Transcript Measures of Association for contingency tables 4

Measures of Association for
contingency tables
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• Figure 8.2 : lambda – association; +-1:
strong; near 0: weak
• Positive association: as value of the
independent variable rises (falls), the
dependent variable rises (falls)
• Negative association: as value of the
independent variable falls (rises), the
dependent variable rises (falls)
Measures of Association for
nominal variables
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• lambda – a measure of association for use with
nominal variables, i.e. it is used whenever both of
the variables in a pair are nominal, or when one is
nominal and one is ordinal
• Lambda is a measure of association which reflects
the proportional reduction in error when values of
the independent variable are used to predict values
of the dependent variable.
• A value of 1 means that the independent variable
perfectly predicts the dependent variable, while a
value of 0 means that the independent variable is
no help in predicting the dependent variable
Lambda 
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• =(E1-E2)/(E1), where E1 is the number of errors
you would make guessing the dependent variable
if you did not know the independent variable, and
E2 the number of errors you would make guessing
the dependent variable if you knew the categories
of the independent variable.
• To find E1, subtract the largest row marginal total
from N
• To find E2, add up the highest frequencies of each
category of the independent variable and subtract
the sum from N
Lambda  (cont.)
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•  will always result in a positive number with
value between 0 and 1.
• If negative, something wrong
• Calculation: subtract the single highest row
marginal frequency for each category of the
independent variable and subtract each result from
N.
• Skills 2, p. 300 (using their table, p. 329, don’t
peek) [excel ch8sk2]
• Gen ex 2, p. 338
Lambda  (cont.)
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•  by SPSS ( p. 301)
• Reading the table:
• Symmetric value of : neither variable is
treated as independent—they are
“associated”, without a cause and effect
relationship
• Asymmetric value of : treats one as
independent in relation to the other
Other measures of Association
for nominal variables
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• Goodman and Kruskal’s tau - index of
strength of association
• Phi and Cramer’s V - Only used with
contingency tables of four or fewer cells
(each variable has only two categories)
• P 306, Skills 3
Other measures of Association
for nominal variables (cont)
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• Gamma – a measure like  that has a “proportional
reduction in error” interpretation
• Comparing the responses to questions by
individual respondents
• Concordant pairs: when performing bivariate
analysis of ordinal variables, a relationship in
which the values of the independent and
dependent variables are higher in one case than in
another, comparison case.
Other measures of Association
for nominal variables (cont)
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• Discordant pairs: when performing bivariate
analysis of ordinal variables, a relationship in
which the values of the independent variable is
higher in one case than in another, comparison
case, while the value of the dependent variable is
lower.
• =(C-D)/(C+D)), where C is the number of
concordant pairs and D the number of discordant
pairs
Other measures of Association
for nominal variables (cont)
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• Tied pairs: when performing bivariate analysis of
ordinal variables, a relationship in which the
values of the independent or dependent variable in
one case is identical to one of the corresponding
values in another, comparison case.
• Tied pairs do not factor in the computation of 
• Skills 4, p. 308
• Computation of : =(C-D)/(C+D))
• C=2,D=2  =0weak association
• P. 309-312 determining the nature of the pairs
Other measures of Association
for nominal variables (cont)
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Avoiding common pitfalls (p. 314)
THURS 6/20:
Hw/ Skills 6, 7 p. 315-16
p. 337/ 1,3,5
Hand in /p. 337/ #2, p. 341/#11 (do not do
the portion of 11 that deals with control
variables)
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