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Measures of Association

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Measures of Association

Categorical Variables

- 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

- 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.

- 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

- 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

Arranging Categories of Tables

For Ordinal Variables arrange as follows:

Yule’s Q= ad-bc/ad+bc

- 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

- Extend the set up for Yule’s Q

- 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.

- Tests of Independence
- 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 ) .

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

- 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.

- 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