Statistical Concepts Series

Effect Size &
Cohen’s d

Beyond p-values: Understanding the magnitude of differences.

The Big Picture

Effect size tells us how big the difference is between two groups—not just whether the difference is statistically significant.

One of the most common measures in t-tests is Cohen’s d. It measures the magnitude of the difference expressed in standard deviation units.

"How much do the two groups differ, regardless of sample size?"
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Practical Importance

Even a tiny difference can be statistically significant with a huge sample size. Effect size helps you judge if that difference actually matters in the real world.

Interactive Lab: Visualizing Cohen's d

Drag the slider to change the difference between group means and watch the effect size change.

0 (No Diff) 4 (Huge Diff)
Calculated Cohen's d
0.50
Medium Effect
Group 1
Group 2

🧮 The Formulas

1 Independent Samples t-test

d =
X̄₁ - X̄₂ spooled
  • X̄₁, X̄₂: Group means
  • spooled: Pooled standard deviation

2 Paired Samples

d =
sD
  • D̄: Mean of the differences
  • sD: Standard deviation of differences

📊 Interpreting the Results

These rules of thumb are widely used, but remember: context is key! In education or medicine, even a small effect (0.2) can change lives.

0.20 Small Effect
0.50 Medium Effect
0.80 Large Effect
1.20+ Very Large Effect

Example Scenario

  • Group A Mean 75
  • Group B Mean 70
  • Pooled SD 10
d = (75 - 70) / 10 = 0.5

Result: Medium Effect Size

✅ Reporting Best Practices

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Report It

Always report Cohen's d after every t-test in your thesis or paper.

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Contextualize

Include it in tables alongside means, SDs, and p-values for a complete picture.

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Calculation

SPSS doesn't always do it automatically. Use Excel, online calculators, or plugins.