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Section 10.7. Chi-Square Test for Association. Objectives. Perform a chi-square test for association. Chi-Square Test for Association. Null and Alternative Hypotheses for a Chi‑Square Test for Association. Chi-Square Test for Association. - PowerPoint PPT Presentation

Transcript of Section 10.7

Section X.X

Section 10.7Chi-Square Test for AssociationHAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.ObjectivesPerform a chi-square test for association.

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Chi-Square Test for AssociationNull and Alternative Hypotheses for a ChiSquare Test for Association

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Chi-Square Test for AssociationExpected Value of a Frequency in a Contingency TableThe expected value of the frequency for the ith possible outcome in a contingency table is given by

where n is the sample size.

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Chi-Square Test for AssociationTest Statistic for a Chi-Square Test for AssociationThe test statistic for a chisquare test for association is given by

where Oi is the observed frequency for the ith possible outcome andEi is the expected frequency for the ith possible outcome.

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Chi-Square Test for AssociationDegrees of Freedom in a Chi-Square Test for AssociationIn a chisquare test for association, the number of degrees of freedom for the chisquare distribution of the test statistic is given bydf = (R 1) (C 1)where R is the number of rows of data in the contingency table (not including the row of totals) and C is the number of columns of data in the contingency table (not including the column of totals).HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Chi-Square Test for AssociationRejection Region for ChiSquare Tests for AssociationReject the null hypothesis, H0, if:

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Example 10.32: Performing a Chi-Square Test for AssociationSuppose that the following data were collected in a poll of 13,660 randomly selected voters during the 2008 presidential election campaign.

Is there evidence at the 0.05 level to say that gender and voting choice were related for this election?Observed Sample of 13,660 VotersObamaMcCainOtherTotalMale34552764656284Female35413762737376Total6996652613813,660HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Example 10.32: Performing a Chi-Square Test for Association (cont.)Solution Step 1:State the null and alternative hypotheses. We let the null hypothesis be that gender and voting preference are independent of one another.

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Example 10.32: Performing a Chi-Square Test for Association (cont.)Step 2:Determine which distribution to use for the test statistic, and state the level of significance. We wish to determine if there is an association between gender and voting preference. Since we are told that we can safely assume that the necessary conditions have been met for the examples in this section, we will use the chisquare test statistic to test for this association. We are told that the level of significance is a = 0.05. HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Example 10.32: Performing a Chi-Square Test for Association (cont.)Step 3:Gather data and calculate the necessary sample statistics. Before we begin to calculate the test statistic, we must calculate the expected value for each cell in the contingency table.

HAWKES LEARNING SYSTEMSStudents Matter. Success Counts.Copyright 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.Example 10.32: Performing a Chi-Square Test for Association (cont.)Lets calculate the c2 -test statistic.