Advanced ANOVA/One-way ANOVA

This tutorial teaches use of one-way ANOVA, a statistical technique for testing mean differences betweeen three or more independent groups on a single dependent variable. Practical exercises are based on using SPSS.

Purpose

 * Assesses the statistical significance of differences between three or more group means for a single dependent variable
 * Extension of a t-test
 * Use one-way ANOVA in preference to multiple pairwise comparisons (t-tests) because:
 * Computationally easier
 * Limits the probability of type I and type II errors.
 * With multiple comparisons, if they are all independent (which is unlikley) in a series of 100 tests we would expect to get five Type I errors with a .05 level of significance
 * By simultaneously computing all possible comparisons in a single significance test, the ANOVA avoids these inflated error rates
 * However, use of one-way ANOVA limits error rates at the expense of specificity - statistic tells us that there is a significant difference somewhere among the sample means, but does not tell us which means differ significantly (have to use post-hoc and a priori comparison procedures)

Examples

 * Experimental study: Examine reaction time under different levels of alcohol consumption by randomly assigning participants to four conditions (none, low, medium, and high alcohol)
 * Quasi-experimental study: Examine whether students with behaviour problems behave better in classrooms where teachers have a humanistic philosophy and have control of their classrooms. Classify teachers as (1) humanists with control, (2) strict disciplinarians, and (3) laissez-faire.

General steps

 * 1) Establish hypothesis/hypotheses
 * 2) Examine assumptions - If assumptions are not met, use the Kruskal-Wallis non-parametric procedure
 * 3) Examine descriptive statistics, particularly the four moments (M, SD, Skewness, Kurtosis) overall, and also for each group
 * 4) Examine graphs, e.g.,:
 * 5) * Histograms
 * 6) * Normal probability plot
 * 7) * Error-bar graph
 * 8) Conduct inferential test (ANOVA) and interpret significance of F
 * 9) Conduct follow-up tests (planned contrasts or post-hoc tests) if F is significant
 * 10) Calculate and interpret effect sizes
 * 11) * Eta-square (omnibus - equivalent to R2)
 * 12) * Standardised mean effect size (difference b/w two means) - e.g., Cohen's d

Visual ANOVA

 * 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

Error bar graphs

 * 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?

Data

 * 1) AQUES.sav
 * 2) Motiv.sav