MEDIAN?

On Thu, 13 Nov 2003 12:40:46 -0600, Al. Lohse <[email hidden]>

Quoted message said:

from:
http://www.pfizer.com/are/news_releases/mn_2003_1112.html
we have:
"Lipitor-treated patients experienced a
median 0.4% reduction in total plaque volume,
defined as all of the plaque present within a
segment of a single artery—while patients who
received Pravachol showed a
significant increase in total plaque volume
(2.7% median)."

The results look good, but are presented as
changes in **** median ****. Who uses median?

If you also add-in that "total plaque volume" is a poorly standardized
method to follow regression of atherosclerosis, I too have difficulty
accepting the current study as a reason to change prescription practice.

Quoted message said:

If there are an odd number of patients, then
the result of only one patient represents the
median. If there are an even number of
patients, then the result of only two
patients represent the median. The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

My recollection of statistics suggested that
the difference between a mean and a median
was a quick measure of skew. If mean and
median are similar in value then a
distribution can reasonably be expected to be
somewhat symmetrical, even though that would
not always be the case. If mean and median
are far apart, then one can expect skewed
data. Never have I seen comparisons of
medians.

Definitions of mean and median are given
below.

While they do not always tell the whole
story, statistically speaking, surely
comparisons of the means would be a
reasonable first step. If these comparisons
are undramatic, I do not think one can just
consider comparisons of the medians. What if
medians are misunderstood? Are there tests of
significance dealing with medians? Ever hear
of standard deviations about the medians? I
can think of a way to get medians to change
with absolute disregard to the different
treatments of the two groups.

Is comparing medians at all valid?

A.L.

================================================
definitions:
=================================================
http://www.shodor.org/interactivate/dictionary/m.html#median
=================================================
mean The sum of a list of numbers, divided by the
total number of numbers in the list.
==================================================
median "Middle value" of a list. The smallest number
such that at least half the numbers in the
list are no greater than it. If the list has
an odd number of entries, the median is the
middle entry in the list after sorting the
list into increasing order. If the list has
an even number of entries, the median is
equal to the sum of the two middle (after
sorting) numbers divided by two. The median
can be estimated from a histogram by finding
the smallest number such that the area under
the histogram to the left of that number is
50%

