Measures of Association

1. Measures of Association Categorical Variables

2. 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

3. 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

4. Lambda • 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.

5. 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

6. 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

7. Calculating Yule’s Q Arranging Categories of Tables For Ordinal Variables arrange as follows: Yule’s Q= ad-bc/ad+bc

8. 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

9. 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 ) .

10. 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

11. 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.

12. 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