Week 4. MANOVA.2024

Multivariate Statistical Analyses Research Methods II

  • Course: OCCT 6386

  • Institution: University of Texas Medical Branch

  • Department: Occupational Therapy

  • Instructor: Claudia L. Hilton, PhD, MBA, OTR, FAOTA

Understanding Regression

Types of Regression Questions

  • Linear Regression Example: Predicting outcomes based on a continuous variable.

  • Logistic Regression Example: Determining the probability of an event occurring (binary outcome).

Necessary Sample Size for Regression

  • Minimum number of subjects needed to ensure statistical power during regression analysis.

Entry Methods for Regression

  • Stepwise Regression: A method of selecting predictors based on statistical criteria.

Key Definitions

  • Residual: The difference between the observed value and the predicted value in regression analysis.

  • Standard Error of the Estimate: Represents the average distance that the observed values fall from the regression line.

  • Coefficients: In the linear regression equation, b represents the slope (rate of change for the dependent variable) and a represents the y-intercept.

Correlation Coefficient vs Coefficient of Determination

  • Correlation Coefficient (r): Measures the strength and direction of a linear relationship between two variables (range -1 to +1).

  • Coefficient of Determination (R²): Represents the proportion of variance explained by the independent variable(s) in the regression model.

Statistical Analysis Objectives

  • Describe various statistical analyses:

    • ANCOVA (Analysis of Covariance)

    • MANOVA (Multivariate Analysis of Variance)

    • MANCOVA (Multivariate Analysis of Covariance)

    • Principal Component Analysis

    • Factor Analysis

    • Cluster Analysis

    • Rasch Analysis

Comparing Statistical Methods

Correlation, ANOVA, and Regression

  • Correlation: Examines the relationship between two variables.

  • ANOVA: Used to identify differences between three or more groups.

  • Regression: Used for predicting values of a dependent variable based on independent variables.

Covariance

  • Definition: Occurs when two sets of scores vary together in similar patterns.

Covariance vs Correlation

  • Covariance results often hard to interpret; correlated variables are standardized to create a correlation coefficient valued between -1 and +1.

Examples of Covary and Correlate

  • Covary: Two variables that change together without implying causation (e.g., height and weight).

  • Correlate: Implies a statistical relationship with predictability.

ANOVA (Analysis of Variance)

Purpose of ANOVA

  • Compares means of three or more groups.

Example Applications

  • One-way ANOVA: Compares means based on one independent variable (e.g., group differences based on education level).

  • Two-way ANOVA: Examines interaction effects among two independent variables.

Types of Tests

Parametric and Non-Parametric Tests

  • Independent T-test: Compares means between two independent groups.

  • Mann Whitney U: Non-parametric test for two independent groups that does not assume normal distribution.

  • Paired T-test: Compares means in related groups.

  • Wilcoxon Signed-ranks Test: Non-parametric test for related samples.

  • H Tests: Kruskal-Wallis for comparing more than two groups non-parametrically, Friedman’s for repeated measures.

ANCOVA, MANOVA, MANCOVA

ANCOVA

  • Adjusts for covariates in one-way ANOVA models.

  • Useful in research where randomization is not possible.

MANOVA

  • Examines multiple dependent variables simultaneously.

  • Useful for understanding relationships between variables.

Examples of ANCOVA and MANOVA Applications

  • ANCOVA Example: Testing the effect of hours studied on test scores while controlling for prior academic performance.

  • MANCOVA Example: Investigating the impact of educational level on test scores adjusted for study habits.

Factor Analysis Concepts

Techniques and Analysis Types

  • Principal Component Analysis (PCA): Data reduction technique aiming to explain variance with fewer factors.

  • Exploratory Factor Analysis (EFA): Testing theories through variable relationships.

Factor Rotation Methods

  • Orthogonal Rotation: No correlation among factors (e.g., Varimax).

  • Oblique Rotation: Allows for correlations among factors.

Factor Loadings

  • Measures the strength of relationship between individual items and their factors. Higher values indicate better item-factor association.

Rasch Analysis

  • A statistical technique that transforms ordinal data for interval scaling. Useful in occupational therapy assessments.

Recent Studies and Applications in Occupational Therapy

Out-of-School Participation in Children with Autism

  • Study examining activity participation differences between typically developing children and those with HFASD.

  • Results highlighted significant differences in participation, indicating the need for targeted interventions.