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Measures of Association. Categorical Variables. Today we will discuss. Purpose of Measures of Association with Categorical Variables Different Measures of Association When to use How to calculate How to interpret The Different Measures of Association Lambda Yule’s Q

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measures of association

Measures of Association

Categorical Variables

today we will discuss
Today we will discuss
  • Purpose of Measures of Association with Categorical Variables
  • Different Measures of Association
    • When to use
    • How to calculate
    • How to interpret
  • The Different Measures of Association
    • Lambda
    • Yule’s Q
    • Goodman and Kruskal’s Gamma
    • Chi Square
purpose of measures
Purpose of Measures
  • To determine the strength and sometimes the direction of relationship between variables.
  • Choice of Measures May Depend on
    • Level of measurement
    • Number of categories in variables
    • What you want to know about the relationship between the variables
  • Used with nominal level variables
  • Based on Proportionate Reduction in Error (PRE)
    • How much error would be reduced in predicting the distribution of the DV, if knew the distribution of IV compared to error if have no knowledge about IV.
  • Interpreting Lambda
    • Ranges from 0-1
    • 0 means no reduction in error
    • 1 means totally reduce PRE if knew IV distribution
    • Most scores are in between range of 0-1, a .30 or better is a good association.
calculating lambda
Calculating Lambda
  • Information Needed
    • Number of errors knowing distribution of DV only
    • Number of fewer errors knowing the distribution of DV within categories of IV
  • To calculate
    • Lambda=item (2) above/ item (1) above
yule s q
Yule’s Q
  • Use in a 2x2 Table
  • Indicates strength and direction of association between variables
  • Interpreting Yule’s Q
    • Range for positive association (+0.01) to (+1.00)
    • Range for negative association (-0.01) to (-1.00)
    • A zero indicates no association
    • SEE Box on page 401 of Baker to Interpret in words
calculating yule s q
Calculating Yule’s Q

Arranging Categories of Tables

For Ordinal Variables arrange as follows:

Yule’s Q= ad-bc/ad+bc

goodman and kruskal s gamma
Goodman and Kruskal’s Gamma
  • Extension of Yule’s Q
  • Used when Table is larger than 2X2
  • Interpreted in the same manner
  • Especially useful with Ordinal Variables
  • Table set-up for ordinal variables
    • Extend the set up for Yule’s Q
      • Columns for IV should go from Hi to Lowest value
      • Rows with DV should go from Hi to lowest value
chi square
Chi Square
  • Use when variables are nominal or ordinal
  • Most commonly used test of significance
    • Tests of Independence
      • Chi square (2 ) measure if the relationship between the variables differs significantly from the model of independence or chance.
  • Interpretation of (2 )
    • The chances that the observed relationship between the variables would occur by chance.
    • Examine in combination with other measures of association to determine if relationship is statistically significant
    • Does not speak to direction of association or that one causes the other merely that the chances of observing such a value of (2 ) .
calculating chi square
Calculating Chi Square

Using the following table:

a expected frequencies =P1*n1 b expected frequencies =P2*n1

c expected frequencies =P1*n2 d expected frequencies =P2*n2

2 = (observed frequencies – expected frequencies)2

expected frequencies

significance of chi square
Significance of Chi Square
  • To determine probability that the value of 2 by chance must look it up in a chi square table (see p472 of Baker text)
  • Steps
    • Calculate 2
    • Calculate Degrees of Freedom for Table
      • DF = (r-1)(c-1)
    • Look up in Chi Square table to see the minimum value of 2 must achieve to assure less .05 probability that a chi square of the value you have occurred by chance.
using spss
Using SPSS
  • All of the measures of association we have discussed are calculated by SPSS
  • Using Frequencies Procedure
    • Go to Crosstab command
    • Check the box with statistics and click on all of the items you wish SPP to calculate