One of the advantages of having your work as your hobby is that you get
to do it all the time. Of course, the disadvantage is that you
have to do it all the time.
One of the enjoyable sides of statistics this fall has been shifting
over from Splus to R. R is open source (read “FREE”), but
maintained by some very smart people (who provide a lot of code for
Splus as well). I can do nearly everything I want in R and I
don’t have to fight with the Splus license manager to be able to do
it. There are a few occasional perks of Splus that I miss – but
since they’ve decided in the last couple of years to focus on the
people with the big bucks (financial institutions, drug companies), I
don’t really miss much.
Today I’ve been working on a project that involves looking at two
cognitive tests that were done in several hundred women who were at
different stages of the menopausal transition. The tests work
like this. An interviewer reads a brief story and then asks the
interviewee to name as many story elements as they can. There are
12 elements that are scored, so everyone gets a score from 0 to
12. This is called immediate recall. The interview goes on
to other items and then, a few minutes later, the interviewer repeats
the question (this is called delayed recall – sneaky, isn’t it?) and
notes how many elements the interviewee can remember. Got
it? On average the women in our study could name about 10 of the
12 elements. Pretty good!
The part of the brain that is working when we do immediate and short
term memory tasks like this involves the prefrontal cortex (which is in
the front of our brains). This part of our brain happens to have
more estrogen receptors (ie things that make cells sensitive to the
presence or absence of estrogen), so it is reasonable to think that
this type of memory might reasonably be enhanced (or not) as a woman’s
estrogen balance changes during the menopausal transition.
Everyone wants to know if there are differences in the level of
functioning and, if so, what those are. Some colleagues out in CA
had been working with this data and had not found any significant
differences. I recently started working with the same measures
(immediate and delayed recall), looking at the relationship between
various genotypes found in blood samples and scores on our memory
tests, and realized that there was a better way to approach the
analysis of these measures of immediate and delayed recall. My
colleagues were thinking of them as a continuous score on a scale of 0
to 12 and examining means and standard deviations as if they were
normally distributed (as in “bell-shaped curve”). The problem
with that approach is that there is a clear “ceiling effect” – that is,
you can’t get more than 12. So, you could have a standard
deviation of 2 and a mean of 10, but you would never be able to get 2
standard deviations above the mean (10+2*2=14), because the maximum
score is 12. That’s bad, because in a normal distribution you
would expect to see about 15% of your people have scores above 12.
Another way of thinking about it is like 12 flips of a coin. How
is that? Well, there are 12 elements and the interviewee either
succeeds (heads) or fails (tails) to name each one. Statisticians
call this kind of collection of successes and failures a binomial
random variable. There is the tacit assumption that the
probability of successfully naming each element is the same, which is
not strictly true. (Some are probably easier to remember.)
But as a famous statistician (I think it was Dr. George Box) once
pointed out: “All statistical models are wrong! But some of
them are useful.” In this case thinking of the test results as a
binomial random variable is more useful than thinking about it as
having a normal distribution with a mean and standard deviation.
Cut to the chase. When you treat the results using means and
standard deviations, there are no significant differences.
However, when you treat it as flips of a coin, there are significant
differences, even after you adjust for a whole bunch of other things
that are also related to cognitive functioning (age, education,
ethnicity, BMI, poor health, vasomotor symptoms, poor sleep, somatic
symptoms, mood symptoms, estrogen levels and FSH levels). The
primary finding will be that there is a small but significant decrease
in the number of elements named by women who are post-menopausal
compared to those who are late peri-menopausal. And the effect is
significant at the 0.001 even after adjusting for multiple comparisons,
which is statistician-speak for “WOW!”.
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