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{\it Greg Monfette and Brandon Nunn -- The Shape of a Baseball Career and Steroids}
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I think both your in-class presentation and the final paper turned out
{\it very well}! The paper is well-written (see the hardcopy for some comments about a few
remaining ``fine points'' that might still be improved a bit). I think
the work you did to edit and improve the first draft you showed
me {\it really} ``paid off!''  The final product is well-organized and follows the
suggested organization from the assignment description very closely.  You
are using all the terms correctly and with insight.  You are clearly on
top of your material.  This is a first-rate report on your statistical work.

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{\it Some Specific Comments}
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\item{1.}  The formula you give here for the ``variance'' $V$ for the
Mann-Kendall computation is not completely general.  The correction
term after the $N(N-1)(2N+5)/18$ would be different depending on
{\it how many different groups} of repeated values there are,
and on {\it how many times each repeated value occurs}.  For instance,
if there were three groups of repeated values all together, one
with 3 repeats, one with 4, and one with 2, then the variance would
be computed like this:
$$V = n(n-1)(2n+5)/18 - (3)(2)(11)/18 - (4)(3)(13)/18 - (2)(1)(5)/18.$$
Similarly, your formula for the Mann-Kendall $Z$ is only valid
if $S > 0$, so what you are saying does not cover every possible case.
The general computation of the Mann-Kendall $Z$ statistic depends on
whether $S > 0$ or $S < 0$:
$$Z = \cases{ {S - 1\over \sqrt{V}} & if $S > 0$\cr
                                    & \cr
                 0 & if $S = 0$\cr
                     & \cr
               {S + 1\over \sqrt{V}} & if $S < 0$\cr}$$
\item{2.} Maybe it would be better to say that Pujols' data would not be
what one would expect to see {\it over a complete career} if the
player did not use any ``chemical enhancements.''
\item{3.} I know I suggested that you should not necessarily put in {\it every
plot} you generated.  But since you did discuss Aaron's career, and also
Clemens and Grove in some detail in the text, it would have been nice to
have those figures to refer to to back up what you are saying about those
players too.
\item{4.}  A technical point:  When you refer to a web site in a references,
you should provide a bit more information.  Give the full URL for the exact
page where you found the information -- unless it's one of the totally
unreadable 200-character long ones.  Also, provide the date when you
accessed the information, since things do tend to change over time (unlike
the case for print sources!)
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{\it Paper:}
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{\it Presentation:}
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{\it Nick Foster and John Vatalaro -- Baseball's Last 50 Years.}
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On the whole, you have some very interesting ideas here.  As I said about the
presentation, you have clearly done a lot of work and distilled a number of
interesting observations from the data.  The idea of comparing the league leaders
versus the league averages in these categories is original and enlightening.
This is also well-written for the most part (see some comments below on
small issues).

However, as a formal written research report, there are a few serious problems with what
you have submitted.   First, you did not follow the directions about documenting
all of your sources.  You need at the very least to list the sources of the data
you were using in a References section for a paper like this.  {\it Get in the habit
of doing this right away because it is expected for this kind of formal writing assignment.}

Also, it would have been good to follow the suggested outline from the assignment
sheet about the final projects even more closely.  For instance, you could have
put in section headings for the Introduction, Methodology, Results, Discussion, and
Conclusion sections to give more structure to what you were presenting and give
the reader some signposts about where you were in your argument at all times.

