Lecture 9 - Three-Factor ANOVA

PSYC214: Statistics for Group Comparisons

Definition: Three-factor ANOVA (Analysis of Variance) is a statistical method used to examine the interaction effects among three independent variables on a dependent variable, allowing researchers to understand how various factors impact outcomes simultaneously.
a x b
a x c
b x c
or three way interaction - a x b x c
Commonality in Psychology: This technique is particularly prevalent in psychological research, where understanding complex interactions between different variables is crucial for drawing valid conclusions about behavior and mental processes. It helps in isolating the precise influences of each independent variable while considering their interactions.
if a two way is significant we can examine the simple main effect of factor a and b or which ever factors are significant

Memory and Context Data
- Purpose: Investigates the effects of contextual factors on memory recall and recognition, such as environmental influences on cognitive processes and memory performance.
ANOVA Tables
- Recall ANOVA Table: Utilizes statistical testing to analyze and illustrate differences in memory recall across varying conditions, pinpointing where significant effects occur.
- Recognition ANOVA Table: Focuses on differences in memory recognition across conditions, enabling an assessment of how context affects the ability to recognize previously learned information.
- Simple Main Effects Table: Analyzes the effects of a single factor while controlling for the influence of other factors, providing clarity on how one variable impacts the dependent measure when isolating other influences.

Understanding Procedures: Learn foundational procedures for analyzing and interpreting results from three-factor ANOVA, including familiarity with software tools for data analysis.
Decomposition of Interactions: Study techniques for breaking down complex three-way interactions into more manageable two-factor ANOVAs, facilitating a clearer interpretation of interactions between variables.
- Examples include:
  - 2 × 2 × 2 fully within-participants ANOVA
  - 2 × 2 × 2 mixed ANOVA
General Considerations: Emphasize essential factors to consider during analysis, such as sample size, effect size, and the balance between groups to ensure reliable results.

Types of Interactions:
- Two-Way Interactions: Focus on interaction effects between any two of the three factors, allowing researchers to explore combinations such as A × B, A × C, and B × C.
- Three-Way Interactions: Investigate scenarios where all three factors interact, represented as A × B × C, which offers insights into how complex relationships between variables affect outcomes.
Significance Complexity: Recognize that significant three-way interactions can present major challenges in interpretation, necessitating careful stepwise approaches to unpack interactions to derive meaningful insights.

A significant three-way interaction occurs when there are different-way interactions between two of the factors according to the levels of the third factor
• The simplest way to analyse a significant three-way interaction is to analyze it as a series of two-factor ANOVAs,
e.g. (factor A: level A1 vs. level A2) × 2 (factor B: level B1 vs. level B2)ANOVA at level C1 of factor C2 a
(factor A: level A1 vs. level A2) × 2 (factor B: level B1 vs. level B2)ANOVA at level C2 of factor C•
Any significant interactions would be followed up with a simple main effects analysis

Basic Design Considerations:
- Earlier principles learned in past lectures regarding experimental design principles remain applicable with added complexity.
- Between-participants designs are recommended for their simplicity as they involve a single error term, making data analysis more straightforward.
- A minimum sample size of N = 20 per cell is recommended to maintain statistical power, indicating that a 2 × 2 × 2 design requires at least 160 participants to detect significant effects effectively.

Non-Significant Three-Way Interaction: When the analysis reveals a non-significant three-way interaction, the focus should shift to exploring significant two-way interactions to provide insight into the relationships between pairs of factors.
Significant Three-Way Interaction: Requires analysis by breaking down the design into two-factor ANOVAs, identifying which factor should be the primary focus for splitting and analyzing the data appropriately.

Objective: Examine whether memory performance is enhanced when testing occurs in the same context as the learning environment, exploring the significance of contextual stability on recall.
Factors of Interest:
- Memory Test: Types include Recall vs. Recognition, with different memory processes and retrieval cues.
- Learning Context: Examine memory performance differences when tested under varying conditions: Underwater vs. On Land.
- Testing Context: Also assess performance in different testing environments to determine the influence of context on memory retrieval.
- Dependent Measure: The primary measure will be the number of words remembered correctly, serving as an indicator of memory effectiveness in the context framework.

Objective: Study children's abilities in pronouncing irregular words, which provides insights into language development and the challenges faced in phonetics.
Design Type: Implement a 2 × 2 × 2 mixed design, combining between-participants factors for age with within-participants factors for frequency and word type, enhancing the complexity and depth of analysis.
Results Measures: Collect data on the number of pronunciation errors recorded during testing, which informs the evaluation of phonetic capabilities across different contexts.

Begin your analysis by examining the implications of the three-way interaction to set the stage for deeper insights.
If significant, proceed with conducting two-factor ANOVAs to uncover further relationships and interaction effects for a comprehensive understanding.
Focus on interpreting results based on both interactions and main effects, ensuring a robust analytical approach.

Roberts, M. J., & Russo, R. (1999). A student’s guide to Analysis of Variance. Routledge: London.

Focus on practical application: running a three-factor ANOVA in R, with an emphasis on software proficiency for statistical analysis and interpretation of results.