Lecture Notes: Paired T-Tests

Introduction

• Paired t-tests are used when you have two conditions comprised of the same elements or subjects.
• Difference from Independent T-Test:
  • Independent test: Different subjects in each group (e.g., children vs adults).
  • Paired test: Same subjects in both conditions (e.g., pre-and post-treatment observations).
  • Also known as repeated measures or within-subjects design.

Applications

• Measure changes over time (e.g., pre and post-intervention like yoga or meditation).
• Compare performance under different conditions (e.g., sober vs intoxicated reaction times).
• Example: Students reporting sleep habits on weekends vs weekdays.

Advantages of Repeated Measures Design

• Fewer subjects needed as same subjects are used in both conditions.
• Useful for studying changes over time or practice effects.
• Removes individual differences between groups, subjects serve as their own control.

Disadvantages of Repeated Measures Design

• Time-related factors may influence results (e.g., progressive diseases in health studies).
• Practice effects: Performance improvement due to familiarity with the task.

Example: Factory Safety Program

• Objective: Reduce accidents in widget building factories.
• Method: Measure accidents before and after safety training.
• Results:
  • Mean accidents decreased from 54 to 48.6.
  • Significant change assessed using paired t-test.

Paired T-Test Analysis

• Focus on difference scores (e.g., before and after accidents per factory).
• Hypotheses:
  • Null: Mean of difference scores is zero (no effect of safety program).
  • Alternative: Mean of difference scores is not zero.
• Calculate the mean of difference scores and standard deviation.
• Example Calculation:
  • Mean difference score: -5.2.
  • Standard deviation: 4.08.
  • Degrees of freedom: n - 1 (number of pairs).
• Perform t-test:
  • Mean difference score divided by standard error.
  • Compare t-value to critical value (e.g., 2.262 for 9 degrees of freedom).
• Conclusion:
  • Reject null hypothesis if t-value falls in rejection region.
  • Safety program significantly reduced accidents (t(9) = -4.02, p < 0.05).

Conclusion

• Paired t-tests are essential for evaluating changes in the same subjects under different conditions.
• Consideration of advantages and disadvantages is crucial in experimental design.