Factorial ANOVA and Correlation Overview

Factorial ANOVA Overview

  • Factorial ANOVA allows for investigation of effects of multiple independent variables (IVs) on a dependent variable (DV).
  • Differences from one-way ANOVA:
    • One-way ANOVA considers one IV with multiple levels.
    • Factorial ANOVA examines two or more IVs, leading to a more complex analysis.

Key Concepts of Factorial ANOVA

  • Analysis Structure:
    • Assess relationships between variables and differences between groups.
    • Determine whether the same participants are tested and how many groups/factors are involved.
  • Factorial Design Notation:
    • Notation indicates the number of factors and their levels.
    • Example notations:
    • 2 x 2 (two factors, each with two levels)
    • 2 x 3 (two factors, one with two levels and one with three levels)
  • Calculating Conditions:
    • Total conditions = product of the levels of each factor.
    • Example: 2 x 2 results in 4 conditions; 2 x 3 results in 6 conditions.

Factorial Design Examples

  • Testosterone and Aggression Study:

    • Grouping participants by age (young vs. old) and treatment (testosterone vs. placebo).
    • Denoted as 2 x 2 (two factors, each with two levels).

  • Cognitive Mapping Study Example:

    • Factors: compass usage (2 levels) and location distance (3 levels).
    • Design notation is 2 x 3.

Main Effects and Interactions

  • Main Effects:
    • The overall effect of each IV while ignoring other factors.
  • Interactions:
    • When the effect of one IV depends on another IV.
    • Found by calculating differences within rows/columns in the data.

Data Analysis through Factorial ANOVA

  • Calculate row and column means across other variables to understand general trends, not for significance testing.

  • Example Tables for Weight Loss Data:

    • Mean weight decreases by age and exercise type.
    • Older adults generally lost more weight than younger adults.

  • ANOVA Testing: Use significance testing to confirm if main effects or interactions observed are statistically significant.

Important Statistical Elements

  • Example of statistical notation:
    • F(1,16) = 248.55, p < .001
    • Significance tests divide variance into sources and provide p-values for each.
  • Writing up ANOVA results:
    • Clearly state main effects and interactions with proper statistical values.

Conclusion and Significance Testing

  • Ensure clear interpretations are made based on statistical results, especially focusing on significant effects.
  • Consider correlations as an added measurement of relationship dynamics in factorial designs, distinguishing from causal relationships.

Correlation Basics

  • Correlation Coefficient (r):
    • Single number indicating the strength and direction of a relationship between two continuous variables.
    • Ranges from -1 (perfect negative) to 1 (perfect positive); 0 indicates no relationship.
  • To test significance of correlation:
    • Hypothesize null (H0: r = 0) and alternative (H1: r ≠ 0) hypotheses, with critical values determined by sample size.