Gene,
You have made extended comments about
the IWF report "Confession without Guilt?"
(at http://www.iwf.org/news/mitfinal.pdf
about women biologists at MIT.
Some background information:
------------
The IWF is the second in a series criticizing
the MIT report on the Status of Women.
The original MIT report may be downloaded
from http://mindit.netmind.com/proxy/http://web.mit.edu/fnl/
An earlier IWF report by Judith Kleinfeld revealed many
of the serious shortcomings of the
MIT report. Kleinfeld's report is at
http://www.uaf.edu/northern/mitstudy/#note9back
I would urge all students to download and read
all three of these papers, so they can get a better
feel for who, MIT or its critics,
is more objective and scientific in
their treatment of a very touchy subject.
-----------------
Gene, although you apparently intended
them as honest criticism, your
comments revealed a deep, fundamental
confusion about statistical inference.
I expect any trained statistician would recognize
the error in your argument immediately,
but some students may have been misled.
So let me try to alleviate some
of the confusion your posts may have
generated, and try to help you see
the error of your ways. And,
might I suggest, strongly,
that you show this post to
your ECOS611 class? This might
make an excellent discussion piece
for them.
Your comments apparently derive
from a misconception, i.e., that the
IWF report was using the MIT Biology
Dept. data to make inferences about
some larger population. It wasn't.
The IWF authors were not evaluating
male and female scientists in general.
This was clearly a question about
MIT biologists, and what
their data might imply about
the honesty and validity of the
MIT Report.
The MIT Report claimed that it found
major differences in outcome variables
for its male and female faculty IN THE FACULTY
OF SCIENCE that could not be explained by
differences in productivity. And the
MIT report discussants have
repeatedly implied in public that
the women Biologists at MIT are
the equal of their male counterparts.
The IWF report showed that MIT senior
biologists were definitely NOT
the equal, on some standard
performance measures, of a
matched male cohort.
*If* the IWF data were a random sample
from the general population [they
were not] and *if* the IWF
authors were trying to make inferences
about that general population [they were not],
then your significance testing might
be of relevance.
However, neither of the above conditions hold,
and it is difficult to imagine how you 1
could have thought otherwise.
So, whereas you should congratulate yourself
[but not too much] on your ability to
construct an Excel file and
to coax a Mann-Whitney test out of statistical
software, you should give yourself
failing marks on your ability to think
rationally about the relationship
between numbers and substantive issues
they address.
Keep in mind that, at the time the original
MIT report alleging discrimination
was constructed, there were a TOTAL
of about 22-25 women in the faculty
of science at MIT. It turns out,
then, that nearly half the women
scientists at MIT were in the
Biology department, and that,
consequently, the IWF report
contained information on about
half the female scientists at
MIT, and,indeed, the half where
you might expect the women to be
most competitive with the men.
What the IWF report shows is that
the senior female Biologists [including
the chief complainant, Nancy Hopkins] were
substantially outperformed by a
matched cohort of males. This is
a statement about a population.
There were HUGE differences in the citation rates
of senior men and women. The mean number of citations was,
as I recall, roughly 7000 for the men and 1400
for the senior women.
All such performance statistics are,
of course, problematic. I agree
with concerns about serious limitations of citation counts and
publication rates as measures of
academic quality. But the IWF
authors stayed within one department,
and studied comparable groups,
precisely because that is where the most
meaningful comparisons could be made.
There is more meaningful
data in one page of the IWF
report than in 15 pages of the
MIT report.
To try to bring this into focus,
let me ask you some questions.
1. Suppose the IWF report had gathered
data on ALL female scientists at MIT,
compared them to a group of males
matched for seniority, and had
shown huge differences in performance.
Would you still be doing a significance test?
2. Suppose Mary has 1051 citations
in the last 10 years, and has earned
4 million in grants, and Fred, in the
same department, and about the same
age and seniority, has 12000+
citations and has earned 23 million
in grants, and Fred finds out that
Mary is making the same salary he is.
Should Fred consult you about doing
a statistical "significance" test
before asking for a raise?
3. Suppose you go to a nursing school,
and find 5 female faculty
with 7,000 citations apiece, and,
in the same department, 5 female
faculty of the same seniority with
1400 citations apiece. Would
you expect their salaries and
departmental influence to be the same?
If you still don't get it,
let me suggest the following
potential exam question for you,
and your students.
[Comment: Your invoking of the term "Rush
Limbaugh dittohead" suggests
that you may have let your political
views interfere with clear analysis in
this case. I suspect
some of your students may have recognized
this as an inappropriate argumentative
technique. Because your sense of
political correctness may have misled
and confused you, I've reversed the
"political correctness"
status of the protagonists. ]
-----------------------------------------------------------
4. (10 points). [Disclaimer: this is a hypothetical example.]
The white players on the Detroit Pistons
believe that they are victims of salary discrimination.
They have discovered that the black players have higher
salaries.
The notion that the black players might be
more productive basketball players was raised, but
dismissed by the white players as "the last refuge
of the bigot."
The white players approached the
team owner, who appointed 3 of the 4 white players
to a committee to study the problem. The committee
found that, indeed, white players were a declining
minority in the NBA, and suggested that this was
due to "unconscious, unintentional, systemic"
discrimination by black players. They suggested
a number of reforms to overcome this discrimination,
and also urged salary raises for the white players.
