Measures of Association Two Variables

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Measures of Association Two Variables

• Session 33

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Aspects of Association

• Strength
• Direction

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Strength
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Strength

• Perfect Relationship values of the independent
  variable perfectly predict values of the
  dependent variable
• Weak Relationship little difference in values
  of the dependent variable across values of the
  independent variable
• No Relationship distribution of cases is the
  same across the values of the independent variable

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Direction

• When variables are ordinal or interval
• positive high values on one variable are
  associated with high values on the other
• negative high values on one variable are
  associated with low values on the other

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Measures of Association

• Nominal
• Lambda
• Ewithout Ewith
• Ewithout
• PRE proportional reduction in error
• Proportion in errors in prediction provided by
  knowledge of the independent variable.

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• Whats your educated guess about how voters voted
  based on marginal totals?

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• whites 600 x .5 300
• blacks 300 x .67 201
• hispanics 50 x .25 25
• asians 50 x .5 25
• 300 99 25 25

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• Ewithout 590
• Ewith 449
• 590 449/590 .24
• Errors in prediction are reduced by 24

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Measures of Association

• Ordinal Level
• Kendalls tau b
• Kendalls tau c
• Somers d
• Goodman and Kruskals gamma

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• Components of the formula
• concordant pairs
• discordant pairs
• tied pairs
• Range for results
• 1 to 1

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Formulas

• P number of concordant pairs
• Q number of discordant pairs
• T1 number of ties on row variables
• T2 number of ties on column variables
• m the smaller of the number of rows and columns
• n the number of cases

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Formulas

• tau b P Q/sq rt (P Q T2)(P Q T1)
• tau c P Q/1 / 2(n)2 (m 1)/m
• somers d P Q/P Q T1
• gamma P Q/P Q

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Education and Interest
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Education and Interest
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• P 60(1008050100)
• 30(50100)50(80100)100(100)
• 43,3000