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2-Way ANOVA

2-Way ANOVA. Learning Objectives. Compute 2-Way ANOVA by hand Calculate sums of squares for main effects and interaction Complete ANOVA source table Correctly interpret results Compute 2-Way ANOVA using SPSS Correctly interpret output. ANOVA Partitions Variance.

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2-Way ANOVA

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  1. 2-Way ANOVA

  2. Learning Objectives • Compute 2-Way ANOVA by hand • Calculate sums of squares for main effects and interaction • Complete ANOVA source table • Correctly interpret results • Compute 2-Way ANOVA using SPSS • Correctly interpret output

  3. ANOVA Partitions Variance • Total variance is divided into • Within groups – individual differences, nuisance variance, error • Between groups – treatment effects & random error • With 2-Way ANOVA, you have 2 IVs instead of 1. Variance between groups is partitioned into 2 Main Effects and an Interaction.

  4. ANOVA Significance Test • ANOVA with 1 IV has 1 F test • ANOVA with multiple IVs has multiple F tests, one for each Main Effect and one for each Interaction. • With 2-Way ANOVA, there are two main effects and 1 interaction, so there are 3 F tests. All, some, or none may be significant. Critical values change depending on df for denominator.

  5. Example 1: 2 kinds of Therapies • Treatment of panic attacks. • IV1: psychotherapy. 3 levels: conventional, experimental, and control (wait list). • IV2: Anti-anxiety drug. 2 levels: drug vs. control. • DV is number of panic attacks during 1 week after 6 wks therapy. • See handout for data. Work thru example.

  6. Example 2: Types of training • Military electronic troubleshooters fix radar, missile guidance systems, etc. • Standard training is experience with common problems. • New training. • on top of standard training. • IV1: Theory of electronics (new module). • IV2: Practice of troubleshooting (new module). • Work thru handout.

  7. SPSS • Download file. • Run SPSS & match to hand computations. • Produce a graph of the cell means.

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