The NAACP felt that this analysis was biased,
and incomplete. It gathered performance data
on the players on the Pistons. Figures are points
per 48 minutes of playing time. [This being a
hypothetical example, assume, for the sake of argument,
that this is a valid and complete measure
of basketball performance.]
White Black
-------------
12.8 13.7
11.1 22.3
19.9 20.9
13.9
16.8
17.1
13.0
-------------
Salary data are not available, as the club
has declared them confidential. The NAACP
points out that, however, the black
players have higher performance than the
white players. The mean performance for
the black players is 16.83, for the white
players 14.6. According to the NAACP spokesman,
"Although the NBA refuses to release salary
data, this furnishes an alternative
explanation for the salary differences,
and calls into question the NBA's
assertion that there are no meaningful
performance differences between
black and white Piston players. On average,
black Piston players have produced about 2 points
more per game than white players."
At this point, a spokesman for the
white players, Gene Gallagher,
intervenes. Gene considers himself
an expert statistician. Gene says
that, "No, actually these data
don't show that the black Pistons
players have been producing more
than the white players. I
performed a t-test, and found
t=.82, df=8, non-significant.
The Pistons' black players have not
performed significantly better than
the Pistons white players."
[Ignore, for the sake of simplicity,
little niceties like the assumption of
independent observations.]
The NAACP spokesperson responds.
"No Gene. The question is
not whether the data from the Pistons
allow us to generalize about all
white players vs. all black players.
IF the Pistons data represented
random sampling, and IF we were interested
in answering questions about ALL black
and white players, THEN your analysis might
be relevant."
"But we weren't trying to answer
that question, and we do not
believe that the Pistons represent
a random sample. We were simply
interested in whether the Piston
black players had performed as
well as the Piston white players.
Statistical testing is
inappropriate, and, in fact, misleading."
Who is right? Gene or the NAACP? Why?
-----------------------------------------------------
Ponder this, Gene, and you may,
hopefully, realize that
it was perfectly reasonable
for a statistician to attach
his name to the IWF study, and that there is
more to being a statistician than the ability
to grind out inappropriate statistical tests with
canned software.
Sincerely,
Jim Steiger
--------------------------
James H. Steiger, Professor
Department of Psychology
University of British Columbia
Vancouver, B.C., Canada V6T 1Z4
Note: opinions expressed herein
are strictly those of the author.
---------------------------
On Fri, 09 Feb 2001 17:19:20 GMT, Gene Gallagher
<[EMAIL PROTECTED]> wrote:
>Here is an interesting stats problem from this week's Boston Globe.
>In 1999, an internal MIT report concluded that women faculty at MIT had
>received lower pay and fewer resources then their male colleagues. This
>week, the Independent Women's Forum (IWF) released a statistical
>analysis showing that MIT "may have reacted to political correctness
>before checking all the evidence." This report supposedly documents,
>"compelling differences in productivity, influence and grant funding
>between the more senior males and females." The report argues that the
>gender difference in MIT salary and lab space was justified because "few
>would question the fairness of rewarding those who publish more widely,
>are more frequently cited, or raise the most in grant funds (p. 8, IWF
>report)"
>
>The Independent Womens Forum 13-p report is available at:
>http://www.iwf.org/news/mitfinal.pdf
>
>With the headlines "Fuzzy math on women" and "MIT bias claims
>debunked," the Boston Globe reported the IWF's major conclusion, that
>women professors probably deserved their lower pay and smaller labs
>because of their lower productivity:
>http://www.boston.com/dailyglobe2/039/metro/MIT_bias_claims_debunked+.sh
>tml
>An Globe op-ed piece by Cathy Young on 2/7/01 states, "Monday, the
>Women's Forum followed up with another report that demonstrates that the
>senior women in MIT's biology department, however distinguished in their
>field, did not quite measure up to their male colleagues in the number
>of publications, frequency of citation, or outside grants." <Young's
>2/7 op-ed piece can be obtained from the Globe archive for $2.95. -
>don't bother IMHO>
>
>I had just presented an example of sex discrimination to my graduate
>stats class (Chapter 2 in Ramsey & Schafer's Statistical Sleuth), and I
>told the class that the IWF had probably done a multiple regression
>analysis showing that gender wasn't a significant term in a regression
>of salary after publication number or citation frequency had been added
>as an explanatory variable. When I downloaded the IWF report, I was
>quite frankly amazed that a statistician had attached his name to it.
>Admittedly, the IWF was hamstrung by being unable to get any of the
>relevant data from MIT, but that didn't prevent the IWF from reaching
>the conclusion that the productivity of women faculty was less than men.
>
>I typed the publication and citation data from p. 11-12 of the report as
>an SPSS file and exported it as an excel file. Both are available in a
>zipped file on my web site:
>
>http://www.es.umb.edu/edg/ECOS611/MIT-IWF.zip
>
>As a class exercise, you could have your stats classes use
>non-parametric tests (or parametric) to test whether there really is a
>significant difference between male and female faculty in the biology
>department at MIT in publication number or citation frequency (the grant
>data isn't provided). Note, that the authors of the IWF study divided
>the biology faculty into older and younger groups and did separate
>analyses on each group. The Rush-Limbaugh dittoheads in your class, who
>want to find striking gender differences in productivity, will be
>profoundly disappointed with these IWF data (not one null hypothesis can
>be rejected at alpha=0.05 using a Mann-Whitney U test).
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