Chapter 12: Dependent-Groups Designs

Research Methods, Statistics, and Applications, Third Edition by Stephen Lippi, Ph.D.

Repeated-Measures Designs

• Definition: The dependent variable is measured multiple times for each individual in a single sample.
• Same Group: The same group of subjects is used in all treatment conditions.
• Advantage: No risk of participants in one treatment group being different from those in another.

Dependent-Groups Design

• Powerful Design: Reduces random error in participant characteristics.
• Minimizes Standard Error: By selecting related samples.
• Computing Difference Scores: Prior to computing the test statistic reduces between-person error and increases test power.

Types of Dependent-Groups Designs

• Repeated Measures Design: Participants experience every condition.
• Matched-Subjects Design: Participants are matched based on characteristics or traits.

Matched-Subjects vs. Repeated Measures

• Matched Subjects: Individuals in one sample are matched with individuals in another.
• Repeated Measures: The same individuals experience both treatment conditions.

Comparison with Independent-Measures Designs

• Fewer Subjects Needed: Repeated-measures design requires fewer subjects.
• Advantages: Reduces/eliminates problems caused by individual differences.
• Power: More likely to detect differences since extraneous differences are constant across conditions.
• Disadvantages:
  • Potential for order effects: Solution is counterbalancing.
  • Might not be practical for all studies (e.g., teaching methods).
  • Demand characteristics can change participant behavior.

Avoiding Order Effects

• Counterbalancing:
  • Full Counterbalancing: All possible orders are presented.
  • Partial Counterbalancing: Some orders are used (e.g., Latin Square).

Disadvantages of Within-Groups Designs

• Order Effects: Potential influence of treatment order on scores.
• Not Practical: Not suitable for all studies.
• Change in Behavior: Participants may act differently after experiencing all levels of the IV.

The t Statistic for Repeated-Measures Design

• Based on Difference Scores: Rather than raw scores.
• Formula and Calculation:
  • Mean Difference (MD) and Standard Error of the Mean Difference (SMD).
• Hypothesis Testing:
  • Follow a four-step process: State hypotheses, select alpha, calculate t statistic, and make a decision.

Hypotheses for Related-Samples t Test

• Null Hypothesis (H0): Mean difference is zero.
• Alternative Hypothesis (H1): There is a treatment effect (difference exists).

Assumptions of the Related-Samples t Test

• Independence: Observations within each condition must be independent.
• Normal Distribution: Difference scores must be normally distributed.

Degrees of Freedom

• Formula: df = nD - 1 (similar to one-sample t test).

Directional Hypotheses and One-Tailed Tests

• Specific Predictions: Directional predictions can be incorporated into hypotheses for one-tailed tests.

Example Study

• Caffeine and Heart Rate Study:
  • Participants given both decaf and regular coffee.
  • Hypothesis Test Steps:
    1. State Hypotheses: H0: D = 0, H1: D ≠ 0
    2. Set Criteria: Significance level 0.05, df = 9
    3. Calculate Test Statistic
    4. Decision: Reject null if test statistic exceeds critical value.

Effect Size and Confidence Intervals

• Effect Size: Measured using Cohen's d.
• Confidence Interval: Estimates the range where the true mean difference lies.
• Example: 95% CI for heart rate study shows range of true mean difference.

Formula Recap

• Cohen's d: Estimated effect size (MD/sD).
• Confidence Intervals: Range of the true mean difference.