Measures of Association for contingency tables 4

1
Measures of Association for contingency tables
4

• 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)

2
Measures of Association for nominal variables
4

• 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

3
Lambda ? 3

• ?(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

4
Lambda ? (cont.) 4

• ? 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,
  dont peek) excel ch8sk2
• Gen ex 2, p. 338

5
Lambda ? (cont.) 4

• ? by SPSS ( p. 301)
• Reading the table
• Symmetric value of ? neither variable is treated
  as independentthey are associated, without a
  cause and effect relationship
• Asymmetric value of ? treats one as independent
  in relation to the other

6
Other measures of Association for nominal
variables 3

• Goodman and Kruskals tau - index of strength of
  association
• Phi and Cramers V - Only used with contingency
  tables of four or fewer cells (each variable has
  only two categories)
• P 306, Skills 3

7
Other measures of Association for nominal
variables (cont) 3

• 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.

8
Other measures of Association for nominal
variables (cont) 2

• 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)/(CD)), where C is the number of
  concordant pairs and D the number of discordant
  pairs

9
Other measures of Association for nominal
variables (cont) 6

• 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)/(CD))
• C2,D2 ? ?0?weak association
• P. 309-312 determining the nature of the pairs

10
Other measures of Association for nominal
variables (cont) 5

• 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)