Measuring Strength of Association

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Measuring Strength of Association

• Or, Relationships Revisited

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What We Are Looking For Covariation

• When two variables change (vary) with regards to
  each other in a predictable manner, they are said
  to co-vary
• Is also called association, and correlation
• Important properties
• Direction
• Strength

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Two Directions

• Positive or direct
• As one grows larger, the other grows larger
• Negative or Inverse
• As one grows larger, the other grows smaller
• None
• No predictable change

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Strength

• Some associations are quite pronounced
• Some are relatively weak

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Identifying Measuring Associations

• By using tables
• Crosstabulations
• Elaboration tables
• By using summary statistics

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Analyzing Tables

• 5 or greater difference(s) across cells
• Is a rule of thumb
• Is easy to apply with small tables (2 x 2)
• Is harder to assess as tables grow larger, and
• Sometimes tables are cumbersome

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Summary Measures of Association

• Single numbers
• Summarize strength of association

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Summary Association Measures

• There are many available in MicroCase
• Which to use depends upon
• Level of measure
• Technical considerations (number of rows
  columns, etc)

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Interpreting Measures of Association

• Direction by sign
• Range from -1.0 to 1.0 (no negatives for
  nominal association measures)
• Closer to 1.0 implies stronger association
• Closer to 0.0 implies weaker association
• See LeRoy, Tables 10.1 10.2 (pg. 194) White,
  pgs. 326 327 for additional information

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Nominal Measures

• Yules Q (not in MicroCase)
• Chi-squared based measures
• Contingency Coefficient (square tables)
• Cramers V (rectangular tables)
• Phi (2 x 2) tables
• Proportional reduction in error (PRE) measures
• lambda

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Ordinal Measures (All PRE)

• Gamma
• Somers D
• Kendalls Tau
• Taub is for square tables
• Tauc is for rectangular tables
• Can use PRE interpretation for all

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Which One To Use?

• Be consistent
• Be aware of the implications of level of
  measurement
• Check LeRoy, Table 10.2 (pg. 194) and White, pg.
  325

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Interpreting Summary Association

• Again, see LeRoy, Table 10.1 (pg. 194)
• Weak .10 - .19
• Moderate .20 - .29
• Strong .30

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Presenting Summary Association Measures

• If using with crosstabulations, present at the
  bottom of the relevant table
• See Statistical Tables lecture slides, or
• Check this
• If there are a large number of associations to be
  discussed, can present just the summary measures
  in a table by themselves

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Summary Association Nominal Measures
Two by two tables
Yules Q
Q ad - bc / ad bc
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