 C1.

<p>Ask statisticians or probabilists what the phrase
&quot;six sigma&quot; means to them, and the answer will
probably involve the tails of a normal distribution.  In
recent years, &quot;six sigma&quot; has been appropriated
by the business community to refer variously to
methodologies and goals in the area of quality control.

<p>In the Six Sigma model, if one wants to increase the
probability that a product is defect-free, one first
determines all of the steps that are currently used to
produce that product. The present article use the example
of a diagnostic scanner, which is a device used in medicine
to produce images of the inside of the human body. Such a
scanner is of course very complicated to design and build.
In an effort to increase the quality and longevity of the
product, engineers at General Electric Medical Systems
(Gems), broke down their existing scanner into its
component parts, and considered how to design each part so
that it was more reliable.

<p>The next step in the Six Sigma model consists of
considering how much the improvement of each part's design
contributes to the overall quality of the finished product.
Using computers, one can simulate trial runs in which
various possibilities for improving certain parts are
assumed, and then the change in overall quality is
computed. By making many such computer runs, one can
determine which parts are most worthy of attention.  In the
case of the scanner, this revealed several different ways
to obtain the same change in overall quality of the
product. Some of these ways were more expensive and/or more
time-consuming than others. Given such comparisons, the
design engineers were able to make more informed choices
about which parts to concentrate on.

<p>The &quot;six sigma&quot; phrase is widely reported as
corresponding to a production process that produces no more
than 3.4 defects per million. But if one calculates the
probability that a normal random variable takes on a value
at least 6 standard deviations from the mean, one obtains
the value 2 per billion, which is orders of magnitude
smaller than the 3.4 out of one million figure.  The
following explanation seems to shed some light on the
issue.  The six sigma approach deals with the production
process, and does not take into account the fact that raw
materials used in this process are themselves subject to
variation, which in many cases affects the degree of
variability of the finished product.  It is reported that a
value of 1.5 sigma is a good one to assume for the degree
of variability of many types of inputs.  Accepting this
means that one is really striving for 4.5 sigma quality
(4.5 = 6 - 1.5) when one says six sigma. Calculating the
probability that a normal random variable exceeds its mean
by more than 4.5 standard deviations, we obtain the value
3.4 out of one million.</p>

<hr>

<h2>&quot;College Board Study Shows Test Prep Courses Have Minimal Value&quot;</h2>
<p>by <NAME>, <cite>The New York Times</cite>, 24 November 1998, A23.

<p>There has been a long-running debate over whether
students can improve their SAT scores by taking preparation
courses, such as those offered by Kaplan Educational
Centers or Princeton Review. Kaplan advertises that the
average increase in one's SAT scores after taking their
course is 120 points (out of 1600 possible points);
Princeton claims an average increase of 140 points.  The
College Board has long maintained that their tests are
objective measures of a student's academic skills, and that
preparation courses do not improve students' scores.
(Nevertheless, the College Board itself publishes
preparatory material for the tests, explaining that
familiarity with the test styles is beneficial!)

<p>It is not easy to design a study to settle the debate. 
First, the set of people who choose to take preparation
courses is self-selected. Second, those who choose to
enroll in such courses seem to be more likely to employ
other strategies, such as studying on their own to help
them get a better grade. Third, if one takes the SAT test
several times, it is likely one's scores will vary to a
certain extent.

<p>The College Board's own study, undertaken by <NAME>.
Powers and <NAME>, is the focus of this article. 
It found that students using one of the two major coaching
programs were likely to experience a gain of 19 to 39
points more than those who were uncoached.  This is
considerably less than was claimed by these coaching
services.  Moreover, since the College Board estimates a
standard error of 30 points for differences in tests taken
at two different times, the study concludes that there was no significant improvement in scores 
due to the coaching.</p>

<hr>

<h2>&quot;Madison Avenue and Violence Don't Mix&quot;</h2>

<p>by <NAME>, <cite>The Wall Street Journal</cite>, 1 December 1998, B9.


<p>A study in the December issue of <cite>The Journal of
Experimental Psychology: Applied</cite> reports that
viewers who watched a violent film clip had poorer recall
of advertising messages than viewers who watched nonviolent
material.  This suggests that violent TV shows may not be
desirable for advertisers.

<p>The study involved 720 undergraduate students at Iowa
State University.  Scenes from ten different movies were
used. &quot;The Karate Kid III,&quot; &quot;Die Hard,&quot;
&quot;Cobra,&quot; &quot;Single White Female,&quot; and
&quot;The Hand that Rocks the Cradle&quot; provided violent
scenes; &quot;Gorillas in the Mist,&quot; &quot;Awakenings,&quot;
&quot;Chariots of Fire,&quot; &quot;Field of Dreams,&quot;
and &quot;Never Cry Wolf&quot; were sources of nonviolent
scenes. Included with each clip was one of three possible
commercial messages, chosen at random.  One was for Wisk
laundry detergent, one for Plax mouth rinse, and one for
Krazy Glue.  When the students were later tested on
brand-name recognition, brand-name recall, and advertising
message, those who had watched the violent scenes scored
lower.

<p>Professor <NAME>, the Iowa State professor who directed the
study, explained that the students who saw the violent scenes
reported feeling angrier.  He reported that such anger appears to
be the major reason people had trouble remembering the ads.
Critics of the study expressed concern about generalizing from
college students to the population at large.  Furthermore, <NAME>, president of the Advertising Research Foundation,
expressed concern about the use of movie clips.  The research
might say something about the reaction to feature films shown on
TV, but this does not represent the majority of programming.

<p>Bushman countered by saying that all the movies he used
had in fact appeared on television.  As to the first
criticism, he says: &quot;My question is, why would we
expect the memory of college students to differ from the
memory of others?&quot;</p>


<hr>

<h2>&quot;Ask Marilyn&quot;</h2>

<p>by <NAME>. <cite>Parade Magazine</cite>, 3 January 1999, p. 16.

<p>Marilyn's latest response to a probability puzzle could
be used to discuss the distinction between sampling with or
without replacement. In an earlier column (<cite>Parade Magazine</cite>, 29
November 1998, p. 26) she responded to the following
question:

<blockquote>     You're at a party with 199 other guests when robbers
     break in and announce they're going to rob one of you.
     They put 199 blank pieces of paper in a hat, plus one
     marked &quot;you lose.&quot; Each guest must draw a piece, and
     the person who draws &quot;you lose&quot; gets robbed.  The
     robbers think you're cute, so they offer you the option
     of drawing first, last or any time in between.  When
     would you take your turn?
</blockquote>

<p>Marilyn said she would choose to draw first, explaining
that &quot;It would make no difference to my chances of
losing -- any turn is the same -- but at least I'd get to
leave this party as soon as possible.&quot;  Not all of her
readers agreed, and the present column contains responses
from some of them.

<p>One letter argues for drawing first:  &quot;You said any
turn is the same, but I believe that would be true only if
the partygoers all had to replace the papers they drew
before another selection was made.  But if they keep the
papers (the scenario intended by the question), wouldn't
the odds