What is an effect size?
You might have come across the term ‘effect size’ in your statistics course. It’s one of those things lots of students pretend to understand…but don’t really. Or you might know how to use a table to determine the if the Cohen’s D value is small, medium or large without knowing what that actually means.
Don’t worry, here’s a simple explanation that actually makes sense.
First off, let’s zoom out and understand the big picture of what statistics is really concerned about.
In a nutshell, stats is concerned with 2 questions:
- Are these variables actually related? Or is it random chance?
- If they are related. How…strong is this relationship?
To put it simply: an effect sizes answer the second question.
Effect sizes are numbers that tell you how big a difference or relationship between values is.
Important note! The effect size is NOT the same as the p value. They give us completely different information.
So…it’s not the same as the p value?
Correct.
The p value tells us whether the relationship even exists. It answers the first question and tells us whether the correlation between variables is actually statistically significant…or if it’s just chance.
Think about it this way. The p value might tell you that there is a statistically significant relationship between drinking coffee and exam performance.
Cool. But, how much does exam performance improve with the coffee? Are we talking a tiny improvement? Moderate? Massive?
That’s what the effect size tells you.
The 3 main things effect sizes can measure
1. Distance between groups
A great of example of this is Cohen’s D and t-tests. In a t-test, we are comparing the average scores between two groups. The larger the difference in the scores…the greater the difference between the two groups, right?
The greater the distance between the groups, the stronger the effect is. Think back to our coffee example.
Let’s say group 1 completes the exam with no coffee and group 2 are provided with coffee. For the effect strength of the coffee to be significant, we would expect a big gap between the marks of the 1st and 2nd group.
Or in other words, if we were to run a t-test, we would expect a moderate to large Cohen’s D value.
Cohen’s d example (distance between groups)
| Group | Mean Score | Standard Deviation |
|---|---|---|
| No Coffee | 70 | 8 |
| Coffee | 78 | 8 |
Cohen’s d = 1.0
Interpretation:
Students who drank coffee scored about one full standard deviation higher than those who didn’t.
2. Strength of relationships
Some effect sizes measure the strength of a relationship between two variables. We call this a correlation.
An example of this would be Pearson’s correlation coefficient. Or you might see it as r.
Unlike Cohen’s D, correlation coefficients aren’t measuring the differences between groups. They are looking at how one variable directly influences another.
You could run a correlation test on the relationship between Coffee and exam marks. As the amount of caffeine in a person increases, do their marks also increase? Is there a connection between these two values?
A higher correlation value = a stronger relationship
Pearson’s r example (strength of relationship)
Now imagine instead of groups, we measure how much coffee students drank and their exam score.
| Student | Cups of Coffee | Exam Score |
|---|---|---|
| A | 0 | 68 |
| B | 1 | 72 |
| C | 2 | 76 |
| D | 3 | 82 |
| E | 4 | 88 |
Correlation (r) = 0.82
Interpretation:
There is a strong positive relationship between coffee consumption and exam score.
3. Amount of variance explained
Other effect sizes might measure how much of the outcome is explained by the variable you are studying.
We know that everything is influenced by complex interaction of multiple variables.
A student performing better in an exam might have had better sleep the night before, in addition to the coffee.
A student in the no-coffee group might have been sick, causing them to perform below average.
Effect sizes such as regression effects can help us determine how much of the variation in our data is attributed to our chosen variable.
If the effect size is large? A large chunk of variation is due to the variable. If it’s small? Most of the variation is actually coming from other variables.
Regression example
A regression model predicts exam score from coffee intake.
R² = 0.67
Interpretation:
67% of the variation in exam scores is explained by coffee consumption.
That’s a large proportion.
It means coffee explains most of the performance differences in this sample.
The remaining 33% is due to other factors.
Common effect sizes & interpretation
| Effect Size | Small | Medium | Large | What It Means |
|---|---|---|---|---|
| Cohen’s d | 0.2 | 0.5 | 0.8+ | Distance between two group means |
| Pearson’s r | 0.1 | 0.3 | 0.5+ | Strength of relationship between variables |
| R² / η² | 0.02 | 0.13 | 0.26+ | Amount of variance explained |
*Make sure to check your university’s specific ranges and cut-offs
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