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Section 13.2
Chi-square Test of
Association /
Independence
AP Statistics
March 30, 2010
Berkley High School
Housekeeping
Χ2 with df=10 can be expressed using the
shorthand notation: Χ2(10)
 The answer to question 4 on the sample
test is wrong; the correct answer is C.

AP Statistics, Section 13.1
2
Example


Chronic users of cocaine need the drug to feel
pleasure. Perhaps giving them a medication that
fights depression will help them stay off cocaine.
A three-year study compared an antidepressant
call desipramine with lithium (a standard
treatment for cocaine addiction) and a placebo.
The subjects were 72 chronic users of cocaine
who wanted to break their addiction.
AP Statistics, Section 13.1
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Observed
No Relapse
Yes Relapse
Desipramine
14
10
24
Lithium
6
18
24
Placebo
4
20
24
24
48
72
AP Statistics, Section 13.1
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Expected (assuming
independence)
No Relapse
Yes Relapse
Desipramine
24
Lithium
24
Placebo
24
24
AP Statistics, Section 13.1
48
72
5
Formula for expected counts
row total  column total
expected count=
table total
 
2
O  E 
2
E
df   rows-1 columns-1
AP Statistics, Section 13.1
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Observed
No
Relapse
Yes
Relapse
Desipramine
14
10
24
Lithium
6
18
24
Placebo
4
20
24
24
48
72
 O-E 
 
2
E
Expected
Yes
Relapse
Desipramine
8
16
24
Lithium
8
16
24
Placebo
8
16
24
24
48
72
2
8
AP Statistics, Section 13.1

14  8   10  16 
8
16
6  8


No
Relapse
2
 4  8
8
 10.5
2
2
2
18  16 


2
16
20  16 


2
16
df  (3  1)  2  1  2
7
AP Statistics, Section 13.1
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What new for Chi-squared Test for
independence


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H0: the categories are independent.
Ha: the categories are not independent.
You can safely use the chi-square test with
critical values from the chi-square distribution
when no more than 20% of the expected counts
are less than 5 and all individual expected
counts are 1 or greater. In particular, all four
expected counts in a 2X2 table should be 5 or
greater.
AP Statistics, Section 13.1
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On the calculator
The “observed” data goes into matrix,
typically, A
 Run the χ2-Test from the Stats:Test
 You specify where you want the expected
matrix to go.

AP Statistics, Section 13.1
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Exercises
13.15-13.29 odd
 Chapter Review: 13.31-39 odd

AP Statistics, Section 13.1
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