Along those lines, you never really discussed the methodology you were using
(the Mann-Kendall trend statistic, the Sen estimated trend line and how they work)
at all.   It would have
been good to say what the methods were and how you were applying them (via
the MAKESENS spreadsheet).
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\noindent
{\it Some Specific Comments}
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\item{1.} Say ``number'' here rather than ``amount''
\item{2.} Same comment!
\item{3.} I do not quite understand your point here.  It is true that each team plays (approximately) the same number of games each year.  But the league average number of wins per pitcher (say for starting pitchers) would be something meaningful, even though there would be lots of variation (i.e. a big SD) due to injuries, promotions/demotions from/to the minor leagues, etc.
\item{4.}  You should explain what this is (do not assume the reader already knows).
\item{5.}  Better:  ``fans love offense,'' or maybe ``fans love the offensive game.''
\item{6.}  Say ``evolution in''
\item{7.}  No hyphen here:  ``counterparts''
\item{8.}  No apostrophe here:  ``trend lines''
\item{9.}  You have the wrong Red Sox left fielder here – the person who batted
.301 in 1968 was Carl Yastrzemski.  Ted Williams had retired  by 1968.
\item{10.}  Say ''almost all of''
\item{11.}  There might be a slightly different alternative or
supplementary explanation here too – batters did not have the full
season to  get ``up to speed'' and hit their stride either.
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{\it Paper:}
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{\it Presentation: }
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{\it Pat Jarvis and Jonathan Ye -- ``Small Ball''}
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This is generally a very good job on the application of
Mann-Kendall tests to discern trends in baseball data.  
Your conclusions about ``small ball'' tactics seem sound,
although you never actually come out and state what seems
to me to be the obvious explanation for the differences
between the two leagues (see comments 5 and 6 below).
There is a relatively minor organizational issue about
the paper (see comment 2 below).  There are also a few
places where I have suggested rewording or rephrasing things.
But overall, this is very good work!
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\noindent
{\it Some Specific Comments}
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\item{1.}  This reads strangely -- the usual meaning of this phrase is 
different from the way you are using it here!  Say ``offensive production increased
greatly'' or something like that.
\item{2.}  The two paragraphs starting at the point I marked 
seem somewhat out of place.  They seem to follow what you said 
in the very first paragraph of the paper.  You have ``moved on'' to 
discuss the particular statistics you will consider, so going back
to the history is backtracking, in a way.
\item{3.}  You are leaving out a step in the computation of the
$p$-value, so, taken literally, what you are saying here is 
not correct.  The $z$-statistic is first compared with the 
normal table to get an area in a tail of the distribution (the
chance of getting that value or ``something more extreme''
if the null hypothesis is true), {\it then} you divide
to get the $p$-value the way that it is usually reported.
\item{4.}  The $p = .0012$ is not correct here.  For $z = 1.16$, the
$p$-value should be about $p = .12$.  I think you divided by 100
{\it twice}!  (Don't forget, the only reason why the division
by 100 is necessary is the way the normal curve areas are
presented in the table in our text -- as percents, rather than
as numbers between 0 and 1.  If you were getting
a $p$-value some other way, the division by 100 might
already have been done, in effect.)
\item{5.}  I know you are probably {\it thinking} this,
but it would be good to say it explicitly too:  The
main reason for the persistence of ``small ball'' tactics
in the National League is undoubtedly the fact that 
the NL has never adopted the {\it designated hitter}.  Pitchers
still bat, and if they try to have any offensive impact
at all, it is probably going to come by bunting, sacrificing,
etc.  
\item{6.}  The ``flip side'' of the last comment is 
that in the American League, you don't have pitchers batting
and they are replaced, in fact, by offensive specialists
who don't have to do anything else besides hitting(!)
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{\it Paper:}
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{\it Presentation:} 
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{\it Mary Arnold and Shelby Proft -- Atmospheric CFC 113 and ${\rm CCl}_4$.}
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Most of this paper is really good.  However I don't think you really 
tied things up with a good section about conclusions and suggestions
for further work (see comment 4 below).  Moreover, even though you 
did put in footnotes, which is great, there should still be a complete
list of all the sources you used at the end of the paper (a References
section).  Plus you really need to provide additional information about
when you consulted Internet sources.  
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{\it Some Specfic Comments}
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\item{1.}  ${\rm O}_2$ molecules are the usual form of atmospheric oxygen, of course.
It is true that they are somewhat unstable, because they tend to combine with
other things in oxidation reactions.  But the main point here is that normal oxygen 
molecules have different physical properties -- they do not reflect UV rays
