there, they LOOK the same it is
>>just that ts are somewhat wider) ... seems like whatever applies to one ...
>>for good or for bad ... applies about the same for the other ...
>>
>>i would be appreciative of ANY good logical argument or empirical data that
>>suggests that if we use unit normal distributions .... and z values ... z
>>intervals and z tests ... to INTRODUCE the notions of confidence intervals
>>and/or simple hypothesis testing ... that students somehow UNDERSTAND these
>>notions better ...
>>
>>i contend that we have no evidence of this ... it is just something that we
>>think ... and thus we do it that way
>>
>>
>>
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------------------------------------
Paul R. Swank, PhD.
Professor & Advanced Quantitative Methodologist
UT-Houston School of Nursing
Center for Nursing Research
Phone (713)500-2031
Fax (713) 500-2033
soon to be moving to the Department of Pediatrics
UT Houston School of Medicine

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