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Understanding Group Differences: Independent Variables, T-tests, and ANOVA Explained

This guide explores the statistical analysis of group differences, focusing on independent variables (IV) like gender (male, female) affecting a dependent variable (DV) such as happiness. It explains the significance of confidence intervals (CI) in determining whether observed differences are real or due to chance. We will discuss t-tests for two groups and ANOVA for three or more, including methods for post-hoc comparisons and controlling for familywise error. Learn how to interpret results, calculate effect sizes, and understand group variability.

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Understanding Group Differences: Independent Variables, T-tests, and ANOVA Explained

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Presentation Transcript

  1. Group Differences: 1 Independent Variable 1 IV. 2 groups t-test 3+ groups ANOVA

  2. Theory • IV: male, female • DV: happiness • There is a difference • Due to chance?

  3. Theory • Confidence Interval • 95% within interval • If Overlap • No real differences (non-significant) • If no Overlap • Difference is real (significant)

  4. Theory • Can make significant: • Move points away (larger between group variation)

  5. Theory

  6. Theory • Can make significant: • Smaller intervals (less within group variation)

  7. Theory • Summarizing theory behind “group differences”: between group variation within group variation • Notice how that translates into formulas: T-test: independent T-test: repeated ANOVA (I’ll show you later)

  8. 2 groups • A single pairwise comparison (e.g., males to females) • Is there a significant difference (e.g., p = .025) • What are group means (e.g., 4.84, 5.61) • What is the effect size (e.g., by hand, website)

  9. 3+ groups • Same as before: 95% CI Overlap = n.s. No overlap = sig • Difference: Multiple pairwise comparisons So FIRST see if “overall” Then SECOND test each pairwise

  10. 3+ groups (1) Overall “F” (2) Post-hoc or Planned Comparisons • Overall “F” • F = between group variability within group variability • Can’t simply start with multiple pairwise comparisons because must control for familywise error

  11. 3+ groups (1) Overall “F” (2) Post-hoc or Planned Comparisons • Overall “F” • F = between group variability within group variability • Can’t simply start with multiple pairwise comparisons because must control for familywise error .95 x .95 x .95 =.857 1-.857=.14

  12. 3+ groups (1) Overall “F” (2) Post-hoc or Planned Comparisons • Overall “F” • F = between group variability within group variability • Can’t simply start with multiple pairwise comparisons because must control for familywise error 1 - (1 - )C = 1 - (1 -.05)3=.14 .95 x .95 x .95 =.857 1-.857=.14

  13. 3+ groups (1) Overall “F” (2) Post-hoc or Planned Comparisons • Post-hoc • Testing all possible pairwise comparisons • Control for familywise error (keep alpha=.05) • Many options. I suggest LSD or Tukey • Planned Comparisons • Testing only specific pairwise comparisons • Must be “apriori hypotheses” • Can do one-tailed tests

  14. 3+ groups • Overall F (e.g., p = .003) • Post-hoc (e.g., see table) • What are group means (e.g., see table) • What is the effect size (e.g., by hand, website)

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