from the Sun as well as ozone (${\rm O}_3$) molecules do.
\item{2.}  I think it is fair to say that almost all scientists would agree with
the statements you are making here.  However, as you probably know, there are
still a lot of people who do not accept that this is happening (or who don't
believe that the case has been made convincingly), and who don't accept
that anything humans are doing is causing it, even if it is happening.  It might
be good to acknowledge that this connection is still somewhat controversial.
\item{3.}  This sentence reads as being somewhat self-contradictory because
you are not explicitly saying that the concentrations of the chemicals in these
two different settings are quite different.  It would be good to
break it up into two statements.  First, say exposure to these chemicals in the 
concentrations observed in the atmospheric data has not been shown to have major 
effects.  But then say:  There are concerns, however, with exposure to the 
much higher concentrations that would be found in workplaces where the chemicals
are present in much larger quantities and people would be directly working
with them, etc.
\item{4.}   The major ``issue'' I see with the paper is that it just sort
of ``ends'' without coming to any good conclusion.  There are several interesting
conclusions you could draw too, so this struck me as a real lost opportunity,
or maybe a case where you ran out of time to do everything you should have
done.
The first possible conclusion, of course, is that there seems to be evidence that the 
limits on chlorofluorocarbon usage {\it are really having a measurable effect}.
The extended ``downward trend'' period for both hemispheres in both data sets
shows this really well.  But then, on the other hand,
the second conclusion could be that even though this is true, it does 
not seem that the goal of the Vienna Convention (the 2050 date) 
is going to be met because the rate of decrease seems to be too slow. 
(This is why I suggested that you look at the Sen's estimated trend lines
and see how long it would take to get back to the original levels.)
Finally, you could also mention the need for continued monitoring and
regulation of other atmospheric pollutants that react with the 
ozone layer, etc.
Saying all this would have been a major addition to your paper and 
a perfect way to tie together everything you did.  It's a shame you 
did not do this.
\item{5.}  For a research paper like this, as I said in the guidelines
in the assignment, a References section is a necessary component,
even if you use footnotes the way you did.  Moreover, for the
sources from the Internet, it is necessary to give both a URL
and the date you consulted the site, because things tend to change
over time(!) 
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{\it Paper:}
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{\it Presentation:}
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{\it Stephanie Craig and Kyle Walraven -- Statistics and Discussion of Trends ... in Baseball}
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{\it Some Specific Comments}
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\item{1.}  Avoid sentence fragments like this in formal writing.  (This would be fine as
a section title, but not as a first ``sentence'' of a paper.)
\item{2.}  You are using a name incorrectly here.  The thing that started around 1869 was
one of the first professional baseball leagues.  It was a forerunner of MLB, but MLB
was only incorporated much later when the American and National leagues had already 
been around for many years (and were, in effect, allowed to form a legal monopoly
for professional baseball in this country).  
\item{3.}  This is one of those funny word choice things -- no one ever
says ``baseball match'' (``cricket match,'' yes, but never ``baseball match'').
It's always a ``baseball game.''
\item{4.}  Careful about this term.  ``Confounder'' has a specific technical
meaning that does not match what you are saying.  A confounder in a (non-randomized)
study with a treatment group and a control group is a factor that is associated with
both membership in the treatment group and with the outcome of the treatment.  You
mean something like ``alternate explanation.''
\item{5.}  It would be good to say where the spreadsheet came from, etc.
\item{6.}  The major potential issue I see with the way you carried out
the statistical analysis is the way you only took the data points every 10 years.
I know you also looked at year-by-year data in some cases, and that was good.
However, leaving out the intermediate years and taking only one year per decade
is problematic for estimating trends.   I'm just not convinced that
this approach is valid for this kind of analysis.
\item{7.}  Maybe it would be better to say hitting lots of triples
requires a {\it combination of factors} including hitting balls into areas
that take a long time for the fielders to reach and retrieve the ball, plus running speed,
plus a certain amount of luck.  Not all triples are long fly balls of course.  There are
the booming triples into the ``Triangle'' in center field at Fenway Park, for instance.
But I have also
seen an exceptionally hard-hit ground ball  down the first base line at 
Fenway get turned into a triple.  If the right fielder misplays the ball as it bounces around the 
curve of the right-field stands, the ball can easily get behind him.  If the batter
has some speed, then he can end up on third base in that situation too.  So it's not 
only a matter of hitting skill.  In fact, I would be willing to bet that the main
contribution to this trend is the smaller outfields that most modern ballparks have.
The outfielders can get to most batted balls 


\bye
