MEDIAN?

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

Quoted message said:

from: pfizer.commn 2003 1112.htmlOpen ↗ 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:
=================================================
shodor.orgm.htmlOpen ↗
=================================================
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
familydoctor.orgblanchardOpen ↗

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

Quoted message said:

from: pfizer.commn 2003 1112.htmlOpen ↗ 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

Al. Lohse said:

from: pfizer.commn 2003 1112.htmlOpen ↗ 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.

Patrick Blanchard said:

Al. Lohse said:

from: pfizer.commn 2003 1112.htmlOpen ↗ 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: pfizer.commn 2003 1112.htmlOpen ↗ 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 .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

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

Bypass Bill W

"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: pfizer.commn 2003 1112.htmlOpen ↗ 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 .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.

"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:

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.

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

Quoted message said:

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,

I think you are mistaken here. You may be talking about the average location, but the median
location will be a place that a person actually is (or the mid point between two people). But lets
chalk all that up to a poor analogy...

What you are missing here is that this is *not* normally distributed data. Normal distributions
assume that data can range infinitely high and infinitely low. Plaque volume has a minimum of 0 and
a maximum of the volume of the circulatory system. What a researcher presents is what they think
will best represent the findings without subjecting the reader to having to analyze the entire data
set for him/herself.

In this case the data were presented at a meeting, but presumably a paper is in publication. At that
point, it is up to the reviewers to determine if the statistical treatment of the data is
appropriate and to decide if the presentation of the data are useful to readers. But at the
presentation by all accounts, the excitement was tempered by what is seen as the greatest weakness
of the study - it was not big enough to look at morbidity and mortality. It is assumed that plaque
volume correlates, but we have no way of knowing (yet).

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

Nigel said:

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

Quoted message said:

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,

I think you are mistaken here. You may be talking about the average location, but the median
location will be a place that a person actually is (or the mid point between two people). But lets
chalk all that up to a poor analogy...

My mathematical intuition tells me I can describe any point I want inside a sphere as the midpoint
of two points on its surface. Once done, invent a datum such that some descriptive value is greater
than that of one of the points and equal numbers less than that of the other.

but,............... that is not the point, and this is not a mathematics forum.

A better description of the location of the participants would be to count them by continent, or by
country. Failing that, even by hemisphere, would be more descriptive than the MEDIAN.

Quoted message said:

What you are missing here is that this is *not* normally distributed data. Normal distributions
assume that data can range infinitely high and infinitely low. Plaque volume has a minimum of 0
and a maximum of the volume of the circulatory system. What a researcher presents is what they
think will best represent the findings without subjecting the reader to having to analyze the
entire data set for him/herself.

All you have to do is offer an example in which the effects on two populations can ** best ** be
summarized by comparing the median values. I have not suggested such do not exist, I have suggested
that I have not seen one and therefore they ** probably ** do not exit.

Also, I was not the one who suggested a normal distribution. I need not speak to that. Medians are
not very descriptive of nonsymmetrical distributions.

Quoted message said:

In this case the data were presented at a meeting, but presumably a paper is in publication. At
that point, it is up to the reviewers to determine if the statistical treatment of the data is
appropriate and to decide if the presentation of the data are useful to readers. But at the
presentation by all accounts, the excitement was tempered by what is seen as the greatest weakness
of the study - it was not big enough to look at morbidity and mortality. It is assumed that plaque
volume correlates, but we have no way of knowing (yet).

My doctor had told me years ago, something to the effect that, "We believe atherosclerosis can be
reversed by treatment with statin drugs." The release of this study seems to reinforce that belief.
Dr. Kendrick's analysis suggests that such a belief is garbage. The link:
medscape.com608 pntOpen ↗ suggests strongly that it is not garbage.

I told my doctor, when hearing his view, that my 40% blockage at age 52 allows me to allow "them" to
GET THE SCIENCE RIGHT. My blockages would nearly have to double before becoming evident on a stress
test. That, at my rate of blockage growth, may never happen. Perhaps real problems at age 104 when
blockages double.