===================================================

--
~~~
Patrick Blanchard, M.D., A.B.F.P.
Board Certified in Family Practice
http://www.familydoctor.org/blanchard

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

from:
http://www.pfizer.com/are/news_releases/mn_2003_1112.html
we have:
"Lipitor-treated patients experienced a
median 0.4% reduction in total plaque volume,
defined as all of the plaque present within a
segment of a single artery-while patients who
received Pravachol showed a
significant increase in total plaque volume
(2.7% median)."

The results look good, but are presented as
changes in **** median ****. Who uses median?

If there are an odd number of patients, then
the result of only one patient represents the
median. If there are an even number of
patients, then the result of only two
patients represent the median. The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

That is totally and absolutely false. It was the other patients who determined
what the median was. If there were, say, 101 patients there would be 50
patients below the median and 50 pateients above and one patient right on. It
is really the 50 above and below him who determine what the median is. That
is, they put very tight bounds on what the median could be.

Quoted message said:

My recollection of statistics suggested that
the difference between a mean and a median
was a quick measure of skew. If mean and
median are similar in value then a
distribution can reasonably be expected to be
somewhat symmetrical, even though that would
not always be the case. If mean and median
are far apart, then one can expect skewed
data.

That is, in general, correct.

Quoted message said:

Never have I seen comparisons of
medians.

I often have. It is most useful when you do not want a few results at the end
of a distribution to skew the results. For example, if you wanted to get a
sense of a typical famalies' wealth in Bill Gates' hometown you would probably
be better off using the median than the mean.

-cuts-

Bill

Patrick Blanchard said:

On Thu, 13 Nov 2003 12:40:46 -0600, Al. Lohse <[email hidden]>

Quoted message said:

from:
http://www.pfizer.com/are/news_releases/mn_2003_1112.html
we have:
"Lipitor-treated patients experienced a
median 0.4% reduction in total plaque volume,
defined as all of the plaque present within a
segment of a single artery—while patients who
received Pravachol showed a
significant increase in total plaque volume
(2.7% median)."

The results look good, but are presented as
changes in **** median ****. Who uses median?

If you also add-in that "total plaque volume" is a poorly standardized
method to follow regression of atherosclerosis, I too have difficulty
accepting the current study as a reason to change prescription practice.

Quoted message said:

Quoted message said:

>>>>>>>>> snipped >>>>>>>>>>>>..

Hope you appreciate the multidisciplinary
interaction here, as I do. Most of us, I am
sure, do not know about "total plaque volume"
as a measure. Would guess that lengthening
plaque would be far less dangerous than
thickening plaque while both contribute to
volume.

Do observe, GINA KOLATA of the New York
Times, in thread "interesting study lipitor
and pravachol.... " seems to have been fooled
by the use of `median,' she ignored it
completely.

Maybe that was as intended; How many hundred
rewrites, along these lines, are produced for
each peer reviewed "scientific looking" paper
in order to make it appear as if there is
overwhelming general consensus in the results
and conclusions?

A.L.

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

from:
http://www.pfizer.com/are/news_releases/mn_2003_1112.html
we have:
"Lipitor-treated patients experienced a
median 0.4% reduction in total plaque volume,
defined as all of the plaque present within a
segment of a single artery-while patients who
received Pravachol showed a
significant increase in total plaque volume
(2.7% median)."

The results look good, but are presented as
changes in **** median ****. Who uses median?

If there are an odd number of patients, then
the result of only one patient represents the
median. If there are an even number of
patients, then the result of only two
patients represent the median. The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

That is totally and absolutely false.

I beg to differ. Both the above number of
patients and the below number of patients
have values in a semi-infinite range. The
contributions to a measure like the mean or
even thirds, quartiles, deciles and so forth
are entirely lost if dealing only with
median.

Do you still have a problem with my problem
with median?

Indeed, nearly 50%, those in the lower half
of the sponsor's least favourite group could
have had total loss of plaque volume, and
that would have been lost, discarded and
ignored.

Likewise, nearly 50% in the upper half of the
sponsor's favourite group could have had
massive, like 1000% increases in plaque
volumes, and that data would have been, you
guessed it, lost, discarded and ignored.

Quoted message said:

It was the other patients who determined
what the median was. If there were, say, 101 patients there would be 50
patients below the median and 50 pateients above and one patient right on. It
is really the 50 above and below him who determine what the median is. That
is, they put very tight bounds on what the median could be.

Quoted message said:

My recollection of statistics suggested that
the difference between a mean and a median
