Prepared by: James Tarver

Mathematical Modeling (Math 471)

Spring 2000

This is a picture of me, taken for the CLU baseball website.

My
name is James Tarver and I am a senior at California Lutheran University.
This page is not designed to talk to you about CLU baseball, but instead
my senior research project. I am a math major and for my capstone class,
mathematical modeling, I prepared a project on Title IX and CLU Sports.
My project invloved breaking down a survey passed around the campus of
CLU inquiring about athletic preferences and desires of CLU students. I
am a pitcher at CLU and have been invloved in athletics my whole life.
Issues with Title IX have arose more commonly in recent times, so I became
interested. That is why I chose this topic for my research project.

__Summary__

In
my senior project for mathematical modeling, I worked towards accomplishing
3 tasks: presenting some of the data from the survey CLU took involving
Title IX, making conclusions about the data and including suggestions on
how the survey could be improved. To do this, I observed the results from
the survey and put together some histograms to display the data. Then I
made some conclusions about what the limited amount of data told us. Lastly,
I used some of my math knowledge and reasoning ability to suggest how the
survey can be improved for the benefit of CLU athletics. It must be noted
that some of the results of this survey may be skewed because the sample
size was so small. By this I mean that a certain group of athletes (possibly
the baseball team) could have all filled out this survey giving results
that may not be as accurate as CLU had hoped.

__What is Title IX?__

In 1972, the U.S. Congress enacted Title IX of the Education Amendments to the Civil Rights Act of 1964. It reads "No person in the U.S. shall, on the basis of sex, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under the education program or activity receiving Federal financial assistance." In other words, Title IX calls for gender equity in all aspects of sports. Title IX strives to answer "yes" to the question: do women and men have equal opportunities in athletics?

__CLU and Title IX__

The athletic department of CLU wanted to see where we stood in accordance with Title IX, so they distributed a survey to 250 CLU students. The survey contained 22 questions exploring the athletic desires of some of CLU's students. The survey covered topics including past (high school) experiences in sports, present interest in sports, interest in intramurals and club sports at CLU and interest in playing sports CLU offers, to name a few. The CLU athletic department was curious to see if men and women were getting an equal opportunity to participate in sports at CLU.

__Cal Lutheran Sports : By The
Numbers__

This
table displays the sports CLU offers at the NCAA Division III level. As
you can see, men have one more sport than women. What is interesting is
that if football were removed, which I hope never happens, men and women
have an equal number of sports and an equal number of athletes. Maybe we
just need a women's football team.

Men's Sports |
Women's Sports |

Baseball ( 34 ) | Basketball ( 9 ) |

Basketball (13) | Cross Country ( 18 ) |

Cross Country ( 7 ) | Soccer ( 24 ) |

Football ( 85 ) | Softball ( 17 ) |

Golf ( 11 ) | Tennis ( 14 ) |

Soccer ( 27 ) | Track and Field ( 26 ) |

Tennis ( 12 ) | Volleyball ( 13 ) |

Track and Field ( 17 ) | |

Total : 206 : 63 % | Total : 121 : 37 % |

Here is some of the data recorded form the survey...

The percentage of males and females that answered the survey

The interest in participating in athletic activities

Varsity sports played in high school

Interesr in participating in particular sports at CLU

__Suggestions
for a Better Survey__

(1) Increased sample size - how is the sample size determined? By using a formula for finding sample sizes from probability and statistics. The formula looks complicated:

m = ( z ( @ / 2 ) )^ 2
* p * ( 1-p )

(Max error of the estimate for p) ^2

n =
m

1 + (m-1) / N

Let me define some variables now:

- n : calculated sample size

- N : the number of students

- z( @ / 2 ) : is a measure of how "confident"
we are with our p value.

( for example if we are 95% confident with p,
z(@/2) = 1.96 : these values come from probability and statistics).

- p : is an estimated proportion, usually we
use 0.5 for p.

- max error estimate for p : a value that sets
up a interval of confidence for p. For example if our max error is 0.05
or 5%, our interval for p looks like [ p - 0.05, p + 0.05 ]. We can now
look at this interval and determine how confident we are that the proportion
p is actually contained in the interval.

Now that we know a little about the equation for finding sample size we can experiment with some different values for z(@/2) and the max error estimate, using p = 0.5 and N = 1,500.

__Confidence__
__Max Error__
__Sample Size__

80%
0.05
148

80%
0.03
350

90%
0.05
230

90%
0.03
502

95%
0.05
307

95%
0.03
625

99%
0.05
461

99%
0.03
827

Note: I only used errors of 3% and 5% while any percentage would work. Also, a higher percentage of confidence and a lower the max error, resulted in a higher the sample size and thus better and more usable results.

(2) Another example of how to better the survey would be to break down the results (answers to the questions) by certain categories. This is a very important idea. The results of the survey should be sorted into categories so that the the responces of particular groups of people can be known. Some examples: male responses vs. female responses, varsity athlete responses vs. non-varsity athlete responses, or freshmen responses vs. senior responses.

(3) Include the questions: Are there any sports
not offered at CLU which you think there should be?

If so, what sport do you think CLU should include?

(4) Make sure the survey is not distributed in classes that are populated by one designated group of athletes. For example, the survey should not be distributed in the class "Coaching Baseball" or "Coaching Football". CLU needs an equal distribution among it's students for this survey to give quality results.

__Conclusions__

The Title IX survey CLU distributed had only 250 respondents. This was
the only major problem with the survey. In a school of about 1,500, the
survey needed to be filled out by more people. This way CLU can be more
confident about where our athletics stand in compliance with Title IX.
The questions in the survey would give much useful information if there
had been responses. From the data that was recorded, it appears that the
student body of CLU is satisfied with CLU athletics. The majority of the
respondents to the survey had participated in or were interested in athletic
programs CLU offered. In my opinion, CLU is a college of opportunity in
athletics. Of the 1,500 students, 327 (or about 22%) participate in CLU
athletic programs. Men and women both have the option of playing numerous
intramural and club sports. From the data above, notice that a little over
80 % of the student body is at least somewhat interested in sports. That
is a high number. CLU's athletic prowless is expanding. With improvements
in and new facilities coming soon, I believe the students of CLU will participate
even more in athletic activities offerred at CLU. My suggestion: pass this
survey around again in a few years and compare results. I think that both
the men and women of CLU will be very happy with the athletic programs
at CLU.

__References__

(1) Hogg, Robert V. and Tanis, Elliot A. Probability
and Statistical Inference : Fifth Edition. New Jersey: Prentice-Hall,
1997.

(2) Gravetter, Fredrick J. and Wallnau, Larry
B. Statistics for the Behavioral Sciences : 4th Edition. Minnesota: West,
1996.

(3) Grant, Dr. Christine H.B. A Basic Title IX Presentation.
Internet. 4 April 2000. Available: http://bailiwick.lib.uiowa.edu/ge/present.html.

(4) Cal Lutheran Athletics Home Page. Internet. March
20. Available:http://www.clunet.edu/Sports/Sports.html

(5) Owens, Amy. Personal interview. 28 April
2000.

(6) Hill, Tina. Personal interview. 15 March
2000 and 24 April 2000.

__Special Thanks To____
__

My Advisor, Dr. Wyels

Dr. Tong

Dr. Fogel

Dr. Lofstock

My Classmates