I did not see the original post, and have no idea whether "she" is a
middle school student, a teacher, or someone else. But for the
description quoted below, I have a preliminary suggestion. If MINITAB
is available for massaging the data, use the "oneway" routine (one-way
analysis of variance) on the five age groups defined by the
investigator. Output includes a graphical display of the five group
means in their 95% confidence intervals, which would provide visual
confirmation (or not) of the hypothesis proposed, and it might then be
apparent whether the more analytical approach Radford suggests is likely
to be worth the effort. The output (displayed in a monospaced font such
as Courier) could be cut-and-pasted into a report, without having to
explain the meaning(s) of assorted coefficients in a regression model:
not everyone reads algebra fluently, but most people can apprehend
distances on a graphical output medium.
(It might also be apparent whether a quadratic equation in chronological
age looks likely to suffice; which I suspect will depend in part on the
actual ages available in the data. I would expect short term memory as
a function of age to look rather more like an exponential decay curve as
age increases beyond some ("optimal"?) value, and NOT to look much like
the right branch of a negative parabola, which will try to descend
toward negative infinity as age increases.)
While Radford's recommendation of using individual ages rather than
group mean ages is in general a good one, it may not be useful in the
present case: if the five age groups were, e.g., 5th-graders,
8th-graders, 11th-graders, college sophomores, and young adults,
only the last group would show enough variability in age to be
noticeable, if by "age" one means "number of years old at most recent
birthday", as usual.
On Sat, 3 Jan 2004, Radford Neal wrote:
> 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
-----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
