Lecture7_24s - Tagged

Psychological Research Skills Lecture Notes

7. Mixed-Design ANOVA

Recap from Last Week

  • Within-participants Factorial Design ANOVA

    • Advantages

    • Assumptions

  • Statistical Power

    • Reliability & replicability

    • Type I and Type II errors

Hypothesis Testing

  • Distinction between distributions:

    • H0: Null Hypothesis

    • H1: Experimental Hypothesis

Errors in Hypothesis Testing

Type I and Type II Errors

  • Type I Error (α): Rejecting H0 when it is true.

  • Type II Error (β): Failing to reject H0 when it is false.

  • Decision Table:

    • Fail to reject H0: Correct decision if H0 true, Type II error if H0 false.

    • Reject H0: Correct decision if H0 false, Type I error if H0 true.

Statistical Power

  • Power (1 - β): Ability to correctly reject null hypothesis.

  • Influenced by:

    • Type I error rate (α)

    • Type II error rate (β)

    • Sample size

    • Effect size

    • Experimental design

    • Statistical test choice

Maximizing Statistical Power

Methods to Increase Power

  • Increase sample size: reduces sampling error

  • Eliminate poor methodology to reduce experimental error

  • Use within-participants design: no individual differences error decreases β and increases power.

Effect Size

Understanding Effect Size

  • Measures practical importance beyond statistical significance.

  • In SPSS, effect size statistic for ANOVA is called Partial Eta Squared (ηp²)

    • Formula: ηp² = SS effect / (SS effect + SS error)

    • Larger effect size indicates greater statistical power.

Mixed-Design ANOVA

Definition

  • Combines between-participants and within-participants factors.

  • Example: Two-way mixed-design ANOVA with one independent variable from each design type.

Application of Mixed-Design ANOVA

Example Experiment

  • Investigating effect of breakfast types on mid-morning snack intake by weight category.

  • Factors:

    • Between-participants: Weight (typical, obese, formerly obese)

    • Within-participants: Breakfast fat content (zero, low, medium, high, very high fat)

Assumptions of Mixed-Design ANOVA

  • Between-Participants Factors:

    • Normality

    • Homogeneity of variance

    • Interval or ratio measurement

    • Independence of observations

  • Within-Participants Factors:

    • Normality

    • Sphericity

    • Interval or ratio measurement

Results Analysis

Steps in SPSS

  1. Check assumptions using SPSS.

  2. Calculate sphericity and homogeneity of variance.

  3. Report significant interactions and main effects.

Example Results Write-up

  • Hypothesis: Breakfast fat content affects snack intake.

    • Mean consumption scores for weight categories provided in a table format.

  • ANOVA results:

    • No significant main effects observed for weight (F(2, 9) = 0.64, p = .55) or breakfast type (F(4, 36) = 0.85, p = .50), but significant interaction (F(8, 36) = 8.14, p < .001, ηp² = .64) noted.

Graphical Representation

  • Line graphs depict cupcake consumption broken down by breakfast type across weight categories.

  • Observations:

    • Typical weight: Consumption decreases with higher breakfast fat content.

    • Obese: Shows opposite trend.

    • Formerly obese: Minimal relationship noted.

Conclusion

  • Mixed-design ANOVA is valuable for understanding interactions between different participant and intervention characteristics.