Factorial Designs Lecture Notes

This set of vocabulary flashcards covers the fundamental concepts, benefits, issues, and analytical methods associated with factorial designs in research.

Factorial design

A design that tests the effects of more than one independent variable, typically simultaneously.

Main effects

The effect of an independent variable on a dependent variable without regard to the level of other possible independent variables in a study.

Interaction

When the effect of one independent variable depends on the level of one or more other independent variables.

Two-way interaction

The simplest form of interaction, involving the interaction of $2$ independent variables on some dependent variable.

Three-way interaction

The interaction of $3$ independent variables on a dependent variable.

Conditional effect

Another way of saying dependent; it represents the effect of one independent variable on the outcome, given some level of the other independent variable(s).

$2 \times 2$ design

A design that has $2$ independent variables with $2$ levels each.

$2 \times 3$ design

A design with $2$ independent variables, where one has $2$ levels and the other has $3$ levels.

$2 \times 2 \times 3$ design

A design with $3$ independent variables, two having $2$ levels and one having $3$ levels.

Independence of Effects

The requirement in factorial designs that independent variables and main effects be independent so that the level of one variable cannot be determined from the level of another.

Orthogonality

Being independent in both a math and statistics sense, ensuring that independent variables are not confounded or correlated with each other.

Crossed design

A design wherein each level of your independent variables is paired with each level of every other independent variable.

Increased Power

A benefit of factorial designs achieved by reducing unexplained variance (error) in outcomes, making effects become larger relative to the remaining variance.

Complexity

An issue with factorial designs where adding extra variables increases the number of potential sources of error and possible points of failure.

Order Effects

An issue that arises when independent variables are not applied simultaneously, creating a possible interaction between presentation order and the variables.

Interaction Effect Size

The characteristic that interactions are typically much smaller than main effects, meaning considerably more people are needed to detect them.

Chi-squared test of independence

The analysis used when all variables (independent and dependent) are measured at the nominal level.

Factorial ANOVA

A statistical test used when independent variables are nominal and the dependent variable is interval or ratio, allowing for the simultaneous testing of main effects and interactions.

Multiple regression

An analysis that assesses how well a set of variables predicts some outcome, used when there is at least one interval/ratio independent variable and an interval/ratio dependent variable.

Moderation analysis

A specific form of multiple regression used to test for interactions.