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Sociology
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SOCY 211
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Carl Keane
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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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