# Advanced ANOVA/One-way ANOVA

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This tutorial teaches use of |

## Purpose[edit]

- 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)

- Use one-way ANOVA in preference to multiple pairwise comparisons (

## Examples[edit]

- 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[edit]

- Establish hypothesis/hypotheses
- Examine assumptions - If assumptions are not met, use the Kruskal-Wallis non-parametric procedure
- 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
*R*^{2}) - Standardised mean effect size (difference b/w two means) - e.g., Cohen's
*d*

- Eta-square (omnibus - equivalent to

## Visual ANOVA[edit]

- 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[edit]

- 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[edit]

## See also[edit]

## External links[edit]

- ANOVA (ucspace)