Lecture on Conducting Two-Way ANCOVA in SPSS

Overview

Presenter: Dr. Gandhi
Subject: Conducting a two-way ANCOVA using SPSS with fictitious data
Data Setup:
- Referral Variable: 2 levels (Voluntary, Involuntary)
- Treatment Independent Variable: 3 levels (Cognitive Behavioral Therapy (CBT), Psychodynamic Therapy, Gestalt Therapy)
- Pretest: Administered before the treatment and referral status determined (covariate)
- Post-test: Measured after treatment

Pretest and Post-test Scores: Derived from a psychometric instrument measuring mental health-related constructs (e.g., depression, anxiety)
Score Interpretation: High score = More severe symptoms; Low score = Less severe symptoms

Variables Included: Referral, Treatment, Post-test
Steps:
- Go to Analyze > General Linear Model > Univariate
- Dependent Variable: Post-test
- Fixed Factors/Independent Variables: Referral, Treatment
- Post-hoc Test: Tukey for treatment (3 levels)
- Options:
  - Display means for main effects
  - Confidence Interval Adjustment with Bonferroni
  - Descriptive Statistics, Estimates of Effect Size, Observed Power, Homogeneity Tests
Results:
- Referral Variable: Not statistically significant (p = 0.062)
- Treatment Variable: Statistically significant (p = 0.013)
- Interaction Effect: Significant for Referral x Treatment (p = 0.037)

Custom Model Creation:
- Set the model to custom to test homogeneity of regression
- Include all three possible two-way interactions and the three-way interaction
Results:
- No statistically significant findings for interactions; assumption of homogeneity of regression is met

Additional Assumptions to Test:
- Normality of the dependent variable for each combination of independent variable levels
- Homogeneity of variance
- Linear relationship between independent variables and dependent variable
Steps for ANCOVA:
- Analyze > General Linear Model > Univariate
- Add Pretest as a Covariate
- Go back to Model and select Full Factorial
Results:
- Descriptive Statistics: Voluntary level in CBT had the lowest mean score, suggesting less severe symptoms
- Levene's Test: p = 0.254 (not significant), satisfying homogeneity of variance
- Tests of Between-Subjects Effects:
  - Pretest (covariate): Statistically significant
  - Referral Variable: Not statistically significant (p = 0.131)
  - Treatment Variable: Statistically significant main effect (p = 0.002)
  - Interaction Effect: Statistically significant
- Pairwise Comparisons:
  - Significant differences between:
    - CBT and Psychodynamic (p = 0.003)
    - CBT and Gestalt (p = 0.02)
  - No significant difference between Psychodynamic and Gestalt (p = 0.161)
Profile Plots Interpretation:
- CBT shows an increase from voluntary to involuntary
- Gestalt remains stable
- Psychodynamic decreases from voluntary to involuntary