Question: Below we have data on the winloss 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 ttest comparing two proportions and the chisquare 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 ttest for a
significant difference between the homewin and road win proportions is
presented in the table below.
Calculation of ttest 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

tstatistic

2.093

pvalue

0.036

The
calculation of the chisquared 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

(OWHEWH)2/EWH

0.91

(OLHELH)2/ELH

1.22

(OWAEWA)2/EWA

0.91

(OLAELA)2/ELA

1.22

Chi Square

4.27

Pvalue

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 chisquare test is commonly used for
small as well as large samples. The
ttest is most commonly used for larger samples.
Note three: The pvalues from the two tests are close
0.039 for the chisquare test and 0.036 for the ttest. The test results presented here are
twotailed. We reject the null
hypothesis that the homewin proportion is identical to the roadwin
proportion.
Note four: The ttest 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 homefield advantage testing problems:
http://www.dailymathproblem.com/p/homefieldhypothesistestingproblems.html
http://www.dailymathproblem.com/p/homefieldhypothesistestingproblems.html
No comments:
Post a Comment