m v wrote:
>
> My wife and I both have degrees in math and have taken undergrad
> statistics courses long ago but are having trouble helping our child
> determine the appropriate statistics to use for her middle school
> science project and how to translate the result into english for her
> conclusion.
>
> Her project was to find if short term memory was better for young
> adults than for younger or older age groups. She devised a memory
> test and tested 10 people in each of five different age groups.
Taken literally, this is a compound hypothesis with a compound
negation. This is not a good model to work with. How would she
interpret a set of results suggesting that short term memory was the
same up till age 40 and then declined? Declined slowly till 40, then
declined faster? If her hypothesis were to be taken literally, she would
simply have to report "hypothesis not true" and leave it at that.
The correct approach would be first to test the simple hypothesis that
no differences exist across age groups, using one-way ANOVA. If a
difference is found, it is then valid to interpret it, using (say)
Tukey's method.
MINITAB can do all these, is easy to use, and will let her download a
30-day trial version.
In my opinion, the idea that every experiment must have a hypothesis at
all is a terrible mistake. A professional chemist trying to determine
the boiling point of a chemical does not hypothesize that it will boil
at 100 C (because water does) or at 0 K (because that's the only
"objective" choice) and then test that hypothesis; he or she measures
the boiling point. But I've seen students doing the equivalent all too
often.
Another common howler is using the experimental mean as the null value.
I believe that the usual irrationale goes something like:
"I have these data. I've looked at them like I was told, and now I need
to do a hypothesis test because that will give me a yes-or-no answer.
"Hmmm. I need a null hypothesis mu = mu-nought. What's mu-nought? It's
got to be something the mean might be. Well, I guess I can use the
sample mean, 17.23501. I don't see anything else to use. OK, I'll type
that in.
"OK, the software says my p value is 1.00000. I'll write that down."
(NOTE: Subject, using Technology, has not observed that the test
statistic is 0.0000 and was obtained by subtracting the sample mean from
itself.)
-Robert Dawson
.
.
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