In article <[EMAIL PROTECTED]>,
m v <[EMAIL PROTECTED]> wrote:
>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.
>
>What would be an appropriate statistical test for this hypothesis and
>data (considering it is for a middle school project)?
Her hypothesis is apparently that the memory is best at some
intermediate age, and worse for both smaller and larger ages. It's
not clear whether she thinks she knows which age memory is best at.
Probably it would be wise to assume that this isn't known for sure.
It seems to me that this might best be handled as a regression problem.
A suitable model would say that the test result for a person can be
modeled as
result = a + b age + c age-squared + residual
where a, b, and c are regression coefficients to be estimated, and
"residual" is the random variation in the results that isn't explained
by age. Here, age-squared is just the square of the person's age.
The inclusion of the square term in the model allows for there to be a
"hump" at some age, where the results tend to be greater than at both
younger and older ages (I'm assuming a larger value for "result"
corresponds to better memory). This will happen if the coefficient
"c" in the model is negative. Any stats package should be able to fit
this model, producing an estimate for c. If the estimate is negative,
you should also be able to look at a p-value for the null hypothesis
that c is actually zero. A p-value close to 0 would be an indication
that the true value of c is likely to also be negative - ie, that the
hump is real. It should also be possible to figure out from a, b, and
c where the peak of the hump is. If it's outside the range of ages
tested, then one couldn't assume that it's real (even if the p-value
is small), since the model may not be good for extrapolating beyond
the range of the data.
Note that rather than round off the age of each person to the centre
of the the "group" that they are in, it would be better if she could
actually find out the exact ages of each person tested, and use them.
Hope this helps,
Radford Neal
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Radford M. Neal [EMAIL PROTECTED]
Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
University of Toronto http://www.cs.utoronto.ca/~radford
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