Paired t-test

PAIRED T-TEST SUMMARY

  • Also known as dependent sample t-test.

  • Compares means of two samples measured twice (before/after).

  • Common in evaluation research.

STEPS IN CARRYING OUT PAIRED T-TEST

  1. Define hypotheses:

    • Null Hypothesis (H0): No difference between means.

    • Alternative Hypothesis (H1): Difference exists.

  2. Compare group means (e.g., pre-test vs. post-test).

  3. Calculate t-statistic and effect size (Cohen's d).

  4. Interpret results.

ASSUMPTIONS

  • Normality of differences between pairs must be met.

  • No extreme outliers present.

HYPOTHESES EXAMPLES

  • Null Hypothesis: μ1 = μ2 (means are equal).

  • Alternative Hypothesis (two-tailed): μ1 ≠ μ2 (means are not equal).

DATA ANALYSIS

  • Use paired t-test for means comparison.

  • Example data results: Before mean = 37.2, After mean = 40.2, df = 39, t Stat = -6.50.

  • P-value < 0.05 indicates rejection of H0 (statistically significant difference).

EFFECT SIZE

  • Effect Size (Cohen's d): 0.245 (small effect); standard thresholds: 0.2 (small), 0.5 (medium), 0.8 (large).

WRITING RESULTS

  • Format: "A paired samples t-test was performed to compare…"

  • Example conclusion: Significant difference in wellbeing (M = 37.2, SD = 12.46; M = 40.2, SD = 12.01; t(39) = -6.50, p < .05).

SUMMARY

  • Understand when to use paired t-test.

  • Know calculation process and result interpretation.