Chi-Square test
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Transcript of Chi-Square test
Chi-Square test
PRESENTED BYPRESENTED BY::
Dr.Zhian Salah RamziDr.Zhian Salah Ramzi
Head of community andHead of community andFamily medicine/ sulaimani universityFamily medicine/ sulaimani university
Chi-Square TestChi-Square Test
Evaluates whether observed Evaluates whether observed frequencies for a qualitative frequencies for a qualitative variable (or variables) are variable (or variables) are adequately described by adequately described by hypothesized or expected hypothesized or expected frequencies.frequencies.
Qualitative (or categorical) data is Qualitative (or categorical) data is a set of observations where any a set of observations where any single observation is a word or code single observation is a word or code that represents a class or category.that represents a class or category.
Nonparametric StatisticsNonparametric Statistics
Chi-Square (Chi-Square (22 )Test )Test Used to analyze data in situations where one wishes Used to analyze data in situations where one wishes
to test whether the observed number of responses in to test whether the observed number of responses in a category differs from the expected number that a category differs from the expected number that fall in that category.fall in that category.
Dependent Variable is nominal.Dependent Variable is nominal. HHoo represents the expected proportion of responses represents the expected proportion of responses
falling in a given category.falling in a given category.
• Where k = # of categories, Oi = observed number of cases in each category, Ei = expected number of cases in each category.
• When Ho is true, Oi Ei and 2 will be small. If Ho is false,
then Oi Ei and 2 will be large.
Simple and complex – one variable or multiple variables
k
Ei
EiOi 22 )(
Recent studies have found that most teens are knowledgeable about AIDS, yet many continue to practice high-risk sexual behaviors. King and Anderson (1993) asked young people the following question: “If you could have sexual relations with any and all partners of your choosing, as often as you wished, for the next 2 (or 10) years, but at the end of that time period you would die of AIDS, would you make this choice?” A five-point Likert scale was used to assess the subjects’ responses. For the following
data, the responses “probably no,” “unsure,” “probably yes”, and “definitely yes” were pooled into the category “other.” Using the .05 level of significance, test for independence.
Definitely No Definitely No OtherOther
MalesMales 451451 165165
FemalesFemales 509509 118118
Chi-Square Test for Chi-Square Test for IndependenceIndependence
State the research hypothesis.State the research hypothesis. Is willingness to participate in Is willingness to participate in
unprotected sex independent of unprotected sex independent of gender?gender?
State the statistical hypothesis.State the statistical hypothesis.
HH0:0: Response to the question and gender are not relatedResponse to the question and gender are not relatedResponse to the question and gender are relatedResponse to the question and gender are relatedHHA:A:
Chi-Square Test for Chi-Square Test for IndependenceIndependence
To find expected values:To find expected values: Find column, row, and overall totals.Find column, row, and overall totals.
Definitely NoDefinitely No OtherOtherTotalTotal
MalesMales 451451 165165 616616
FemalesFemales 509509 118118 627627
TotalTotal 960960 283283 12431243
Chi-Square Test for Chi-Square Test for IndependenceIndependence
To find expected values:
Definitely NoDefinitely No OtherOtherTotalTotal
MalesMales 451 (475.75) 165 616
FemalesFemales 509509 118118 627627
TotalTotal 960960 283283 12431243
EiEi
EiEi
EiEi
Chi-Square Test for Chi-Square Test for IndependenceIndependence
To find expected values:
Definitely No OtherTotal
Males 451 (475.75) 165 616
Females 509 (484.25) 118 627
Total 960 283 1243
EiEi
EiEi
Chi-Square Test for Chi-Square Test for IndependenceIndependence
To find expected values:
Definitely No OtherTotal
Males 451 (475.75) 165 (140.25)616
Females 509 (484.25) 118 627
Total 960 283 1243
EiEi
EiEi
Chi-Square Test for Chi-Square Test for IndependenceIndependence
To find expected values:
Definitely No OtherTotal
Males 451 (475.75) 165 (140.25)616
Females 509 (484.25) 118 (142.75)627
Total 960 283 1243
EiEi
EiEi
Chi-Square Test for Chi-Square Test for IndependenceIndependence
Set the decision rule. Degrees of Freedom
(number of columns - 1) (number of rows -1) (c-1)(r-1)
1)1)(1()12)(12( dfDefinitely No
Other
Males 451 165
Females 509 118
Chi-Square Chi-Square
Set the decision rule.
84.3
1
05.
2
crit
df
Chi-Square Test for Chi-Square Test for IndependenceIndependence
Calculate the test statistic.Definitely No Other
Total
Males 451 (475.75) 165 (140.25)616
Females 509 (484.25) 118 (142.75)627
Total 960 283 124375.142
)75.142118(
25.140
)25.140165(
25.484
)25.484509(
75.475
)75.475451( 22222
75.142
56.612
25.140
56.612
25.484
56.612
75.475
56.612
21.11
29.437.426.129.1
k
Ei
EiOi 22 )(
The Chi-Square testThe Chi-Square test
Chi-Square Test for Chi-Square Test for IndependenceIndependence
Decide if your result is significant. Reject H0, 11.21>3.84
Interpret your results. Willingness to engage in unprotected sex
and gender are not independent.Definitely No Other
Total
Males 451 (475.75) 165 (140.25)616
Females 509 (484.25) 118 (142.75)627
Total 960 283 1243