Factorial Design in Experiments

Study Notes

Involves an experiment with multiple independent variables (IVs), typically 2 to 4
Each IV has multiple levels
Factorial notation describes the number of IVs and their levels
Example: 3 x 5 factorial design has two IVs, one with 3 levels and the other with 5 levels.
Number of conditions to be compared is equal to the product of the levels of each IV
Example: 2 x 4 factorial design has 8 conditions (2 x 4 = 8).
In factorial designs, "levels" and "conditions" refer to distinct concepts.

Inferential statistics are used to analyze factorial designs
Main effects refer to the influence of one IV, independent of other IVs
Number of main effects equals the number of IVs
To determine a main effect, data from different levels of other IVs is collapsed (combined).
Interaction effects occur when the effect of one IV depends on the level of another IV
Example: Grades in Science might be higher than Humanities in a lab setting, but lower in a lecture setting.
Interaction effects take priority over main effects and provide more detailed insights
Line graphs are used to visualize factorial data, with each line representing a level of one IV
Non-parallel lines indicate interaction effects.
Data within the matrix of conditions (cells) shows main and interaction effects
Inferential statistics are needed to confirm if effects are statistically significant
Example: A study with imagery vs. control and 2 vs. 4 seconds presentation rate might show main effects for both recall strategy and presentation rate, as well as an interaction effect.

To determine statistical significance of main and interaction effects, a two-way ANOVA is performed.
ANOVA tests the null hypothesis that there are no differences between groups for the main effects.
It also tests the null hypothesis that there is no interaction effect.
If the ANOVA is significant, further analyses (post-hoc tests) are conducted to determine which specific pairs of groups are different.

Describes the number of IVs and levels of each IV
The number of digits equals the number IVs, and the value of the digit equals the number of levels
Example: In a 3x5 factorial there are 2 IVs, one with 3 levels and one with 5 levels.
Example: In a 2x2x 4 factorial, there are 3 IVs with 2, 2, and 4 levels respectively
To determine the number of conditions, multiply the numbers in the notation
Example: 2x4 = 8 conditions
Example: 2x2x4 = 16 conditions
In factorial designs, "levels" and "conditions" are distinct and cannot be used interchangeably

Inferential statistics are used to interpret data.
Main effects refer to the overall effect of a particular IV.
The number of main effects equals the number of IVs
To determine the main effect of one IV, combine data over all levels of other IVs.
Interaction effects occur when the effect of one IV depends on the level of another IV
Factorial designs allow for detecting interactions.
Interaction effects are generally more important than main effects.
A matrix is useful to organize data to make it easier to plot in a line graph.
Each cell of the matrix represents the mean for a given condition.
To visually assess if there’s an interaction in a line graph, check if the lines are parallel.