Awesome Analysis of Variance (ANOVA)

What if you have more than two groups in your experiment

• Could solve using multiple t-test, but probability of Type 1 error increases

• Analysis of Variance (ANOVA) allows for multiple comparisons and protects against Type 1 error

ANOVA

Analysis of Variance (ANOVA)

• Tests for differences in the means of several groups

One-way, between-subjects ANOVA

• “One-way” because only one IV

• “Between-subjects” because participants in only one condition

                                            ← Signal

$f=\frac{variancebetweengroups}{variancewi\operatorname{th}ingroups}$

                                            ← Noise

Variability between groups = MSbetween

Variability within groups = MSwithin

Hypothesis

Null Hypothesis

• ANOVA tests the null hypothesis: means of all groups are the same (like the t-test)

Research Hypothesis

• The means differ

Anova is an omnibus test

• Tests for an overall difference

• Tells us if group means are different

• Doesn’t tell exactly which means differ

Between-Groups Variability

The amount of variability explained by being in a specific group

We want MORE variability, we want what we did to matter

$df$ between = (groups - 1)

Within-Groups Variability

Average of variances in each of the conditions (noise)

Variability of each group INSIDE of the group

$df$ within = (N - groups)