was a quick measure of skew. If mean and
median are similar in value then a
distribution can reasonably be expected to be
somewhat symmetrical, even though that would
not always be the case. If mean and median
are far apart, then one can expect skewed
data.

That is, in general, correct.

Quoted message said:

Never have I seen comparisons of
medians.

I often have.

Do present an example. Life is, after all, a
learning experience.

Quoted message said:

It is most useful when you do not want a few results at the end
of a distribution to skew the results. For example, if you wanted to get a
sense of a typical famalies' wealth in Bill Gates' hometown you would probably
be better off using the median than the mean.

Agreed, except that neither mean nor median
measures of wealth are very important in our
western societies. The top 2% can control 50%
of the wealth while the bottom 2% controls
0.0001% of the wealth. On the other hand,
using median discards and ignores Bill Gates'
contribution entirely, which is actually a
considerable contribution to the wealth of
that hometown. Rejecting outliers and stating
what outliers, and why, should always be an
important part of any statistical study.

Should they not be obliged to tell the reader
why they used median instead of mean?

Quoted message said:

-cuts-

Bill

What concept in the differences of medians
allows one to calculate their confidence
interval, their level of significance?

Cheers and thank you for your contribution to
this discussion.

A.L.
P.S. Perhaps it is the exuberance of youth,
but you will find, Bill, that very few things
are "totally and absolutely false," very few
things. You see, "totally and absolutely"
require only one exception; I gave you
hundreds. My assertion was not even
predominantly or substantially false.

"Patrick Blanchard, M.D." <[email hidden]> wrote in part:

Quoted message said:

Quoted message said:

The results look good, but are presented as
changes in **** median ****. Who uses median?

Percentiles are quite typically used and the median is the 50th percentile.

Many studies make comparisons between various percentiles. Quartiles are often
used.

There are statistical tests of all types for such measures.

Medians are often used where outliers are a concern, and the statistical
treatment of median data is better than the statistical treatment of means
where outliers are either present or thrown out.

The best studies deal with probability distributions over an effect. The
median gives one point on that distribution. The mean collapses the
distribution into a single measure of central tendency.
--
Jim Chinnis Warrenton, Virginia, USA

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

from:
http://www.pfizer.com/are/news_releases/mn_2003_1112.html
we have:
"Lipitor-treated patients experienced a
median 0.4% reduction in total plaque volume,
defined as all of the plaque present within a
segment of a single artery-while patients who
received Pravachol showed a
significant increase in total plaque volume
(2.7% median)."

The results look good, but are presented as
changes in **** median ****. Who uses median?

If there are an odd number of patients, then
the result of only one patient represents the
median. If there are an even number of
patients, then the result of only two
patients represent the median. The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

That is totally and absolutely false.

I beg to differ. Both the above number of
patients and the below number of patients
have values in a semi-infinite range. The
contributions to a measure like the mean or
even thirds, quartiles, deciles and so forth
are entirely lost if dealing only with
median.

Do you still have a problem with my problem
with median?

Indeed, nearly 50%, those in the lower half
of the sponsor's least favourite group could
have had total loss of plaque volume, and
that would have been lost, discarded and
ignored.

Likewise, nearly 50% in the upper half of the
sponsor's favourite group could have had
massive, like 1000% increases in plaque
volumes, and that data would have been, you
guessed it, lost, discarded and ignored.

Quoted message said:

It was the other patients who

determined

Quoted message said:

Quoted message said:

what the median was. If there were, say, 101 patients there would be 50
patients below the median and 50 pateients above and one patient right on.

It

Quoted message said:

Quoted message said:

is really the 50 above and below him who determine what the median is.

That

Quoted message said:

Quoted message said:

is, they put very tight bounds on what the median could be.

Quoted message said:

My recollection of statistics suggested that
the difference between a mean and a median
was a quick measure of skew. If mean and
median are similar in value then a
distribution can reasonably be expected to be
somewhat symmetrical, even though that would
not always be the case. If mean and median
are far apart, then one can expect skewed
data.

That is, in general, correct.

Quoted message said:

Never have I seen comparisons of
medians.

I often have.

Do present an example. Life is, after all, a
learning experience.

Quoted message said:

It is most useful when you do not want a few results at the

end

Quoted message said:

Quoted message said:

of a distribution to skew the results. For example, if you wanted to get a
sense of a typical famalies' wealth in Bill Gates' hometown you would

probably

Quoted message said:

