Inferential Tests Overview

Introduction to Inferential Tests

• Discussing basic inferential tests for differences between variables.
• Understanding relationships and co-variations between variables.

Co-variation between Variables

• Looking for patterns linking variable A with variable B (e.g. increase in family belongingness and religiosity).
• Relationships can include both continuous and categorical variables.

Choosing Inferential Statistics

1. Dependent Variables: How many outcome variables are being tested?

   • Typically one dependent variable in our practice (use ANOVA for one).
   • For more than one outcome variable, use MANOVA (not discussed in this class).

2. Measurement Level: How are dependent variables measured?

   • Categorical or continuous?
   • Continuous: Options include ANOVA, T-Test, Pearson R, Spearman Rho, etc.
   • Categorical: Options are limited (Chi-square, logistic regression).

3. Independent Variables: How many predictor variables are there?

   • More than one independent variable requires multivariate tests.
   • Focus on bivariate statistics for simplicity.

4. Nature of Independent Variables:

   • Categorical (dichotomous or multinomial) vs. continuous.
   • Different tests for two groups vs. three or more groups.

5. Repeated Measures: Are measurements taken from the same participants over time?

   • Distinction between within-group (repeated measures) and between-group analyses.

6. Parametric Assumptions: Does the data meet assumptions for parametric tests?

   • Normal distribution, skewness, kurtosis, etc.

Tests for Difference

Between Groups Tests

• Two Categories:
  • Independent T-Test (parametric).
  • Mann-Whitney U Test (non-parametric).
• Three or More Categories:
  • One-way ANOVA (parametric).
  • Kruskal-Wallis Test (non-parametric).

Within Groups / Repeated Measures Tests

• Two Observations:
  • Paired T-Test (parametric).
  • Wilcoxon Signed-Rank Test (non-parametric).
• Three or More Observations:
  • Repeated Measures ANOVA (parametric).
  • Friedman Test (non-parametric).

Characteristics of Tests

• Parametric Tests:
  • Assume normality, use F-statistics or T-statistics.
  • Provide more insightful findings.
• Non-Parametric Tests:
  • Do not assume normality, use U-statistics or Chi-square statistics.
  • Typically less insightful than parametric.

Conclusion

• Overview of the different tests and how they can be applied in statistical analysis.
• Importance of understanding the structure of your data to choose appropriate tests.