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SOCY 211 (69)
Carl Keane (12)
Lecture

SOCY211 Week 7, Lecture 1

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Department
Sociology
Course
SOCY 211
Professor
Carl Keane
Semester
Winter

Description
NOMINAL MEASURES OF ASSOCIATION FOR TABULAR DATA - Measures of association for nominal level variables will range from 0 to 1.0. - Measure near 0 suggests no association between the variables - Something close to 1.0 has a strong relationship/association - If you get an association of 0.30 or larger it is a strong association (for nominal level) - 0.11 up to 0.30 has a moderate degree of association between the two variables - Anything less than 0.10 is a weak association - Three most common ones for nominal level measurements: • Phi φ • Cramer’s V • Lambda λ - Phi is reported if the table has 2 rows and 2 columns, while V and Lambda can be used for tables of any size. - Phi and V are called:  Symmetric Measures of Association -Phi and V are based on the value of Chi-Square -Phi and V are based on the value of Chi-Square. So, if the chi-square value is statistically significant, so too will be Phi and V. - Phi and V have the same problems that you find with Chi Square χ² Phi = √ ---- N EXAMPLE (statistically significant) Gender and Crime Victimization Chi-Square Tests Value df Asymp. Sig. Exact Sig. Exact Sig. (1-sided) (2-sided) (2-sided) Pearson Chi- 12.792 1 .000 Square To compute Phi: 12.792 Phi = √-------- 1,520 Phi = √0.00842 Phi = 0.0917 (0.092) -Output that we get is given in a table You also get the level of significance 1 Gender and Victimization Symmetric Measures Value Approx. Sig. Nominal by Nominal Phi .092 .000 Cramer's V .092 .000 N of Valid Cases 1520 -Strength of the association between these two variables even if it is statistically significant is the same -This is because the formula for Cramer’s V is essentially the same -The formula for Cramer’s V is: χ² V = √ --------------------- (N) (min r-1, c-1) (min r-1, c-1) = the minimum value of the number of rows minus one, or the number of columns minus one So, in our case: 12.792 V = √ --------------------- (1520) (2 – 1 or 2 – 1) 12.792 V = √ -------------------- (1520) (1) V = 0.092 LAMBDA λ (Guttman’s Coefficient of Predictability)  Asymmetric Measure of Association -The value of Lambda will depend on which variable is independent and which is dependent -Also differs because Lambda is NOT Chi-square based -Doesn’t have the same limitations or problems -Referred to as: “Proportional Reduction in Error” (PRE) -For this, at first you predict something without knowing anything about the independent level -Then you are given information about the independent variable - If two variables are related your level of predictability should increase - Knowing the independent variable should reduce the number of errors 2 EXAMPLE: *Table is larger than two by two so we ignore Phi Gender and feelings of safety You walking alone at night in your area * Sex Crosstabulation Sex Total Male Female You Very safe? Count 422 154 576 walking alone at night in your area % within Sex 52.8% 21.4% 37.9% % of Total 27.8% 10.1% 37.9% reasonably Count 307 344 651 safe? % within Sex 38.4% 47.7% 42.8% % of Total 20.2% 22.6% 42.8% somewhat Count 40 119 159 unsafe? % within Sex 5.0% 16.5% 10.5% % of Total 2.6% 7.8% 10.5% very Count 20 41 61 unsafe? % within Sex 2.5% 5.7% 4.0% % of Total 1.3% 2.7% 4.0% does not Count 10
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