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Comparing Several Means: One-way ANOVA

Comparing Several Means: One-way ANOVA. Lesson 15. Analysis of Variance. or ANOVA Comparing 2 or more treatments i.e., groups Simultaneously H 0 : m 1 = m 2 = m 3 … H 1 : at least one population different from others ~. Experimentwise Error. Why can’t we just use t tests?

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Comparing Several Means: One-way ANOVA

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  1. Comparing Several Means:One-way ANOVA Lesson 15

  2. Analysis of Variance • or ANOVA • Comparing 2 or more treatments • i.e., groups • Simultaneously • H0: m1 = m2 = m3 … • H1: at least one population different from others ~

  3. Experimentwise Error • Why can’t we just use t tests? • Type 1 error: incorrectly rejecting H0 • each comparison a = .05 • Experimentwise probability of type 1 error • P (1 or more Type 1 errors) ~

  4. Experimentwise Error • H0: m1 = m2 = m3 • Approximate experimentwise error • H0: m1 = m2 a = .05 • H0: m1 = m3 a = .05 • H0: m2 = m3 a = .05 experimentwise a » .15 • ANOVA: only one H0 • a = .05 (or level you select) ~

  5. Analysis of Variance: Terminology • Factor • independent variable • Single-Factor Design (One-way) • single independent variable with 2 or more levels • levels: values of independent variable ~

  6. Analysis of Variance: Terminology • Repeated Measures ANOVA • Same logic as paired t test • Factorial Design • More than one independent variable • Life is complex: interactions • Mixed Factorial Design • At least 1 between-groups & within groups variable • Focus on independent-measures ~

  7. Caffeine dose Single-factor design 0 mg 50 mg 100 mg with 3 levels 3 x 2 Factorial design 0 mg 50 mg 100 mg male Sex female e.g., Effects of caffeine on reaction time

  8. Test Statistic • F ratio • ratio of 2 variances • same concept as t tests • F = t2 • Only 2 groups ~

  9. F ratio • MS: mean squared deviations = variance • MSB = MS between treatments • Textbook: MSM • Average distance b/n sample means • MSW = MS within treatments • Textbook: MSR • differences between individuals • same as s2pooled ~

  10. Logic of ANOVA • Differences b/n groups (means) bigger than difference between individuals? • If H0 false • then distance between groups should be larger ~

  11. Partitioning SS • SST = total sums of squares • total variability • SSB = between-treatments sums of squares • variability between groups • SSW = within-treatments sums of squares • variability between individuals * % variance explained by IV

  12. Calculating SS

  13. Calculating MS

  14. Calculating MSW • Same as s2pooledfor > 2 samples

  15. Calculating MSB

  16. SPSS One-way ANOVA • Menu • Analyze • Compare Means • One-way ANOVA • Dialog box • Dependent List (DV) • Factor (IV) • Options: • Descriptives, Homogeneity of Variance • Post Hoc ~

  17. Interpreting ANOVA • RejectH0 • at least one sample different from others • do not know which one(s) • Must use post hoc tests • Post hoc: after the fact • ONLY if rejected H0 forANOVA • Many post hoc tests • Differ on how conservative ~

  18. Post Hoc Test: Pairwise comparisons • Adjusted a levels • LSD (Least Significant Difference) • Basically t-test, no adjustment • Tukey’s HSD • Similar logic to t – test • Scheffe Test • F test with only 2 groups • Differ on how conservative • More conservative  bigger difference required ~

  19. Detour Learning Task • Prenatal exposure to methamphetamine • effects on learning?

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