Chi square test for homgeneity

Conditions and examples of running a chi-square test for Homogeneity

1. Focus Fox Select the best option: Which of the following is a condition that must be met in order to carry out a chi-square goodness-of-fit test? The population must be normally distributed, or the sample size must be greater than 30 The cell counts for our sample have to be approximately the same as the expected counts All observed cell counts must be greater than 5 All expected counts must be greater than 5 More than one of these conditions must be met

2. Chi-Square Test Homgeneity Chi-Square Test for Homogeneity – two way table If Random – random samples from each population or groups in randomized experiment If Large Sample Size – all expected counts are at least 5 If Independent – individual observations & 10% condition H : there is no difference in the distribution of a categorical variable for several populations or treatments H a : there is a difference in the distribution of a categorical variable for several populations or treatments Find expected counts d f = (number of rows – 1)(number of columns – 1) P-value is the area to the right of χ 2 under the density curve

3. Chi-Square Test Homgeneity H0: there is no difference in the distributions of wine purchases at this store when no music, French accordion music, or Italian string music is played. Ha: there is a difference in the distributions of wine purchases at this store when no music, French accordion, or Italian string music is played. Previously calculated test statistic χ 2 = 18.28 Wine No Music French Italian Totals French 30 39 30 99 Italian 11 1 19 31 Other 43 35 35 113 Totals 84 75 84 243

4. Chi-Square Test Homgeneity Previously calculated test statistic χ 2 = 18.28 Use Table C to find the P-value. Now use χ 2 cdf command on calculator Wine No Music French Italian Totals French 30 39 30 99 Italian 11 1 19 31 Other 43 35 35 113 Totals 84 75 84 243

5. Chi-Square Test Homgeneity Previously calculated test statistic χ 2 = 18.28 Interpret the P-value from the calculator in context. What conclusion would you draw? Wine No Music French Italian Totals French 30 39 30 99 Italian 11 1 19 31 Other 43 35 35 113 Totals 84 75 84 243

6. Chi-Square Test Homgeneity Using Technology: Enter the observed data in Matrix A Select χ 2 test - STATS – TESTS – χ 2 - Test Observed: [A] Expected: [B] Choose calculate then 2 nd Enter and Draw Select and enter Matrix [B] Tables are commonly referenced by dimensions row by column – 2x3 Pg. 706

7. Chi-Square Test Homgeneity Follow-Up Analysis The chi-square test for homogeneity allows us to compare the distribution of a categorical variable for any number of populations or treatments. If we reject the null of no difference, follow-up analysis is required Examine which cell in the two-way table show large deviations between observed and expected counts. Look at the which contribute the most to the chi-square statistic Pg. 709 – minitab output and analysis