Quoted message said:

be better off using the median than the mean.

Agreed, except that neither mean nor median
measures of wealth are very important in our
western societies. The top 2% can control 50%
of the wealth while the bottom 2% controls
0.0001% of the wealth. On the other hand,
using median discards and ignores Bill Gates'
contribution entirely, which is actually a
considerable contribution to the wealth of
that hometown. Rejecting outliers and stating
what outliers, and why, should always be an
important part of any statistical study.

Should they not be obliged to tell the reader
why they used median instead of mean?

Quoted message said:

-cuts-

Bill

What concept in the differences of medians
allows one to calculate their confidence
interval, their level of significance?

Cheers and thank you for your contribution to
this discussion.

A.L.
P.S. Perhaps it is the exuberance of youth,
but you will find, Bill, that very few things
are "totally and absolutely false," very few
things. You see, "totally and absolutely"
require only one exception; I gave you
hundreds. My assertion was not even
predominantly or substantially false.

Nope. What you wrote is.

Quoted message said:

Quoted message said:

The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

and that remains totally and absolutely false. Why? Because it was the vast
majority of patients (in fact all of them put together) that determined what
the median was. Which is precisely the opposite of being <entirely> lost,
discarded, and ignored. To help you with an example, if you have 3 numbers 1,
2, 3 the median is 2 - this does not mean that 1 and 3 are ignored. In fact,
if either of these were eliminated the result would be different. However, if
"2" were eliminated the result would be the same. So in that sense it is the
"2" that is lost, discarded, and ignored.

Bill

PS As to your question on whether you can calculate confidence intervals on
the medium. Yes you can, as you can on other percentiles, if you are willing
to assume normality, for example. However, it is typically not done and in my
view statistics like the medium are more useful to help gain a conceptual
understanding of what is going on.

Al. Lohse said:

from:
http://www.pfizer.com/are/news_releases/mn_2003_1112.html
we have:
"Lipitor-treated patients experienced a
median 0.4% reduction in total plaque volume,
defined as all of the plaque present within a
segment of a single artery—while patients who
received Pravachol showed a
significant increase in total plaque volume
(2.7% median)."

The results look good, but are presented as
changes in **** median ****. Who uses median?

If there are an odd number of patients, then
the result of only one patient represents the
median. If there are an even number of
patients, then the result of only two
patients represent the median. The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

No it isn't.

Quoted message said:

My recollection of statistics suggested that
the difference between a mean and a median
was a quick measure of skew. If mean and
median are similar in value then a
distribution can reasonably be expected to be
somewhat symmetrical, even though that would
not always be the case. If mean and median
are far apart, then one can expect skewed
data. Never have I seen comparisons of
medians.

In fact it is extremely common in medical surveys because the median
is less susceptible to large fluctuations on one end or another, and
so is believed to more accurately show the magnitude of the typical
benefit of the treatment.

Quoted message said:

While they do not always tell the whole
story, statistically speaking, surely
comparisons of the means would be a
reasonable first step. If these comparisons
are undramatic, I do not think one can just
consider comparisons of the medians. What if
medians are misunderstood? Are there tests of
significance dealing with medians?

Yes.

In fact there are two-sample tests of significance dealing with
differences of the empirical entire cumulative distributions which are
probably significantly more powerful for difference than just looking
at median. The Kolmogorov-Smirnov test is one such omnibus
statistical test, another more appropriate for looking at differences
of central tendencies is the Mann-Whitney-Wilcoxon test.

Quoted message said:

Ever hear
of standard deviations about the medians?

Yes, but confidence intervals and quantiles are
usually better.

Quoted message said:

I
can think of a way to get medians to change
with absolute disregard to the different
treatments of the two groups.

One can imagine all sorts of pathological
probability distributions, but the question
is whether they are experimentally likely,
or not.

Quoted message said:

Is comparing medians at all valid?

Yes.

The robust non-parameteric statistics which look at empirical
quantiles (a median is one point in this) are less susceptible to
deviations from Gaussianity than say a standard Student t-test.

Quoted message said:

A.L.

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

<<<<<<<<<<<<<< snipped >>>>>>>>>>>>>

Quoted message said:

Quoted message said:

A.L.
P.S. Perhaps it is the exuberance of youth,
but you will find, Bill, that very few things
are "totally and absolutely false," very few
things. You see, "totally and absolutely"
require only one exception; I gave you
hundreds. My assertion was not even
predominantly or substantially false.

Nope. What you wrote is.

Quoted message said:

