Relationships Among Several Variables Multivariate Analysis

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Relationships Among Several Variables
Multivariate Analysis

• Session 16

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Statistical Significance

• chi-square a measure of statistical
  significance for nominal and ordinal level
  measures of association

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Gender and Nuclear Power Plants
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Expected Frequencies

• Cell a (300)(400)/1000 120
• Cell b (300)(400)/1000 120
• Cell c (400)(400)/1000 160
• Cell d (300)(600)/1000 180
• Cell e (300)(600)/1000 180
• Cell f (400)(600)/1000 240

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Gender and Nuclear Power Plants
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• E expected
• O observed

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• Sum is 131.94
• degrees of freedom are (C-1)(R-1) or 2 in this
  case
• criterion value is 9.21 for df 2
• (p. 261 and Table A.4 in your text)

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A Note About Sample Size
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A Note About Sample Size
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Correlation

• r sq rt 1 unexplained variance
• total variance
• Also ranges from 1 to 1
• Relationship must be linear

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• r NSXY (SX)(SY)
• sq rt NSX2S (SX)2 NSY2 (SY)2
• Example the relationship between justices
  ideology and decisions on civil liberties cases
• correlation matrix

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Regression Analysis Example Contacts with Public
Officials
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The Regression Model

• Scatter plot
• The model Y a ßX e
• Regression coefficient ß
• b gt 0
• b lt 0
• b 0

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• Residual
• Observed Value Predicted Value Error
• Predicted and Observed Values of Y
• Yi observed
• Y predicted
• YM mean

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Interpretation of Parameters

• Y-intercept
• Slope