Measures of association for 2 nominal variables: Phi - for 2x2 tables Cramer’s for tables (2x3, 3x3, etc.) V Example 1 - Chi square test The contingency table and data analysis examines the relationship between general happiness and marital status of the respondents. Examples of possible survey questions are noted below. 1. What is your current marital status? ___1 Married ___2 Widowed ___3 Divorced ___4 Separated Never married 2. What is your current level of general happiness with life? ___ Very happy ___ Pretty happy ___ Not too happy SPSS Output of a Contingency Table and Test GENERAL HAPPINESS by MARITAL STATUS (N=494) MARITAL STATUS Total GENERAL NEVER MARRIED WIDOWED DIVORCED SEPARATED HAPPINESS MARRIED Count 81 8 12 1 15 117 VERY % within Marital 33.5% 16.3% 16.0% 9.1% 12.8% 23.7% HAPPY Status Std. Residual 3.1 -1.1 -1.4 -1.0 -2.4 Count 143 33 52 8 83 319 PRETTY % within Marital 59.1% 67.3% 69.3% 72.7% 70.9% 64.6% HAPPY Status Std. Residual -1.1 .2 .5 .3 .9 Count 18 8 11 2 19 58 NOT TOO % within Marital 7.4% 16.3% 14.7% 18.2% 16.2% 11.7% HAPPY Status Std. Residual -2.0 .9 .7 .6 1.4 Count 242 49 75 11 117 494 Total % 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% Chi-Square Tests Asymp. Sig. Value df (2-sided) Pearson Chi-Square 29.537 8 .000 Likelihood Ratio 30.445 8 .000 Linear-by-Linear 22.369 1 .000 Association N of Valid Cases 494 a. 2 cells (13.3%) have expected count less than 5. The minimum expected is 1.29. Symmetric Measures Value Approx. Sig. Nominal by Nominal Phi .245 .000
Measures of association for 2 nominal variables: Phi - for 2x2 tables Cramer’s V for tables (2x3, 3x3, etc.) Example 1 - Chi square test The contingency table and data analysis examines the relationship between general happiness and marital status of the respondents. Examples of possible survey questions are noted below. 1. What is your current marital status? ___1 Married ___2 Widowed ___3 Divorced ___4 Separated Never married 2. What is your current level of general happiness with life? ___ Very happy ___ Pretty happy ___ Not too happy SPSS Output of a Contingency Table and Test GENERAL HAPPINESS by MARITAL STATUS (N=494) MARITAL STATUS Total GENERAL HAPPINESS MARRIED WIDOWED DIVORCED SEPARATED NEVER MARRIED VERY HAPPY Count % within Marital Status Std. Residual 81 33.5% 3.1 8 16.3% -1.1 12 16.0% -1.4 1 9.1% -1.0 15 12.8% -2.4 117 23.7% PRETTY HAPPY Count % within Marital Status Std. Residual 143 59.1% -1.1 33 67.3% .2 52 69.3% .5 8 72.7% .3 83 70.9% .9 319 64.6% NOT TOO HAPPY Count % within Marital Status Std. Residual 18 7.4% -2.0 8 16.3% .9 11 14.7% .7 2 18.2% .6 19 16.2% 1.4 58 11.7% Total Count % 242 100.0% 49 100.0% 75 100.0% 11 100.0% 117 100.0% 494 100.0% Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square 29.537 8 .000 Likelihood Ratio 30.445 8 .000 Linear-by-Linear Association 22.369 1 .000 N of Valid Cases 494 a. 2 cells (13.3%) have expected count less than 5. The minimum expected is 1.29. Symmetric Measures Value Approx. Sig. Nominal by Nominal Phi .245 .000
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