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Chapter 11Chapter 11: Chi–Square : Chi–Square and F Distributionsand F DistributionsSection 1Section 1: Chi-Square: Tests of : Chi-Square: Tests of
IndependenceIndependence
Chi–Square DistributionChi–Square Distribution
- - Greek letter “Chi”Greek letter “Chi” Chi-Square denoted by Chi-Square denoted by graph is not symmetricalgraph is not symmetrical depends on degrees of freedomdepends on degrees of freedom as df increase, graph becomes more as df increase, graph becomes more
symmetricalsymmetrical
2
Chi-Square Test of Independence – used to determine whether two characteristics are related
Formulas Formulas
E =E =
df = (r -1)(c – 1) df = (r -1)(c – 1) E
EO 22 )(
SizeSample
totalColumntotalRow ))((
ExampleExample Use a chi-square test to determine Use a chi-square test to determine
whether there is a relationship between whether there is a relationship between students’ political views and their opinion students’ political views and their opinion about a controversial issue. Use a 5% about a controversial issue. Use a 5% level of significancelevel of significance
Ho: Political view and opinion are independent
H1: Political view and opinion are related
Contingency tableContingency table
DemocratDemocrat RepublicanRepublican IndependentIndependent
approveapprove 1010 1515 2020
disapprovedisapprove 99 22 1616
undecidedundecided 88 22 1818
SolutionSolution
OO EE (O – E)(O – E) (O – E)(O – E)22 (O – E)(O – E)22/E/E
1010 12.1512.15 -2.15-2.15 4.62254.6225 0.38050.3805
1515 8.558.55 6.456.45 41.602541.6025 4.86584.8658
2020 24.324.3 -4.3-4.3 18.4918.49 0.76090.7609
99 7.297.29 1.711.71 2.92412.9241 0.40110.4011
22 5.135.13 -3.13-3.13 9.79699.7969 1.90971.9097
1616 14.5814.58 1.421.42 2.01642.0164 0.13830.1383
88 7.567.56 0.440.44 0.19360.1936 0.02560.0256
22 5.325.32 -3.32-3.32 11.022411.0224 2.07192.0719
1818 15.1215.12 2.882.88 8.29448.2944 0.54860.548611.102