You have just run your analysis, and there it is: p = .03. Significant! Time to celebrate? Not so fast. That p-value tells you your result is unlikely to be pure chance — but almost nothing about whether the difference actually matters. A tiny, meaningless difference can be “significant” with a big enough sample, and a large, important difference can miss significance with a small one.
That is exactly the gap effect size fills. It answers the question your readers — and your examiners — really care about: how big is the effect? This guide explains what effect size is, how it differs from a p-value, the main types you will meet, how to interpret them, and how to calculate Cohen’s d with a worked example.
What Is Effect Size?
An effect size is a number that describes the magnitude of a phenomenon: how strong a relationship is, or how large a difference between groups is. Unlike a p-value, which depends heavily on sample size, an effect size is a standardised measure of size itself. It lets you compare findings across studies, even when those studies used different sample sizes or different measurement scales.
Think of it this way. A p-value answers: “Is there an effect?” An effect size answers: “How big is the effect — and should anyone care?” Good research reports both. Reporting a p-value without an effect size is like telling someone you arrived at your destination without saying how far you travelled.
Effect sizes come in two broad families:
- Difference-based effect sizes — how far apart two groups are (for example, Cohen’s d).
- Association-based effect sizes — how strongly two variables are related (for example, Pearson’s r).
Both families do the same job: they put the size of your finding on a scale your reader can understand.
Effect Size vs p-Value: What’s the Difference?
This is the confusion that trips up most students, so let us settle it clearly.
| p-Value | Effect Size | |
|---|---|---|
| Question it answers | How likely is this result if there were no real effect? | How large is the effect? |
| Depends on sample size? | Yes — heavily. Bigger samples make tiny effects “significant”. | No — it measures magnitude, not sample size. |
| What a “good” result looks like | Small, usually below .05 | Large enough to matter in practice (context decides) |
| Can you compare across studies? | Not meaningfully — p-values are not comparable | Yes — standardised effect sizes are directly comparable |
| Needed for meta-analysis? | No | Yes — meta-analyses combine effect sizes, not p-values |
Here is the classic trap. Imagine a study with 10,000 participants finds that a new study technique raises exam scores by 0.4 marks out of 100. With that many participants, the result is almost certainly “statistically significant” (p < .001). But an improvement of less than half a mark is practically meaningless. The p-value shouts “significant!”; the effect size whispers “trivial”. Both are true — and only the effect size tells you which one matters.
The reverse happens too. A small pilot study of 20 students might find a genuinely large improvement that misses significance simply because the sample is too small. The effect size would reveal the promising finding that the p-value hides. This is one reason reviewers increasingly ask for effect sizes, and why reporting them is now expected by most journals and by the APA Publication Manual (7th edition).
The Main Types of Effect Size
You do not need to memorise every effect size in existence. In student research, you will meet a handful of them again and again. Here are the ones that matter, matched to the analysis you are running.
1. Cohen’s d — for differences between two means
Cohen’s d is the workhorse of effect sizes. It measures the difference between two group means in standard-deviation units. If you compared an experimental group with a control group using an independent-samples t-test, Cohen’s d is the effect size to report. A d of 1.0 means the groups differ by one full standard deviation.
2. Pearson’s r — for the strength of a relationship
When you run a correlation, the correlation coefficient r itself is already an effect size. It ranges from −1 to +1, and its size tells you how strongly two variables move together. An r of .10 is a weak relationship; an r of .50 is a strong one. The same r can also be converted into a d, and vice versa.
3. Eta squared (η²) and partial eta squared — for ANOVA
After an ANOVA, eta squared tells you what proportion of the total variance in your outcome is explained by your grouping variable. Partial eta squared does the same job but controls for the other factors in the model, which is why SPSS reports it by default. An η² of .06 means your grouping variable explains 6% of the variance.
4. Odds ratio (OR) — for categorical outcomes
When your outcome is yes/no — passed or failed, relapsed or not — the odds ratio compares the odds of the outcome in one group against another. An odds ratio of 2.0 means the odds are twice as high in the first group. Logistic regression output is usually interpreted through odds ratios.
5. Cohen’s f — for ANOVA designs
Cohen’s f is the ANOVA counterpart of d, used when you have three or more groups or a factorial design. It is less commonly reported than eta squared, but it is the effect size that power-analysis software such as G*Power asks for when you plan an ANOVA.
