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1. ANOVA EDL 714, Fall 2010

2. Analysis of variance • ANOVA • An omninbus procedure that performs the same task as running multiple t-tests between all groups in question. • Tests the null hypothesis in comparing means of two or more treatments (or populations) • Looking for systematic treatment effects

3. Two forms of variability • Between-treatments (groups) • Variability in scores/measures due to general differences between treatment conditions • Treatment effect, individual differences, experimental error • Within-treatments (groups) • Variability in scores/measures not associated with treatment • Individual differences, experimental error

4. Total variability • Is represented by accounting for both between and within group variability. • This is what an ANOVA is designed to do. • This reduces the risk of a Type I error over simply using multiple t-tests.

5. One-way ANOVA • Analyzes the effect of a single factor on between-group variability. • In ANOVA language, the independent variable is referred to as a factor. Hence, some researchers may use terms like Factor Analysis or Factorial Design when discussing ANOVA procedures. • A factor will have levels along which it varies.

6. One-way ANOVA in SPSS • Analyze • Compare Means • One-way ANOVA • In your output look for the Significance value (Sig.) just like you would on a t-test, and interpret the same way. • We will again use a .05 p value as our criteria for significance. • Note that in the ANOVA output box you will see a break-down of between group and within group variance.

7. Other forms of ANOVA • Two and Three-way ANOVAs • Multiple factors as opposed to one • Repeated Measures • Comparing means of the same samples over time • Analysis of Covariance (ANCOVA) • Multivariate Analysis of Variance (MANOVA)