```Question 139460
explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence.  Please provide an example of using one of these hypothesis test.  Please be specifc providing the steps to the hypothesis test in your exmaple.
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These are large topics. You would have to see a text on statistics or use
Google to get all of what you are looking for.  But here is a little of it.
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Goodness of Fit with a simplified example:
30 horse races are run with horses in 3 lanes.
# of wins from lane one = 8
# of wins from lane two = 12
# of wins from lane three = 10
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Ho: It makes no difference which lane the horse starts in.
Ha: It makes a difference.
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Comment: If it makes no difference there should be 10 wins from each position.
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Run a Chi-Sq on a 2 x 3 Matrix:
row 1: 8....12....10
row 2: 10...10....10
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Chi-Sq results:
Test statistic: Chi-Sq = 0.404040404...
p-value: 0.81707
df=2
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Conclusion: Since p-value is greater than 5%, Fail to reject Ho.
It makes no difference which lane the horse starts in.
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Ch-Sq Test for Independence
You have three horses, A, B, C and you have three lanes on the track 1,2.3.
You keep track of how many wins each horse has on each track.
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------------------A..........B........C
row 1.............2..........4........3
row 2.............3..........5........1
row 3.............4..........2........5
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Ho: Horses and lanes are independent
Ha: They are dependent
Run a Chi-Sq on the 3 x 3 Matrix and get the following
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Test Statistic: Chi-Sq = 0.213447...
p-value = 0.37789..
df=4
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Conclusion: Since p-value is greater than 5%, Fail to reject Ho.
Horses and lanes are independent.
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Hope that helps.
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Cheers,
Stan H.```