Question: The table below has the home and away record
for the Golden State Warriors as of 1/14/26.
Test the null hypothesis that the win percentage of the Warriors is the
same both home and away.
Golden State Home and
Away as of 1/14/2016


Home

Away

Total


Win

18

18

36

Loss

0

3

3

Total

18

21

39

Analysis:
There are several ways to test this hypothesis. I will use the ChiSquare test for difference
in two proportions.
The test statistic for the chisquare test is
Chisquare= sum over all cells (f_{o}f_{e})^{2}/f_{e}
Here f_{o} is the observed outcomes win/losses at
home/away.
f_{e} is the expected number of wins/losses at
home/away under the null hypothesis that the win loss percentage does not
depend on whether the game is home or way.
The overall win percentage is 36/39 or 0.923.
The overall loss percentage is 3/39 or 0.077.
Multiply the overall win/loss percentage by the number of
home/away games to get the expected wins/loss at home/away. The calculation of f_{e} is
presented below.
Calculation of Expected Outcomes


f_{e}

f_{e} calculation


Win/Home

16.62

(0.923*18)

Win/Away

19.38

(0.923*21)

Lose/Home

1.38

(0.076*18)

Lose/Away

1.62

(0.076*21)

The chisquare statistic is calculated in the table below.
Calculation of ChiSquare
Statistic


fo

fe

(fofe)2/fe


Win/Home

18

16.62

0.12

Win/Away

18

19.38

0.10

Lose/Home

0

1.38

1.38

Lose/Away

3

1.62

1.19

Total

ChiSquare Statistic

2.79


pvalue

0.09511

The test statistic is chi squared with 1 degree of freedom. Excel allows for the calculation of the
pvalue for the chi square statistic with the CHIDIST function.
The pvalue of 0.0951 is marginally significant for a
twotailed test. However, it might be
reasonable to use a onetailed test for this problem.
This book, which is on line, is a good reference fort this
type of problem.
The home court or home field issue can be used to illustrate
a bunch of statistical problems or questions.
Why might some sports have higher home court advantages than
other sports?
Why would home court advantage be a more important factor
for some baseball teams and not other teams?
Why might home court advantage be less important for NFL
wildcard games than for subsequent playoff games? (Should this question be addressed with a one
or two tailed test?)
More problems teaching hypothesis tests on proportions and sometimes on means based on the home field issue will follow.
My most popular book on Kindle is Statistical Applications of Baseball. It is a bit dated as it was written in 1996 and it has some typos but it got a good review in the Journal Chance and it has numerous word problems, which can reduce lesson planing time for teachers. I hope it provides some use to you.
http://www.amazon.com/StatisticalApplicationsBaseballStatisticsSportsebook/dp/B006M3PQWQ
Go Back to the Seven HomeField Advantage Hypothesis Testing Problems:
http://www.dailymathproblem.com/p/homefieldhypothesistestingproblems.html
My most popular book on Kindle is Statistical Applications of Baseball. It is a bit dated as it was written in 1996 and it has some typos but it got a good review in the Journal Chance and it has numerous word problems, which can reduce lesson planing time for teachers. I hope it provides some use to you.
http://www.amazon.com/StatisticalApplicationsBaseballStatisticsSportsebook/dp/B006M3PQWQ
Go Back to the Seven HomeField Advantage Hypothesis Testing Problems:
http://www.dailymathproblem.com/p/homefieldhypothesistestingproblems.html
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