Week 8: Analysis of Variance (ANOVA) Concepts

What is the purpose of ANOVA?

To compare means across three or more groups.

What is One-Way ANOVA used for?

When groups are defined by a single variable.

What is the test statistic in One-Way ANOVA based on?

Sum of Squares (SS).

What does Between Groups Sum of Squares (SSb) measure?

How different group means are from one another.

What are the degrees of freedom for Between Groups SS (SSb)?

G - 1, where G is the number of groups.

What does Within Groups Sum of Squares (SSw) measure?

How much individuals within a group differ from their group mean.

What are the degrees of freedom for Within Groups SS (SSw)?

N - G, where N is total observations.

How is total variability calculated in ANOVA?

SStot = SSb + SSw.

What does the F-Statistic represent in ANOVA?

The ratio of between-group variance to within-group variance.

What does a large F imply in ANOVA?

Group means are highly different compared to within-group variability.

What should be included in the write-up of ANOVA results?

Report means and SDs for each group, followed by the F-statistic F(df_between, df_within) = value, p = value.

What function is used in R to calculate SS values in One-Way ANOVA?

aov() function.

What is the purpose of the summary() function in R for ANOVA?

It runs hypothesis tests on the aov object.

How is Effect Size (Eta-Squared, η²) calculated in ANOVA?

Calculated as SSb / SStot.

What does Eta-Squared represent?

The proportion of total variance attributable to the grouping variable.

What is the Bonferroni Correction used for?

To adjust p-values when running multiple comparisons.

How does the Holm Correction differ from the Bonferroni Correction?

It is superior to Bonferroni with a lower Type II error risk.

What test can be used if the residuals are not normally distributed?

Kruskal-Wallis Test.

What is the purpose of Levene's Test in ANOVA?

To check for homogeneity of variance across all groups.

What should be done if the assumption of independence is violated in ANOVA?

Ensure that observations are independent.

What is Two-Way ANOVA used for?

When there is more than one grouping variable (factor).

What does Two-Way ANOVA calculate?

SSb for each factor and for their interaction.

What is an interaction in the context of Two-Way ANOVA?

When the effect of one factor depends on the level of another factor.

How is the effect size calculated in Two-Way ANOVA in R?

Using the EtaSquared() function.