week 8 Two-Factor Mixed and Within-Participants ANOVA

Course Overview

  • Course Title: PSYC214: Statistics for Group Comparisons

  • Instructor: Mark Hurlstone, Lancaster University

  • Contact: m.hurlstone@lancaster.ac.uk

  • Week: Week 8

Course Content Topics

  • Two-Factor Designs

    • Mixed Design ANOVA

    • Fully Within-Participants Design ANOVA

  • Data Handling

    • Raw Data & Cell Means

    • ANOVA Table Interpretation

    • Simple Effects Analysis

    • Interaction Plot Creation

    • Calculation of F Ratios

Learning Objectives

  • Understand and apply two-factor mixed and within-participants designs.

  • Focus on procedures for analyzing data rather than mathematical calculations.

  • Gain skills in interpreting ANOVA tables and graphs.

  • Approach handling significant main effects and simple effects for factors with three or more levels.

Introduction to ANOVA Designs

  • Coverage of Basic Designs:

    1. Between-Participants Design: Splits total variability into between-groups and within-group variability.

    2. Within-Participants Design: Splits within-group variability into between-participant and residual variability.

    3. Two-Factor Design: Splits between-group variability into main effect and interaction.

  • Transition to more complex designs via two-factor mixed design analysis.

Mixed Design ANOVA

  • Definition: Combines at least one between-participants factor and at least one within-participants factor.

  • Application: Widely used in psychological experiments.

Example: Stroop Task

  • Stroop Task Description:

    • Participants name the ink color of color words quickly.

    • Congruent Trials: Ink color matches the word.

    • Incongruent Trials: Ink color does not match the word.

  • Stroop Effect: Increased response times in incongruent trials reflecting a measure of response inhibition.

Detailed Example of Mixed Design

  • Research Hypothesis: Investigating response inhibition in patients with schizophrenia via the Stroop task.

  • Design Layout: 2 × 2 mixed design.

    • Between-Participants Factor: Patient group (healthy vs. schizophrenia).

    • Within-Participants Factor: Trial type (congruent vs. incongruent).

Hypothetical Data Presentation

  • Mixed-Design Data for Stroop Experiment:

    • Table outlining reaction times for each group, divided by factor levels (healthy vs. schizophrenia and types of trials).

Understanding Error Terms in Mixed Design ANOVA

  • Error Term Definition: Used to assess the significance of main effects and interactions in varied designs.

  • Error Terms in Mixed ANOVA:

    1. Between-participants main effect.

    2. Within-participants main effect.

    3. Interaction.

ANOVA Table Interpretation

  • Components:

    • Source lists (e.g., group, trial type, interaction).

    • Statistics such as sum of squares, degrees of freedom, mean square, F-statistic, p-value.

  • Example Results Showcase: Provide mock results and their interpretations for each effect observed.

Simple Main Effects Analysis

  • Approaches for Testing Simple Main Effects:

    • Use pooled error terms to assess significance across various comparisons.

    • Calculation mechanics similar to between-participants design.

Visualization of Interaction Effects

  • Importance of Interaction Plots: Graphs highlighting the relationship between factors for visual interpretation of results.

Future Class Resources

  • Recommended Reading: Reference materials concerning the statistical methods discussed in class (Roberts & Russo, 1999).

  • R Programming: Introduction to running ANOVA tests using R in future classes.

Additional Notes

  • Sphericity Assumption: Discusses the need for corrections in within-participants designs with more than two levels of factors.