6. Cramér’s V — for chi-square tests
When you run a chi-square test on two categorical variables, Cramér’s V measures how strongly they are associated, on a scale from 0 to 1. It is the categorical cousin of the correlation coefficient.
| Your analysis | Effect size to report | What it tells you |
|---|---|---|
| Independent-samples t-test | Cohen’s d | Difference between two means, in standard deviations |
| Correlation | Pearson’s r | Strength and direction of a linear relationship |
| ANOVA | Eta squared / partial eta squared | Proportion of variance explained by the grouping variable |
| Chi-square test | Cramér’s V | Strength of association between two categorical variables |
| Logistic regression | Odds ratio | How the odds of an outcome change between groups |
How to Interpret Effect Sizes
The most widely used interpretation guide comes from Jacob Cohen (1988), who proposed rough benchmarks for small, medium, and large effects:
| Effect size | Small | Medium | Large |
|---|---|---|---|
| Cohen’s d | 0.2 | 0.5 | 0.8 |
| Pearson’s r | 0.1 | 0.3 | 0.5 |
| Eta squared (η²) | 0.01 | 0.06 | 0.14 |
| Cohen’s f | 0.10 | 0.25 | 0.40 |
These benchmarks are useful starting points, but treat them as rules of thumb, not laws — Cohen himself warned that “small”, “medium”, and “large” are relative to the field. In medical research, a “small” effect can save lives; in education, a “large” effect of d = 0.8 for a teaching intervention would be remarkable. Always interpret your effect size in the context of your field and its practical consequences, and report it with its confidence interval and one plain-English sentence explaining what it means.
Worked Example: Calculating Cohen’s d Step by Step
Let us walk through a concrete example. Suppose you tested a new revision technique. Thirty students used the technique (Group A) and thirty studied as usual (Group B). On a 50-mark test, Group A scored a mean of 38, Group B scored a mean of 34, and the pooled standard deviation was 8.
Step 1: Find the difference between the means.
38 − 34 = 4 marks. That is the raw difference.
Step 2: Divide by the pooled standard deviation.
Cohen’s d = (Mean A − Mean B) ÷ pooled SD = 4 ÷ 8 = 0.50.
Step 3: Interpret.
A d of 0.50 is a medium effect by Cohen’s benchmarks. The two groups differ by half a standard deviation — in plain English, the average student using the new technique scored noticeably higher than the average student who did not.
Step 4: Report it in APA style.
“Students using the new revision technique scored significantly higher (M = 38.0, SD = 8.0) than students studying as usual (M = 34.0, SD = 8.0), t(58) = 1.94, p = .057, d = 0.50.”
Notice something interesting: with only 30 students per group, this medium-sized effect narrowly misses the .05 significance threshold — yet the effect size shows a real, meaningful difference. If you had reported only the p-value, you would have concluded “no effect”. The effect size tells the truer story. (In practice, SPSS computes Cohen’s d for you, but knowing the formula helps you understand what the number means.)
Common Mistakes to Avoid
- Reporting only the p-value. The most common mistake in student theses. Always report an effect size alongside every significance test.
- Calling a significant result “large”. “Statistically significant” means unlikely to be chance; it says nothing about size. A significant effect can be tiny.
- Treating Cohen’s benchmarks as fixed cut-offs. A d of 0.49 is not meaningfully different from a d of 0.51. Use the benchmarks as a guide and interpret in context.
- Reporting the wrong effect size for your test. A t-test needs d, an ANOVA needs eta squared, a correlation already gives you r. Matching the effect size to the analysis is part of reporting correctly.
- Ignoring the confidence interval. An effect size of d = 0.50 with a 95% confidence interval from 0.02 to 0.98 is far less certain than the same d with an interval from 0.40 to 0.60. Report the interval whenever your software provides it.
- Confusing statistical significance with practical significance. Your examiner’s real question is not “is p less than .05?” but “does this difference matter in the real world?” Only the effect size — interpreted in context — answers that.
Frequently Asked Questions
Do I need to report an effect size if my result is not significant?
Yes — arguably even more so. A non-significant result with a large effect size suggests your study may simply have been underpowered, which is a very different conclusion from “there is no effect”. Reporting the effect size lets your reader tell the difference.
What is a good effect size?
There is no universal “good” value. In psychology and education, d = 0.5 (medium) is often a solid, publishable finding; in tightly controlled laboratory studies, larger effects are common; in large-scale field research, even d = 0.2 can be important. Judge the number against what is typical — and what is practically meaningful — in your field.
Can I convert one effect size into another?
Yes. The common effect sizes are mathematically related: you can convert between d and r, and between eta squared and Cohen’s f, using standard formulas. This is especially useful in meta-analysis, where studies report different statistics.
Does my sample size affect my effect size?
Not directly. The effect size itself is independent of sample size — that is its main advantage over the p-value. However, small samples give unstable, imprecise estimates of the effect size, which is why reporting the confidence interval matters. With a very small sample, the effect size you observe may over- or understate the true effect considerably.
Where do I report effect sizes in my thesis?
In the Results chapter, right next to each test: report the test statistic, degrees of freedom, p-value, and effect size together, for example “t(58) = 1.94, p = .057, d = 0.50”. Then interpret the effect sizes in your Discussion chapter, explaining what each one means in practical terms.
The Bottom Line
A p-value tells you whether an effect is likely to be real. An effect size tells you whether it is worth caring about. Both belong in every results section you write. The next time you run an analysis, do not stop at “p < .05” — ask how big the effect is, report the right effect size for your test, give its confidence interval, and explain in one plain sentence what it means. Your examiners, your reviewers, and your future self will all be glad you did.