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Measures of Association: Nominal / Ordinal Variables

Measures of Association: Nominal / Ordinal Variables. 1- Lambda (  ) and Gamma (  ). Measures of Association: Lambda Impact of Religion on Abortion Attitudes. 167 people support Abortion for any reason 179 people oppose Abortion for any reason

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Measures of Association: Nominal / Ordinal Variables

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  1. Measures of Association: Nominal / Ordinal Variables 1- Lambda () and Gamma () CRJ 716 - Prof. Kaci

  2. Measures of Association: LambdaImpact of Religion on Abortion Attitudes • 167 people support Abortion for any reason • 179 people oppose Abortion for any reason • We would make less errors if we guessed “No” every time: • We would make 167 errors. ABANY Prot. Cathol. Jew None Other Total 68 38 Yes 41 12 167 8 76 71 No 9 179 2 21 144 109 Total 21 346 10 62 CRJ 716 - Prof. Kaci

  3. Measures of Association: LambdaImpact of Religion on Abortion Attitudes • If we knew each person’s religion we would improve our guess: ABANY Prot. Cathol. Jew None Other Total 68 38 Yes 41 12 167 8 76 71 No 9 179 2 21 144 109 Total 21 346 10 62 CRJ 716 - Prof. Kaci

  4. Measures of Association: LambdaImpact of Religion on Abortion Attitudes • 17.4% reduced error when religion is a known factor in guessing attitudes on Abortion for any reason. ABANY Prot. Cathol. Jew None Other Total 68 38 Yes 41 12 167 8 76 71 No 9 179 2 21 144 109 Total 21 346 10 62 CRJ 716 - Prof. Kaci

  5. Measures of Association: LambdaImpact of Religion on Abortion Attitudes CRJ 716 - Prof. Kaci

  6. Measures of Association: Gamma () CRJ 716 - Prof. Kaci

  7. Significance Tests: Nominal / Ordinal Variables • 2- Chi-square (X2) CRJ 716 - Prof. Kaci

  8. Measures of Association: Chi-squareImpact of Religion on Abortion Attitudes ABANY Prot. Cathol. Jew None Other Total 68 38 Yes 41 12 167 48.3% 8 76 71 No 9 179 51.7% 2 21 144 109 Total 21 346 10 62 CRJ 716 - Prof. Kaci

  9. Measures of Association: Chi-squareCalculating Chi-square ABANY Prot. Cathol. Jew None Other Total 68 38 Yes 41 12 167 48.3% 8 76 71 No 9 179 51.7% 2 21 109 Total 144 21 346 10 62 Expected: 144 * .483 70 53 5 30 10 74 56 5 11 32 144 * .517 CRJ 716 - Prof. Kaci

  10. Measures of Association: Chi-square Calculating Chi-square ABANY Prot. Cathol. Jew None Other Total 68 38 Yes 41 12 167 48.3% 8 76 71 No 9 179 51.7% 2 21 109 Total 144 21 346 10 62 70 53 5 Expected: 30 10 74 56 5 11 32 Difference between: Observed - Expected -2 -15 3 11 2 2 15 -3 -2 -11 CRJ 716 - Prof. Kaci

  11. Measures of Association: Chi-square Calculating Chi-square ABANY Prot. Cathol. Jew None Other Total Expected: 70 53 5 30 10 74 56 5 11 32 Difference between: Observed - Expected -2 -15 3 11 2 2 15 -3 -2 -11 Square the difference and divide by the EXPECTED values (-2)2 / 70 0.06 4.25 1.8 4.03 0.4 0.05 4.02 1.8 0.36 3.78 22 / 74 CRJ 716 - Prof. Kaci

  12. Measures of Association: Chi-square Calculating Chi-square Add these values up. The sum is the Chi-square value. 0.06 4.25 1.8 4.03 0.4 0.05 4.02 1.8 0.36 3.78 CRJ 716 - Prof. Kaci

  13. Measures of Association: Chi-square Calculating Chi-square • Degrees of Freedom • DF = (row - 1) * (column - 1) = • = (2-1) * (5-1) • = 1 * 4 • df = 4 CRJ 716 - Prof. Kaci

  14. Measures of Association: Chi-squareChi-square Formula • Where: • X2  Chi-square • O  Observed Values • E  Expected Values under Ho CRJ 716 - Prof. Kaci

  15. Questions??? CRJ 716 - Prof. Kaci

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