December 9, 2005

• 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!".

  • 2:01 am
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