Your t-test is significant at p < .001. Is the difference large? Not necessarily. With a big sample, a trivial difference can be highly significant. The effect size answers the question the p value cannot: how large is the difference or the relationship? APA style requires an effect size for every main result, and examiners increasingly ask for it in the results and discussion chapters.
This article is part of our guide How to Write a Master’s Thesis by the Mastermind PhD team and relates to our Statistical Analysis service. Sources last checked: November 2026.
What is an effect size? An effect size is a standardized number that expresses the magnitude of a difference between groups or the strength of a relationship between variables, independently of sample size. Common measures are Cohen’s d for the difference between two means, eta squared for the share of variance explained in ANOVA, and R-squared for the share of variance explained by a regression model.
Why does a thesis need an effect size?
A p value depends on two things: the size of the effect and the size of the sample. Report only p and the reader cannot separate them. The effect size isolates the first, so it lets you:
- judge practical importance, not just statistical detectability;
- compare your result with earlier studies that used different sample sizes;
- plan sample size for future work through power analysis (Cohen, 1988; Lakens, 2013).
The Publication Manual (APA, 2020) and the Journal Article Reporting Standards ask for an effect size, with a confidence interval where possible, for each primary result.
Cohen’s d: the effect size for two means
Cohen’s d is the difference between two means divided by a standard deviation, usually the pooled standard deviation:
d = (M1 − M2) ÷ SD pooled
A d of 0.50 means the groups differ by half a standard deviation. SPSS 27 and later print Cohen’s d with the t-test when you tick Estimate effect sizes. For paired samples, d is based on the standard deviation of the differences, and the software states which denominator it used. With small samples, Hedges’ g corrects a slight upward bias in d.
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Eta squared and partial eta squared: the effect size in ANOVA
Eta squared (η²) is the proportion of total variance in the dependent variable explained by a factor:
η² = SS effect ÷ SS total
Partial eta squared (ηp²) divides by the effect plus error only: SS effect ÷ (SS effect + SS error). In a one-way ANOVA the two are identical; in designs with several factors partial eta squared is larger and its values for different factors cannot be added together. SPSS prints partial eta squared when you tick Estimates of effect size under Options in the GLM procedures, so label it correctly as ηp² in your table (Richardson, 2011).
R-squared: the effect size in regression
R² is the proportion of variance in the outcome explained by all predictors together. An R² of .32 means the model accounts for 32% of the variance. Adjusted R² corrects for the number of predictors and is preferred when you compare models or have many predictors. For the contribution of one block of predictors, report the change in R² (ΔR²), and Cohen’s f² = R² ÷ (1 − R²) if your field uses it.
Which benchmarks should you cite?
Cohen (1988) proposed conventional benchmarks for when no better reference exists:
| Measure | Small | Medium | Large |
|---|---|---|---|
| Cohen’s d | 0.20 | 0.50 | 0.80 |
| Correlation r | .10 | .30 | .50 |
| Eta squared (η²) | .01 | .06 | .14 |
| Cohen’s f² (regression) | .02 | .15 | .35 |
Cohen himself described these values as a fallback. When previous studies in your area report typical effect sizes, interpret yours against them; a “small” effect on a hard outcome such as mortality can matter more than a “large” one on a self-reported attitude (Sullivan & Feinn, 2012).
How do you report an effect size in APA style?
Put the effect size right after the test statistic and p value, in italics, with two decimals:
- t-test: t(298) = 3.35, p = .001, d = 0.39, 95% CI [0.16, 0.62].
- ANOVA: F(2, 297) = 6.84, p = .001, ηp² = .04.
- Regression: R² = .32, adjusted R² = .31, F(3, 296) = 46.2, p < .001.
These values are illustrative. In the discussion chapter, translate the effect size into plain language: what a difference of 0.39 standard deviations means on your scale and for your population.
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Frequently asked questions
Can a result be significant with a small effect size?
Yes, and it is common in large samples. With 1,000 participants, a d of 0.15 can be significant while having little practical meaning. Report both and discuss the gap honestly.
Can a non-significant result have a large effect size?
Yes, usually in small samples where the estimate is imprecise. A wide confidence interval around the effect size shows that the study could not settle the question, which is worth stating in the limitations.
What effect size goes with chi-square tests?
Phi for 2 × 2 tables and Cramér’s V for larger tables, both available under Crosstabs, Statistics in SPSS.
What effect size goes with non-parametric tests?
For Mann-Whitney U and Wilcoxon, r = Z ÷ √N is widely used. For Kruskal-Wallis, epsilon squared or an eta squared based on H can be reported.
Do I need effect sizes for descriptive research questions?
No. Effect sizes accompany inferential tests of differences or relationships. Descriptive questions are answered with means, standard deviations and frequencies.
Sources
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
- Richardson, J. T. E. (2011). Eta squared and partial eta squared as measures of effect size in educational research. Educational Research Review, 6(2), 135–147. https://doi.org/10.1016/j.edurev.2010.12.001
- Sullivan, G. M., & Feinn, R. (2012). Using effect size, or why the P value is not enough. Journal of Graduate Medical Education, 4(3), 279–282. https://doi.org/10.4300/JGME-D-12-00156.1
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.); Journal Article Reporting Standards: Quantitative. https://apastyle.apa.org/jars/quantitative
Sources last checked: November 2026. This article is general educational guidance and does not replace your university regulations or your supervisor’s instructions. How we prepare our content.
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