Skip to content

Effect Size Visualization

Run the Effect Size Visualizer Fullscreen

Edit in the p5.js Editor

About This MicroSim

"My tail's tingling—we're onto something!" Sylvia says excitedly. "P-values tell us IF an effect is real, but effect size tells us HOW BIG it is. And that's often what really matters!"

This interactive visualization helps students understand Cohen's d, one of the most common effect size measures for comparing two groups:

\[ d = \frac{\mu_2 - \mu_1}{\sigma} \]

where: - \( \mu_1 \) and \( \mu_2 \) are the means of the two groups - \( \sigma \) is the standard deviation (assumed equal for both groups)

Cohen's d Interpretation Guidelines

Effect Size Cohen's d Visual Appearance
Negligible d < 0.2 Distributions nearly identical
Small 0.2 ≤ d < 0.5 Slight separation, heavy overlap
Medium 0.5 ≤ d < 0.8 Noticeable separation
Large d ≥ 0.8 Clear separation between groups

How to Use

  1. Drag the slider to adjust Cohen's d from 0 to 2.0
  2. Watch the distributions separate as effect size increases
  3. Observe the overlap decrease as d increases
  4. Check the statistics panel for calculations and interpretation

Key Insights

"Here's what I love about effect size," Sylvia explains. "It doesn't depend on sample size! A d of 0.5 means the same thing whether you have 20 participants or 20,000."

Why Effect Size Matters

  1. Sample size independence: Unlike p-values, effect sizes don't get artificially inflated with large samples
  2. Comparability: You can compare effect sizes across different studies
  3. Practical interpretation: Effect size tells you whether the difference is worth caring about
  4. Meta-analysis: Researchers combine effect sizes from multiple studies

Visual Intuition

  • d = 0: The distributions are identical (complete overlap)
  • d = 0.5: About 67% of one group overlaps with the other (medium effect)
  • d = 1.0: About 45% overlap (large effect)
  • d = 2.0: Less than 20% overlap (very large effect)

Embedding This MicroSim

1
<iframe src="https://dmccreary.github.io/statistics-course/sims/effect-size-visualizer/main.html" height="522px" width="100%" scrolling="no"></iframe>

Lesson Plan

Learning Objectives

By the end of this activity, students will be able to:

  1. Define effect size as a standardized measure of difference magnitude
  2. Calculate Cohen's d given two group means and a standard deviation
  3. Interpret Cohen's d values using conventional benchmarks (small, medium, large)
  4. Explain the visual relationship between effect size and distribution overlap
  5. Distinguish between effect size and statistical significance

Target Audience

  • AP Statistics students (high school)
  • Introductory statistics college students
  • Psychology and social science research methods students
  • Anyone learning to interpret research findings

Prerequisites

  • Understanding of normal distributions
  • Concept of mean and standard deviation
  • Basic hypothesis testing concepts

Classroom Activities

Activity 1: Predict the Separation (10 minutes)

Before showing the simulation:

  1. Ask students to draw two normal curves with d = 0 (identical)
  2. Have them draw what d = 1.0 might look like
  3. Show the simulation to check their predictions

Activity 2: Calculate and Verify (15 minutes)

Given: Group 1 mean = 100, Group 2 mean = 115, SD = 15

  1. Have students calculate Cohen's d by hand: d = (115 - 100) / 15 = 1.0
  2. Set the slider to d = 1.0 and verify the calculation
  3. Repeat with different scenarios

Activity 3: Connecting to Research (15 minutes)

Discuss real-world effect sizes:

  • Psychotherapy vs. no treatment for depression: d ≈ 0.8 (large)
  • Gender differences in math ability: d ≈ 0.1 (negligible)
  • Relationship between height and intelligence: d ≈ 0.2 (small)

"Don't worry—every statistician drops an acorn sometimes," Sylvia reassures. "The important thing is learning what these numbers MEAN in context!"

Assessment Questions

  1. If two groups have means of 50 and 58 with SD = 16, what is Cohen's d? Is this a small, medium, or large effect?

  2. A study reports d = 0.3 and p = 0.0001. Explain how both of these can be true simultaneously.

  3. Why might a researcher prefer to report effect size rather than just p-values?

  4. Looking at the visualization, approximately what percentage of Group 2 scores exceed the Group 1 mean when d = 0.8?

  5. Two studies examine the same treatment. Study A (n=30) finds d = 0.7, p = 0.05. Study B (n=300) finds d = 0.3, p = 0.001. Which study provides stronger evidence for a practically meaningful effect? Explain.

References