Study Notes on One-Way ANOVA

Research Methods in Psychology focuses on One-Way ANOVA with Post-Hoc Tests.
Presented by Dr. Yang Yap from the School of Health and Biomedical Sciences at RMIT University.

RMIT University acknowledges the traditional custodians of the lands on which it operates, particularly the Woi wurrung and Boon wurrung language groups of the eastern Kulin Nation.
Recognition is given to their ancestors and elders.

Describe Research Questions: - Understand the research questions that can be addressed using a single-factor (One-Way) between-subjects ANOVA.
Essential Features of ANOVA: - Learn the fundamental characteristics of single-factor between-subjects ANOVA and how the F ratio is generated.
Running ANOVA in Jamovi: - Execute single-factor between-subjects ANOVA using Jamovi software, including post-hoc tests, descriptive statistics, and graphical representations.
Interpretation of Results: - Interpreting statistical analysis results, understanding their implications for the research questions, and conducting post-hoc analyses for further interpretation.

ANOVA (Analysis Of Variance): A statistical method used to compare means among three or more groups.
One-Way ANOVA: - Involves a single independent variable (IV) with multiple levels (groups). - Levels correspond to the number of groups within the independent variable.

A One-Way ANOVA is treated as an upgrade to the Independent Samples T-test.
It can also be referred to as 'between samples ANOVA' or 'between subjects ANOVA'.
Conditions that need to be met include distinct groups defined by the independent variable and the ability to compare more than two groups.

Study 1: Gender and Sleep Duration - Aim: Examine differences in sleep duration across different gender identifications. - Hypothesis: Non-binary individuals will report lower sleep duration compared to males and females. - ANOVA Characteristics: (1 x 4) ANOVA where IV = Gender (4 levels: Man, Woman, Non-Binary, Other) and DV = Sleep Duration (in hours).
Study 2: Attachment Styles and Stress Levels - Aim: Evaluate stress levels across different attachment styles. - Hypothesis: Secure attachment style individuals will exhibit lower stress levels compared to Avoidant or Anxious attachment styles. - ANOVA Characteristics: (1 x 3) ANOVA with IV = Attachment Style (3 levels: Avoidant, Anxious, Secure) and DV = Stress (measured using DASS-21).
Study 3: Mindfulness Therapy Effects on Depression - Aim: Assess the effect of mindfulness therapy on depressive symptoms. - Hypotheses: Mindfulness-Based Therapy will yield better outcomes than both Wait-list Control and Cognitive Behavioral Therapy. - ANOVA Characteristics: (1 x 3) ANOVA where IV = Intervention (levels: CBT, Mindfulness, Wait-list Control) and DV = Depressive Symptoms.

A one-way ANOVA is beneficial when comparing more than two groups.
The dependent variable should remain consistent across groups, measured with the same instrument.
Test variations are indicated as 1 x n ANOVAs based on the levels of the independent variable.
Notably, a 1 x 2 ANOVA parallels the Independent Samples T-test.

Comparison through multiple t-tests: If compared using multiple t-tests: - For 3 groups (e.g., A, B, C), conduct 3 tests: A vs B, A vs C, B vs C. - For 4 groups (A, B, C, D), conduct 6 tests, increasing complexity and possibility for Type I error. - For 5 groups (A, B, C, D, E), conduct 10 tests.
Efficiency and Error Rates: Conducting numerous tests inflates the Type I error rate (false positive) and is inefficient; thereby a single ANOVA is preferable.

ANOVA compares the ratio of systematic variance (variation due to the independent variable) to unsystematic variance (variation due to extraneous factors).
F-ratio Definition: $F = rac{ ext{Systematic Variance}}{ ext{Unsystematic Variance}}$
Interpretation of F-ratio:
- If F ext{ ratio} ext{ } < ext{ } 1, indicates no effect (more unsystematic variance). - If F ext{ ratio} ext{ } > ext{ } 1, indicates that the experimental manipulation had some effect. - A larger F ratio corresponds to a stronger manipulation effect.
P-values correlation: A significant F-ratio alerts us to look at the p-value to determine if the result is statistically significant.

ANOVA is classified as an omnibus test, which means it tests for overall differences but does not indicate where the differences lie among group comparisons.
Effects of the F-test: While useful, it indicates a need for further post-hoc analysis if differences are noted.

If a significant F-test is found, post-hoc tests will clarify which groups differ; if non-significant, further analysis is unnecessary.

Least Significance Difference (LSD): - No corrections; similar to numerous t-tests.
Bonferroni Correction: - Good for small comparisons, conservative in nature. Corrects Type I error successfully.
Tukey's HSD: - Effective for larger numbers of comparisons, robust correction for Type I error.

Normality - The dependent variable must be normally distributed across all groups. Assessed via statistical tests or visual inspection. - If violated, consider: - Non-parametric alternatives, - Transforming outcome variable, - Justification based on central limit theorem.
Outlier Check - Identification and management of outliers are crucial because they can skew results.
Homogeneity of Variance - Variance must be equal across groups, checked with statistical tests. - If violated, Welch's correction applied, especially for post-hoc.

Follow a systematic order for conducting the analysis: 1. Confirm existence of a categorical variable with at least 3 groups tested against a continuous DV. 2. Check assumptions (Normality, Outliers, Homogeneity of Variance). 3. Execute the ANOVA setting. 4. Verify significance via p-value for the F-ratio (p < .05 indicates a significant overall model). 5. Conduct appropriate post-hoc tests (Tukey or Bonferroni) based on significance. 6. Examine p-values for group comparisons to assess specific group differences.

Query: Is there a significant difference in depression levels among therapy groups (Fluoxetine vs Cognitive Behavioral Therapy vs Control)?
Sample of 30 individuals, with 10 in each group (0 = Control, 1 = Fluoxetine, 2 = CBT).

Sample Size, Mean, Median, Standard Deviation, Variance, Interquartile Range (IQR), Range defined for depression scores across conditions.

Shapiro-Wilk Test Results: Non-significant, indicating normality across conditions.
Levene's Test Result: Non-significant, indicating homogeneity of variance holds.

Results of ANOVA indicated overall significant difference in depression across therapy groups: - Statistics: F(2,27) = 27.1, p < .001.
Post-hoc comparisons using Bonferroni's correction showed: - Anti-Depressant (p < .001) and CBT (p < .001) conditions significantly lower compared to Control. - No significant difference observed between CBT and Anti-Depressant (p = .68).