Module 8: Factorial ANOVA

One-Way ANOVA Recap

One-Way Between-Groups ANOVA

Example

• A researcher is investigating cognitive decline in older adults (aged 65-90 years) who do no physical activity, moderate levels of physical activity or high levels of physical activity

• Participants complete a cognitive ability test and report their level of physical activity

Quasi-independent variable: level of physical activity (3 levels: low, moderate, high)

Dependent Variable: cognitive ability on a continuous scale of measurement

One-Way Between-Groups ANOVA:

Main Effect: The cognitive ability of participants significantly differed between the three exercise groups, F(2,12) = 13.34, p < 001. There was a large effect (eta² = .320)

Follow-up tests: Tukey HSD post-hoc tests revealed that the participants who engaged in no physical activity were significantly poorer in cognitive ability than
participants who engaged in moderate (p = 002) or high (p < .001) levels of physical activity. There was no significant difference between the cognitive performance of participants who engaged in moderate and high physical activity (p = .370)

One-Way Repeated-Measures ANOVA

Example

• A researcher is investigating self-control capacity on three different occasions: after placebo, after consuming a low dose of glucose, after consuming a high dose of glucose

• Participants complete a test of self-control (i.e.. executive function or behavioural restraint test) in all three experimental conditions

Independent Variable: glucose consumption (3 levels: placebo, low dose, high dose)

Dependent Variable: self-control on a continuous scale of measurement

Main effect: Self-control significantly differed depending on the level of glucose consumed, F (2, 8) = 60.00, p < .001. There was a large effect size (η2 = .480)
Follow-up tests: Pairwise comparisons using a Bonferroni adjusted alpha (p < .016) revealed that self-control was significantly higher in the high glucose condition, compared to the low (p = .005) and no dose (p = .012) conditions. Self-
control was also significantly higher in the low glucose condition than the no glucose condition (p = .009).

Factorial ANOVA

• Involves the manipulation (experiment) or measurement (quasi-experiment) of 2 or more independent variables.

• Investigate separate effects of each independent variable - main effects

• Investigate the combined effects of all independent variables - interactions

Factors are another way of saying independent variables. Depending on the number of IVs, the ANOVA can be 1-factor, 2-factor, 3-factor, etc. However, the more factors, the more complicated interpretation.

Levels are the experimental conditions for each IV. E.g., IV = age group (children and adolescents) = 2 levels

Cells are the individual treatment conditions. Can be calculated by multiplying the number of levels of each IV

Between-Groups

• At least 2 factors

• All factors are manipulated between-subject

• Each participant provides data in only 1 cell

Within-Groups

• At least 2 factors

• All factors are manipulated within-subjects

• Each participant provides data in all cells of the analysis

Mixed

• At least 2 factors

• At least 1 is manipulated between-subjects and at least 1 is manipulated within-subjects

Interaction of Variables

We say that 2 independent variables interact when the effect of one of the variables depends on the other independent variable.

The more levels of a factor you have the more difficult to interpret the interactions can become.

If an interaction is statistically significant, we would want to understand where those differences are, by using t-test for instance.

Design Statements

Because factorial design are quite complicated we want to organise and clear up misunderstandings by making a design statement, which includes,

• Type of Study, e.g., experiment, quasi-experiment, etc

• Independent Variables, e.g., 2 (time: pre-test, post-test) x 2 (experience: novice, advanced)

  • Name of IV

  • Number of levels in IV

  • Names of the levels of the IV

• Manipulation of IV, e.g., between-subjects, within-subjects, matched, mixed

• Dependent Variable

  • Name and description of dependent variable