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Six Easy Steps for an ANOVA

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  1. Six Easy Steps for an ANOVA • 1) State the hypothesis • 2) Find the F-critical value • 3) Calculate the F-value • 4) Decision • 5) Create the summary table • 6) Put answer into words

  2. Example • Want to examine the effects of feedback on self-esteem. Three different conditions -- each have five subjects • 1) Positive feedback • 2) Negative feedback • 3) Control • Afterward all complete a measure of self-esteem that can range from 0 to 10.

  3. Example: • Question: Is the type of feedback a person receives significantly (.05) related their self-esteem?

  4. Results

  5. Step 1: State the Hypothesis • H1: The three population means are not all equal • H0: pos = neg =cont

  6. Step 2: Find F-Critical • Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = k - 1 (k = number of groups) • dfwithin = N - k (N = total number of observations) • dftotal = N - 1 • Check yourself • dftotal = Dfbetween + dfwithin

  7. Step 2: Find F-Critical • Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = 2 (k = number of groups) • dfwithin = 12 (N = total number of observations) • dftotal = 14 • Check yourself • 14 = 2 + 12

  8. Step 2: Find F-Critical • Step 2.2 • Look up F-critical using table F on pages 370 - 373. • F (2,12) = 3.88

  9. Step 3: Calculate the F-value • Has 4 Sub-Steps • 3.1) Calculate the needed ingredients • 3.2) Calculate the SS • 3.3) Calculate the MS • 3.4) Calculate the F-value

  10. Step 3.1: Ingredients • X • X2 • Tj2 • N • n

  11. Step 3.1: Ingredients

  12. X X = 85 Xp = 40 Xn = 25 Xc = 20

  13. X2 X = 85 X2 = 555 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330

  14. T2 = (X)2 for each group X = 85 X2 = 555 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600

  15. Tj2 X = 85 X2 = 555 Tj2= 2625 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600

  16. N X = 85 X2 = 555 Tj2= 2625 N = 15 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600

  17. n X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Xp = 40 Xn = 25 Xc = 20 X2n = 135 X2c = 90 X2p = 330 T2n = 625 T2c = 400 T2p = 1600

  18. X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SStotal

  19. X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SStotal 85 73.33 555 15

  20. X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin

  21. X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin 2625 30 555 5

  22. X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSBetween

  23. X = 85 X2 = 555 Tj2= 2625 N = 15 n = 5 Step 3.2: Calculate SS • SSBetween 43.33 2625 85 5 15

  24. Step 3.2: Calculate SS • Check! • SStotal = SSBetween + SSWithin

  25. Step 3.2: Calculate SS • Check! • 73.33 = 43.33 + 30

  26. Step 3.3: Calculate MS

  27. Step 3.3: Calculate MS 43.33 21.67 2

  28. Calculating this Variance Ratio

  29. Step 3.3: Calculate MS 30 2.5 12

  30. Step 3.4: Calculate the F value

  31. Step 3.4: Calculate the F value 21.67 8.67 2.5

  32. Step 4: Decision • If F value > than F critical • Reject H0, and accept H1 • If F value < or = to F critical • Fail to reject H0

  33. Step 4: Decision • If F value > than F critical • Reject H0, and accept H1 • If F value < or = to F critical • Fail to reject H0 F value = 8.67 F crit = 3.88

  34. Step 5: Create the Summary Table

  35. Step 6: Put answer into words • Question: Is the type of feedback a person receives significantly (.05) related their self-esteem? • H1: The three population means are not all equal • The type of feedback a person receives is related to their self-esteem

  36. SPSS

  37. Practice • You are interested in comparing the performance of three models of cars. Random samples of five owners of each car were used. These owners were asked how many times their car had undergone major repairs in the last 2 years.

  38. Results

  39. Practice • Is there a significant (.05) relationship between the model of car and repair records?

  40. Step 1: State the Hypothesis • H1: The three population means are not all equal • H0: V = F =G

  41. Step 2: Find F-Critical • Step 2.1 • Need to first find dfbetween and dfwithin • Dfbetween = 2 (k = number of groups) • dfwithin = 12 (N = total number of observations) • dftotal = 14 • Check yourself • 14 = 2 + 12

  42. Step 2: Find F-Critical • Step 2.2 • Look up F-critical using table F on pages 370 - 373. • F (2,12) = 3.88

  43. Step 3.1: Ingredients • X = 60 • X2 = 304 • Tj2 = 1400 • N = 15 • n = 5

  44. X = 60 X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SStotal

  45. X = 60 X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SStotal 60 64 304 15

  46. X = 60 X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin

  47. X = 60 X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SSWithin 1400 24 304 5

  48. X = 60 X2 = 304 Tj2= 1400 N = 15 n = 5 Step 3.2: Calculate SS • SSBetween