1. 13.2 Inference for Two Way Tables

2.  Analyze Two Way Tables Using Chi-Squared Test for Homogeneity and Independence

3. Goodness of Fit HomogeneityIndependence 1 variable -distribution 2 variables (2 way table) -distribution -proportions 2 variables (2 way table) -association -dependent upon -relationship

4.  Expected Counts=  Degrees of freedom (r-1)(c-1) Chi-Squared Test Statistic

5.  H₀:the proportion of ________ is the SAME as __________  Ha: the proportion of ________ is the DIFFERENT than __________

6.  Example 1: Do the boys’ preferences for the following TV programs differ significantly from the girls’ preferences? Use a 5% significance level. HouseGrey’s Anatomy American Idol CSI Boys667867105 Girls4813012361

7.  H₀:the boys preference for TV programs is the SAME as the girls  Ha: the boys preference for TV programs is DIFFERENT than the girls  Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5 HouseGrey’s Anatomy American Idol CSI Boys53.196.988.677.4 Girls60.9111.1101.488.6

8.  Chi-Squared Test (Homogeneity) w/ α=0.05  P(x²>41.08)=0.000000006  df=3  Since p< α, it is statistically significant. Therefore we reject H₀. There is enough evidence to say the preference of TV programs for boys is different than girls.

9.  Example 2: The following data is an SRS of 650 patients at a local hospital. Does the effect of aspirin significantly differ from a placebo for these medical conditions? AspirinPlacebo Fatal Heart Attacks 2060 Non-Fatal Heart Attacks 125220 Strokes75150

10.  H₀:the effects of aspirin is the same as the placebo  Ha: the effects of aspirin is different than the placebo  Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5 AspirinPlacebo Fatal Heart Attacks 27.152.9 Non-Fatal Heart Attacks 116.8228.2 Strokes76.2148.8

11.  Chi-Squared Test (Homogeneity) w/ α=0.05  P(x²>3.70)=0.1573  df=2  Since p∡ α, it is not statistically significant. Therefore we do not reject H₀. There is not enough evidence to say the effect of aspirin differs from the placebo.

12.  H₀: There is no relationship (association) between ________ and ________.  Ha: There is a relationship (association) between ________ and ________.

13.  Example 3: An SRS of 1000 was taken  Is there a relationship between gender and political parties? RepublicanDemocratIndependent Male20015050 Female25030050

14.  H₀: There is no relationship between gender and political party  Ha: There is a relationship between gender and political party  Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5 RepublicanDemocratIndependent Male180 40 Female270 60

15.  Chi-Squared Test (Independence) w/ α=0.05  P(x²>16.2)=0.0003  df=2  Since p< α, it is statistically significant. Therefore we reject H₀. There is enough evidence to say there is a relationship between gender and political party

16.  Example 4: An SRS of 592 people were taken comparing their hair and eye color. Is there an association between hair color and eye color? BlackBrownRedBlonde Brown68119267 Green20841794 Blue15541410 Hazel8291416

17.  H₀: There is no association between hair color and eye color  Ha: There is an association between hair color and eye color  Assumptions: -random sample -all expected counts are ≥ 1 -no more than 20% of the expected counts <5 BlackBrownRedBlonde Brown41.0105.726.347.0 Green40.1103.325.745.9 Blue17.344.711.119.9 Hazel12.532.28.014.3

18.  Chi-Squared Test (Independence) w/ α=0.05  P(x²>134.98)≈0  df=9  Since p< α, it is statistically significant. Therefore we reject H₀. There is enough evidence to say there is an association between hair color and eye color