L9- Factorial Design

What is a factorial design?

A research design that involves more than one independent variable.

What are factors in a factorial design?

Multiple independent variables.

What is an example of a factor with three levels?

Time of day.

What is an example of a factor with two levels?

Drink type.

What type of factorial design is represented by two factors, one with two levels and one with three levels?

Two-way, 2 x 3 between-groups ANOVA.

What are the three F-values calculated in a factorial ANOVA?

Drink type (main effect), time of day (main effect), and drink type x time of day interaction.

What does H0 represent in factorial ANOVA?

The null hypothesis stating that means of different levels of factors are the same.

What does an interaction look like in a factorial design?

An interaction occurs when the effect of one factor depends on the level of another factor.

What is the total sum of squares (SST)?

The variability of all observations in the dataset, regardless of group assignment.

What does SSM represent in a factorial design?

The total variability explained by the experiment.

How is SSM calculated?

By subtracting the group mean from the grand mean, squaring it, multiplying by the number of participants, and summing across groups.

What does SSA represent?

Variability explained by the main effect of factor A.

What does SSB represent?

Variability explained by the main effect of factor B.

What is the formula for calculating mean squares in ANOVA?

Mean squares are calculated by dividing the sum of squares by the degrees of freedom.

What does a significant main effect indicate?

It indicates that there is a statistically significant difference in means across levels of a factor.

What is a simple main effects analysis?

An analysis comparing the effects of one independent variable at different levels of another independent variable.

What was the significant main effect found regarding drink type in the example?

Participants who drank water had lower exam scores than those who drank coffee.

What was the interaction effect found in the example?

There was a significant interaction between drink type and time of day on exam scores.

What does np2 represent in ANOVA results?

It represents the effect size, indicating the proportion of variance accounted for by the factor.

What is the purpose of conducting a simple main effects analysis?

To explore significant interactions by examining the effects of one factor at each level of another factor.

What does it mean if p > .05 in the context of simple main effects?

It indicates that there are no significant differences between the groups being compared.

What is the significance of the F-value in ANOVA?

The F-value is used to determine whether the observed variances between groups are significantly different.