Perhaps you can guess why the preliminary results were presented as they were and even why newspaper
columnists write about them as if they were fact. Perhaps the "paper in publication" will not pass
peer review, yet, the rumour is being ** inadvertently ** spread. The rumour is being spread in the
absence of scientific legitimacy. Any ideas? Good for patients? Follow the money?

A.L.

"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

"Al. Lohse" <[email hidden]> wrote in news:3FB8F5B0.9A5A6A49
@cc.umanitoba.ca:

<Snip>

Quoted message said:

My doctor had told me years ago, something to the effect that, "We believe atherosclerosis can be
reversed by treatment with statin drugs." The release of this study seems to reinforce that
belief. Dr. Kendrick's analysis suggests that such a belief is garbage. The link:
medscape.com608 pntOpen ↗ suggests strongly that it is not garbage.

I think that the study under discussion does demonstrate that atherosclerosis can be reversed. But
does reversing it change mortality and morbidity? The answer there is that we don't know yet.

<Snip>

Quoted message said:

Perhaps you can guess why the preliminary results were presented as they were and even why
newspaper columnists write about them as if they were fact. Perhaps the "paper in
publication" will not pass peer review, yet, the rumour is being ** inadvertently ** spread.
The rumour is being spread in the absence of scientific legitimacy. Any ideas? Good for
patients? Follow the money?

So the newspapers are assuming that reduction in plaque will result in reduction in mortality and
morbididty. A conclusion that we can't make from the evidence.

Is this the fault of the researcher, or is it the fault of the reporter being reinforced by the
editor. The problem is really that newspapers are run by people that have little grasp of
mathematics and science. I would suggest that this is not the fault of the researcher but of the
Universities that are churning out journalism grads with no knowledge of science and math and the
fault of the public for not demanding better journalism (perhaps with letters to the editor pointing
out how studies are being misrepresented).

Indeed though, lets follow the money. Drug companies turn profits that result in dividends and
capital gains for shareholders. Who owns the shares? Mutual funds and pension funds that benefit the
large numbers of people (the very same people taking the drugs they manufacture). It has a nice
symetry to it.

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: forbes.comcx mh 1112pfe.htmlOpen ↗

(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.

I.o.

Al. Lohse said:

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

Median isn't always as powerful as mean (though there are cases where it is more powerful), but it
is less sensitive to outliers. If the distribution of interest is not skewed, the true mean and
median are the same. The mean is then the more powerful, more convenient, and more tractable
estimator. If the distribution is skewed, both statistics are reportable. When nothing is known
about the distribution, as is the case here, the median is traditionally used as a robust estimator.

In general, a median (or other quantile) is useful when thinking about the response of an individual
or event, whereas a mean is more useful when assessing the cumulative response of many individuals
or events.

It's useful for a doc to think, "This patient has a 50% chance of responding this well or
better/worse." To contrast, in the case of oil spills, you think in terms of means, because the mean
times the number of spills tells you about how much oil should accumulate over time.

Medians are not always assessed directly, as you assume. They are typically computed in special
regression analyses (logit or probit) constructed to predict conditional probabilities. A common
example is the prediction of death in lab animals from a dose of poison or medication. The outcome
variable is 0 or 1 depending on whether the animal died. The equation fitted is

ProbabilityOfDeath = NonlinearFunction [A * Dose + Constant]

The dose corresponding to a 50% probability is the median.

Conditional medians are sometimes computed by regression analysis procedures that minimize the least
absolute deviation (LAD) between fitted curve and data points. Such statistics must be computed by
iterative procedures (e.g.; linear programming), whereas conditional means, computed by minimizing
least squared deviations, can usually be computed analytically.

In neither of the above cases is one limited as you surmise, buy the oddness or evenness of the
number of data points.

Regards, -Larry Curcio