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ANOVA and Multiple Comparisons in Statistical Analysis

Learn about Analysis of Variance (ANOVA) and multiple comparison procedures. Understand how to compare population means and identify significant differences. Explore technical conditions and examples in statistical analysis.

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ANOVA and Multiple Comparisons in Statistical Analysis

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  1. Stat 322 – Day 14 ANOVA and Multiple Comparisons

  2. Announcements • No Tuesday 12-1 office hour this week • HW 4 posted online, due Friday • Writing Assignment 4 posted with HW 4, due Monday • Tuesday 11-12 talk, Science North Room 201 • Cost-Sensitive Boosting: An Estimation Procedure when the Average is not the ‘Gold Standard’ • Brian Kriegler, UCLA • Writing Assignment….

  3. Previously • When want to compare several population means (or treatment means), can use Analysis of Variance • H0: m1 = … = mI • Ha: not all miequal • Compare variability in sample means, MSTr, to (pooled) variability within groups, MSE • F = MSTr/MSE with df I-1 and N-I • Is it large?

  4. Handicap Discrimination • Minitab • ANOVA table • MS = SS/df One-way ANOVA: SCORE versus HANDICAP Source DF SS MS F P HANDICAP 4 30.52 7.63 2.86 0.030 Error 65 173.32 2.67 Total 69 203.84

  5. Technical conditions • Normal populations • Normal probability plot for each sample • Equal variances in the populations • Largest SD / smallest SD < 2 • Independent observations • Random samples or randomized experiment

  6. Example 2: Chip melting • H0: mwhite = msemi-sweet = mbutterscotch • Ha: not all mi equal

  7. Demo – ANOVA applet

  8. Next Question: • If do reject H0, how can we decide which group means differ significantly from each other

  9. Multiple Comparison Procedures • How compare?

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