Quoted message said:

The influence
on the results of the vast majority of
patients is entirely lost, discarded, and
ignored.

and that remains totally and absolutely false. Why? Because it was the vast
majority of patients (in fact all of them put together) that determined what
the median was. Which is precisely the opposite of being <entirely> lost,
discarded, and ignored. To help you with an example, if you have 3 numbers 1,
2, 3 the median is 2 - this does not mean that 1 and 3 are ignored. In fact,
if either of these were eliminated the result would be different. However, if
"2" were eliminated the result would be the same. So in that sense it is the
"2" that is lost, discarded, and ignored.

Bill

Hi Bill,

Thank you for helping me make the point. They
were using medians to compare the results of
treatments in two populations. If there were
3 people with values 1,2 and 3 before hand,
the median is, indeed, 2. If the values of
group A change to 0,2,and 2.000000001, the
median remains the same. If the values in
group B change to
2.0539999999999999,2.054,500000000000000000
the median increases by 2.7%. Q.E.D. Any data
lost, discarded, and/or ignored?

Quoted message said:

PS As to your question on whether you can calculate confidence intervals on
the medium. Yes you can, as you can on other percentiles, if you are willing
to assume normality, for example.

My good man, if normality can be assumed,
there is no need for this discussion at all.
The means and medians will be "about" the
same. Can the notion of median be invoked
because it shows larger, more compelling,
differences than the comparison of means? I
think we both know the answer to that one.

Quoted message said:

However, it is typically not done and in my
view statistics like the medium are more useful to help gain a conceptual
understanding of what is going on.

Indeed, an observation of medians may improve
the overall discussion of the applicable
statistics. Used in isolation, they are all
but meaningless. (Please notice, Bill, I shy
away from absolutes lest someone finds an
exception.) The median location of
participants of this newsgroup is 16000
meters under the Atlantic Ocean, 3234 km east
of North Carolina. Useful?

Pleasant regards, A.L.

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Hi Bill,

Thank you for helping me make the point.

You still don't get it.

Quoted message said:

They
were using medians to compare the results of
treatments in two populations. If there were
3 people with values 1,2 and 3 before hand,
the median is, indeed, 2. If the values of
group A change to 0,2,and 2.000000001, the
median remains the same. If the values in
group B change to
2.0539999999999999,2.054,500000000000000000
the median increases by 2.7%. Q.E.D. Any data
lost, discarded, and/or ignored?

Yes the outlier, which is the whole point. Without discarding this, the result
of the experiment would have become the a single point - the large one if you
used the mean. (And, in your terms, everything else would be ignored) Not to
say the outlier should be ignored. It should definitely be mentioned but it is
not characteristic of a larger group.

Quoted message said:

Quoted message said:

PS As to your question on whether you can calculate confidence intervals

on

Quoted message said:

Quoted message said:

the medium. Yes you can, as you can on other percentiles, if you are

willing

Quoted message said:

Quoted message said:

to assume normality, for example.

My good man,

Mostly

Quoted message said:

if normality can be assumed,
there is no need for this discussion at all.

By normality, I meant normaility in the sense of the central limit therom.

Quoted message said:

The means and medians will be "about" the
same. Can the notion of median be invoked
because it shows larger, more compelling,
differences than the comparison of means? I
think we both know the answer to that one.

I simply answered your question as to whether it could be done. And I agreed
that it is usually not useful to do so. So, you seem to be debating with
yourself.

Quoted message said:

Quoted message said:

However, it is typically not done and in my
view statistics like the medium are more useful to help gain a conceptual
understanding of what is going on.

Indeed, an observation of medians may improve
the overall discussion of the applicable
statistics. Used in isolation, they are all
but meaningless. (Please notice, Bill, I shy
away from absolutes lest someone finds an
exception.) The median location of
participants of this newsgroup is 16000
meters under the Atlantic Ocean, 3234 km east
of North Carolina. Useful?

Is your point that the mean location would more useful? Do you have a point
here?

Quoted message said:

Pleasant regards, A.L.

Is it possible to get the raw data as text or Excel? I'd like to
crunch it my way.

Bypass Bill W

"William Wagner" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Is it possible to get the raw data as text or Excel? I'd like to
crunch it my way.

Bypass Bill W

I think the first thing would be to get a full copy of the paper, which you
may be able to do by writing to the lead author. After that you might be able
to discuss the original data with the same source.

Bill

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

<<<<<<<<< snipped >>>>>>>>>>>>>..

Quoted message said:

Quoted message said:

Quoted message said:

understanding of what is going on.

Indeed, an observation of medians may improve
the overall discussion of the applicable
