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Chi-square Procedures

Chi-square Procedures. Chi-square formula. Observed is score we get Expected we would get if there w ere no differences. Chi-square formula. Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: At the Level of Significance we set.

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Chi-square Procedures

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  1. Chi-squareProcedures

  2. Chi-square formula Observed is score we get Expected we would get if there were no differences.

  3. Chi-square formula Once we have found the Chi square value, then we need to go to a Chi-square table of numbers for: • At the Level of Significance we set. • Chi-square value Critical (or cut-off) value we must exceed

  4. The Bungee Cord Jumping Dilemma Director of recreation program wonders if there would be enough takers among his members to warrant a Bungee Cord Jumping program He can ask all his customers. But what if 35 / 100 say yes. How will he decide if that’s a significant number. He decides to set up his inquiry as a scientific study, and so has a hypothetical question – There is not a significant difference between the yes and the nos. This is a null hypothesis, he assumes nothing. His study will look something like this.

  5. Next Step Determine the Chi-square statistic from the data

  6. Chi-square calculationsOur Chi-square value

  7. O- E O-E squared YES -30 900 NO 30 900 YES -30 900 900/50 = 18 NO 30 900 900/50 = 18

  8. Chi-square calculations

  9. Our Calculations • Significance level was 0.5 • Critical value at 0.5 is 3.85 • Our Chi-square value is 36 • This exceeds the critical value at the 0.5 level • We reject the null that there is no difference between the YES and NOs

  10. Different Forms of Table Two types = One – way or Two –way One –way = One Column or Row (df = C – 1)

  11. One-way calculations N= 50 O – E E 7-10 8-10- 10-10 10-10 10-10 10 10 10 10 10 940025 .9 + .4 + 0 + 0 +25 3.8 10 10 10 10 10 No significant differences df = 5 - 1 = 4 Chi critical value = 9.49

  12. Two-way table How do we find the expected? Col + Row Margin Grand Total Nat/won = (60x45) / 80 = 33.75 Nat/lost = (20 x 45) / 80 = 11.25 Art /won = (60 x 35) / 80 = 26.25 Art/ lost = (20 x 35 ) / 80 = 8.75

  13. Two-way cont Nat/won = (60x45) / 80 = 33.75 Nat/lost = (20 x 45) / 80 = 11.25 Art /won = (60 x 35) / 80 = 26.25 Art/ lost = (20 x 35 ) / 80 = 8.75

  14. Two-way cont How we get df? (C-1)(R-1) (2 -1)(2 – 1) = 1 Critical value at 0.05, 1 df = 3.84 Our Chi = 7.47 There is a significant differences between surfaces

  15. Homework One-way calculations N= 50 (O – E) 2 E 15- 4025-40 57-40 66-40 37-40 40 40 40 40 40 6252252896769 40 40 40 40 40 45.6 df = 5 - 1 = 4 Chi critical value = 9.49 Reject Null There are significant differences

  16. Two-way table Col + Row Margin Grand Total YES - 80 x 133 / 240 = 44.34 NO - 80 x 107 / 240 = 35.67 Df = ? Df = (c-1)(r-1) = (2-1)(3-1)= 1 x 2 = 2

  17. Chi value = (O – E) 2 E • YES 45 - 44.34 /44.34 = (O. 66)2/44.34 = 0.01 56 - 44.34 /44.34 = 3.07 32 - 44.34 /44.34 =3.43 • NO 35 - 35.67 / 35.67 = -(0.67)2/35.67 = 0.013 24 - 35.67 / 35.67 = 3.8 48 – 35.67 / 35.67 = 4.26 Sum all= 14.6 Critical value = 5.99 Reject Null

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