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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It's the things we do know that just ain't so." --Artemus Ward
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