statistics. Used in isolation, they are all
but meaningless. (Please notice, Bill, I shy
away from absolutes lest someone finds an
exception.) The median location of
participants of this newsgroup is 16000
meters under the Atlantic Ocean, 3234 km east
of North Carolina. Useful?

Is your point that the mean location would more useful? Do you have a point
here?

No, that would be another useless statistic
in that example. Shows you have an agile
mind, though.

However, as far a plaque volume goes, knowing
the mean would allow calculation of total
plaque volumetric growth of the two
populations. Someone prefers we not think
along those lines. Why?

Infer:
If the plaque growth in the sponsor's
favourite group were significantly less than
the plaque growth in the sponsor's least
favourite group, that, to me, would be far
more useful than knowing the medians of the
two groups. The difference is certainly less
than the 2.7% that use of the median implies.
The median just "does not cut it."
Agreed?

Quoted message said:

Quoted message said:

Pleasant regards, A.L.

Ditto

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

<<<<<<<<< snipped >>>>>>>>>>>>>..

Quoted message said:

Quoted message said:

> understanding of what is going on.

Indeed, an observation of medians may improve
the overall discussion of the applicable
statistics. Used in isolation, they are all
but meaningless. (Please notice, Bill, I shy
away from absolutes lest someone finds an
exception.) The median location of
participants of this newsgroup is 16000
meters under the Atlantic Ocean, 3234 km east
of North Carolina. Useful?

Is your point that the mean location would more useful? Do you have a

point

Quoted message said:

Quoted message said:

here?

No, that would be another useless statistic
in that example. Shows you have an agile
mind, though.

However, as far a plaque volume goes, knowing
the mean would allow calculation of total
plaque volumetric growth of the two
populations. Someone prefers we not think
along those lines. Why?

Infer:
If the plaque growth in the sponsor's
favourite group were significantly less than
the plaque growth in the sponsor's least
favourite group, that, to me, would be far
more useful than knowing the medians of the
two groups. The difference is certainly less
than the 2.7% that use of the median implies.
The median just "does not cut it."
Agreed?

Quoted message said:

Quoted message said:

Pleasant regards, A.L.

Ditto

You are assuming malevolent behavior without even seeing the paper. You might
wish to write to the authors to get a copy.

The whole point is the median is a useful statistic, as is the mean. I would
prefer to know both. But if I had to pick one for this study and perhaps bet
my life on it, I would pick the median - because that is more representative
of a typical individual, which going in I would assume I would be. The mean
can be affected by outliers. So no, I do not agree.

Bill

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

Bill said:

"Al. Lohse" <[email hidden]> wrote in message
news:[email hidden]...
>

<<<<<<<<< snipped >>>>>>>>>>>>>..

Quoted message said:

You are assuming malevolent behavior without even seeing the paper. You might
wish to write to the authors to get a copy.

Malevolent suggests an intent to do harm or
an indifference to doing harm. I suggest
nothing of the sort. I suggest the researcher
reported that statistic which cast their
results into the best light, hoping no one
would notice. Ever use the statistics feature
of a spreadsheet application? All manner of
statistical concepts are calculated and
displayed, almost instantly. It does take
some deviousness to choose the number which
best describes your desired (or is it,
required) conclusion.

Quoted message said:

The whole point is the median is a useful statistic, as is the mean. I would
prefer to know both. But if I had to pick one for this study and perhaps bet
my life on it, I would pick the median - because that is more representative
of a typical individual, which going in I would assume I would be. The mean
can be affected by outliers. So no, I do not agree.

Bill

Please find the quote: "... the mean, median,
and mode. Of these, the mean is by far the
most important" in the article below. Looks
like I am not the only one suffering from
this "misconception."
In:
http://www.arts.ualberta.ca/socweb/faculty/gillespie/INST2.htm#_ftn4

BTW, there was no mention of outliers in the
original text, none. Nor in the Forbes
article below. Also, their median is not
necessarily "typical."

Are these people "typical?" " ... they need
a catheter for another reason"
As in:
"There is not as of yet a clinically proven
link between plaque measured with IVUS and
heart attacks, and IVUS can only be done in
patients whose cardiovascular disease is so
severe that they need a catheter for another
reason. But about three-quarters of heart
attacks and strokes are caused by plaque
fracturing from the side of the artery."
Ref:
http://www.forbes.com/2003/11/12/cx_mh_1112pfe.html

(In this Forbes article, at least, there is
no hype about the reversal of
atherosclerosis; They recognized the -0.4%
was not significant. That gives weight to Dr.
Kendrick's assessment of reversal. But, here
again, is an article based on science which
has not been reviewed. It may, very well, be
more of an advertisement than statement of
fact. Caveat emptor.)

You may remain a median sort of individual,
and many others, a mean sort. NPI.

A.L.