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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