Archive:Advanced ANOVA/One-way ANOVA

Resource type: this resource contains a tutorial or tutorial notes.

Template:50%done This tutorial focuses on one-way ANOVA - testing mean differences between more than two independent groups.

Introduction

Establish hypothesis/hypotheses
- Make these as explicit and clear as possible
- Break complicated hypotheses down into sub-hypotheses
- Each hypothesis should be able to be answered as "yes" or "no"
- It should be clear from the hypotheses what the predicted relation is between an IV and a DV
Identify IV (categorical; between-subjects) and DV (at least interval)
Examine assumptions:
- The data in each cell is normally distributed
- Homogeneity of variance (the variance in each cell is similar)
- Cells are independent
Examine descriptive statistics, particularly the four moments (M, SD, Skewness, Kurtosis) overall, and also for each group
Examine graphs, e.g.,:
- Histograms
- Normal probability plot
- Error-bar graph
Conduct inferential test (ANOVA) and interpret significance of F
Conduct follow-up tests (planned contrasts or post-hoc tests) if F is significant
Calculate and interpret effect sizes
- Eta-square (omnibus - equivalent to R²)
- Standardised mean effect size (difference b/w two means)

Understanding ANOVA Visually (may require viewing with Internet Explorer)
Under what conditions would F be the smallest?
Under what conditions would F be the largest?
Now explore the same ideas with this more advanced Visualisation Tool for One-way and Two-way ANOVA Applet

Use any dataset
Conduct a one-way ANOVA and graphically present the means and confidence intervals using an Error Bar Graph - is this error bar chart consistent with the statistical results? Why? Why not?