Your stats class told you whether a result is significant. It never quite explained whether that result *matters*. That gap — between a p-value and a real-world difference — is exactly where Cohen's d lives, and it trips up students from AP Statistics all the way through introductory college research methods.

This TLDR primer gives you a focused, no-filler guide to Cohen's d: what it measures, how to compute it using the pooled standard deviation, and how to interpret the small/medium/large benchmarks without falling for the common traps. You'll see every formula worked through with concrete numbers, not just symbols on a page. You'll also learn when to reach for Hedges' g or Glass's delta instead — because the right effect size depends on your data, and the textbook rarely tells you that.

By the end, you'll be able to read a published study, spot the reported effect size, pair it with a confidence interval, and explain in plain language what the difference between two groups actually means in practice. That skill shows up on exams, in lab reports, and anywhere you need to move beyond "the p-value was less than 0.05."

Written for high school students tackling AP Statistics or an introductory psychology or biology course, and for college freshmen who need a concise, to-the-point reference without slogging through a doorstop textbook. Short by design, stripped to essentials, and built around worked examples.

If you've ever wondered why statistical significance isn't the same as practical importance, this is the primer that answers it.

• Explain why statistical significance alone doesn't tell you how big an effect is
• Compute Cohen's d from group means and standard deviations using the pooled SD
• Interpret d using Cohen's small/medium/large benchmarks and know their limits
• Distinguish Cohen's d from related effect sizes (Hedges' g, Glass's delta)
• Read effect sizes reported in real studies and judge practical significance

1. 1. Why Effect Size? The Problem with p-Values Alone
   Motivates effect size by showing how p-values confuse statistical significance with practical importance.
2. 2. What Cohen's d Actually Measures
   Defines Cohen's d as a standardized difference between two means, in units of standard deviation.
3. 3. Computing d: The Pooled Standard Deviation
   Walks through the formula for d with the pooled SD and works numerical examples step by step.
4. 4. Interpreting d: Small, Medium, Large — and the Fine Print
   Explains Cohen's benchmarks, what they mean visually, and when they mislead.
5. 5. Cousins of d: Hedges' g, Glass's Delta, and When to Use Which
   Compares d to related effect sizes and explains small-sample bias and unequal variance cases.
6. 6. Reading and Reporting d in Real Studies
   Shows how to spot d in published research, pair it with confidence intervals, and avoid common reporting traps.