Economics of Sports

DATA    0    1    1    0    1    0    0    0    1    0    0    0    1    1    0
# trials    2    1    1    2    1    4    3    2    1    4    3    2    1    1    3
until make

geometric distribution
# trials    1    2    3    4    5    6    7    8    9
freq.    52    28    14    5    1    0    0    0    0
Project 3
Chi-square test

1.  Make a conjecture about some facet of sports.
a.  For example, “Curtis Granderson is a less good hitter when facing left-handed pitching.”
b.  Choose an example with a clear, dichotomous definition of success; e.g. “he gets a hit, not an out.”  This is your dependent variable, and it is given in the columns of the table.
c.  The independent variable (e.g. type of pitching) goes in the rows of the table.  It must also be dichotomous for this assignment.
2.  Write you hypothesis in the space provided on the assignment template.
3.  Write the null hypothesis in the space provided.
4.  Enter which variable is the independent and which is the dependent (success or failure).
5.  Gather the relevant data.  Enter the source of the data in the space provided.
6.  Enter the data in the table on the assignment sheet.
a.  Again, independent variable on the rows; dependent variable on the columns.
7.  Go to http://www.quantitativeskills.com/sisa/statistics/fisher.htm
8.  Enter the data and calculate the chi square statistics.
9.  Enter the p value.
a.  We want the two sided p value, which is starred – not the one based on the “Pearson statistic.”
9.  Interpret your results in the space provided.

Name  ___________________________

Assignment Sheet
Chi-square test

Hypothesis:

Null hypothesis:

Independent variable        _____________________

Dependent variable        _____________________

Source of data            _____________________

Table

________________        __________________

_____________

______________

p-value                __________________

Interpretation

Project 2
Distributions
1.  Peruse (check out) my example.  I entered my data in sheet 1 on row 1 (52% is pitiful).   Then, I compute the number of successes in 10 trials beginning from the first shot and entered that number (4 makes) in cell B2.  I continued by computing the number of successes from attempt 2 through attempt 11.  Again this equals 4 and I entered that in B3.  Continuing along, I have a row from B2 to CN2 with the numbers of makes in 10 trials.  Next, I computed the frequency of each of these numbers and entered that where it is labeled “binomial distribution.  Finally, I plotted the frequencies.  It’s somewhat bell-shaped, but not exactly.  The reason is, of course, that this is only a sample.

2.  Binomial Distribution: number of successes in n trials. (If you are a “spreadsheet wizard,” you can have the spreadsheet make these calculations.)  Here is the manual way to do it.
a.  Count the number of successes in the first 10 attempts.
b.  Count the number of successes from attempt 2 through attempt  11.
c.  Count the number of successes from attempt 3 through attempt 12.
Etc.
d.  Count the number of times  (frequency) that you had 0 successes.
e.  Count the number of times that your had 1 success.
Etc.
f.  Plot the binomial distribution.  (Successes along the horizontal – frequency along the vertical)
g.  Compute the mean and standard deviation.

3.  On sheet 2 is my geometric distribution.  Here again, I entered the data on row 1.  Then I compute the number of trials until success.  You can see that my first make was on the second try; so the number of trials until success  (starting from the first shot) is 2.  I again calculated the frequencies and plotted the distribution.  It looks fairly close to geometric.

4.   Geometric Distribution: number of attempts until next success.
a.  Count the number of attempts until your first success.
b.  Starting from the second attempt, count the number of trails until your first success.  (note: if you first success is on attempt 6, then the answer to part a. is 6, and the answer to part b. is 5.)
etc.
d.  Count the frequency of “success on  first attempt.”
e.  Count the frequency of “success on second attempt.”
Etc.
f.  Plot the geometric distribution (attempts on the horizontal – frequency along the vertical)
g.  Compute the mean and standard deviation.

5.  Turn your work into the dropbox.  Specifically, you will turn in a spreadsheet file.