Saturday, January 16, 2016

Two tests for difference between home and road win proportions

Question:  Below we have data on the win-loss record at home and on the road for the Toronto Blue Jays.

Toronto Blue Jay Record Home and Away 2015
Home
Away
Win
53
40
93
Loss
28
41
69
81
81
162


Use the large sample t-test comparing two proportions and the chi-square test on difference between actual and expected proportions to determine whether home field advantage was important to the Toronto Blue Jays in 2015.

Analysis:  The calculation of the t-test for a significant difference between the home-win and road win proportions is presented in the table below.


Calculation of t-test for difference in home and road win percentages
Label
Number of formula
Observed Win/Home
53
Observed Lose/Home
28
Observed Win Away
40
Observed Lose Away
41
Total Home
81
Total Away
81
Win Prob Home
0.654
Win Prob Away
0.494
Diff Win Probabilities
0.160
Pooled Variance
0.238
Standard Error
0.077
t-statistic
2.093
p-value
0.036


The calculation of the chi-squared test for a significant difference in the two proportions is presented in the table below.


Calculation of chi square test for difference in home
 versus road win percentages
Team
Toronto
Blue Jays
Observed Win/Home
53
Observed Lose/Home
28
Observed Win Away
40
Observed Lose Away
41
Total Home
81
Total Away
81
Total Observations
162
Pooled Win Prob
0.5741
Pooled Loss Prob
0.4259
Expected Win/Home
46.50
Expected Loss/Home
34.50
Expected Win/Away
46.50
Expected Loss/Away
34.50
(OWH-EWH)2/EWH
0.91
(OLH-ELH)2/ELH
1.22
(OWA-EWA)2/EWA
0.91
(OLA-ELA)2/ELA
1.22
Chi Square
4.27
P-value
0.039


Notes:

Note One:  I have arranged the calculators vertically.   The first four lines of each calculator is input.   The remaining lines are formula.   If you want to test home win proportions for some other team just put appropriate input into the first four lines of the calculator and it will update.

Note Two:  The chi-square test is commonly used for small as well as large samples.   The t-test is most commonly used for larger samples.

Note three:  The p-values from the two tests are close 0.039 for the chi-square test and 0.036 for the t-test.   The test results presented here are two-tailed.   We reject the null hypothesis that the home-win proportion is identical to the road-win proportion.

Note four:  The t-test for no difference in home versus road win proportions for all MLB teams in the 2015 regular season along with a nice statistical discussion on the meaning of hypothesis tests is presented in the post below.

Concluding thoughts:  The Toronto Blue Jays did a better job at home than on the road during the regular season in 2015.  I wonder if this is true of all teams.

 Is home field advantage more important for some teams than other teams?  If so, why is it more important for some teams than other teams?   Is home field advantage as important in the post season?   Is home field advantage important in every sport?

Variants of this problem can be used to teach both baseball and statistics.   More will follow.

Authors Note: In 1996, I wrote a short book “Statistical Applications of Baseball”  The book is a bit informal but it has a lot of statistical problems and it got a good review from the academic journal Chance.   If you are interested the book is available on Kindle.



Go back to home-field advantage testing problems:

http://www.dailymathproblem.com/p/home-field-hypothesis-testing-problems.html








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