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One-Way Analysis of Variance (ANOVA)

One-Way Analysis of Variance (ANOVA). 2011, 12, 1. ANOVA : Compare 3 or More Groups. When we wanted to compare differences between two independent groups, we used an independent groups t-test However, if we have 3 or more groups the technique we use is called analysis of variance (ANOVA)

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One-Way Analysis of Variance (ANOVA)

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  1. One-Way Analysis of Variance (ANOVA) 2011, 12, 1

  2. ANOVA : Compare 3 or More Groups • When we wanted to compare differences between two independent groups, we used an independent groups t-test • However, if we have 3 or more groups the technique we use is called analysis of variance (ANOVA) • E.g., class standing has 4 levels: Freshman, Sophomore, Junior, Senior • Instead of a t-obs, we calculate an F-obs

  3. Pain Relief Experiment • Aspirin, Tylenol, and a Herb were tested to see how much pain relief each provides. Pain relief was rated on a five-point scale. • The differences between our three samples vs.the differences within each single sample. • If variance-between > variance within, we know that Aspirin, Tylenol, and Herb have different pain-reducing effects.

  4. Step 1: Form Hypotheses • H0 : • H1 :

  5. Step 2: Set Decision Criteria • = 0.05 • dfb = • dfw = • fcrit =

  6. Step 3: Compute F

  7. Y = Compute SSB and MSB (numerator) MSB =

  8. Compute SSW and MSw (Denominator) MSW =

  9. Step 4: Create ANOVA Source Table SST = SSB+SSW = F = MSB/MSW =

  10. The distribution of F-ratios with df = 2, 10 • Step 5: Compare Fobs to Fcrit. 1 2 3 4 5 6 7 4.10 7.56

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