Why Report Cohen's d?
Statistical significance (p values) tells you whether an effect exists, but not how large it is. Cohen's d fills this gap by quantifying the magnitude of the difference between two groups in standardized units.
APA 7th edition explicitly requires effect sizes alongside significance tests. Cohen's d is the most widely reported effect size for comparing two means, making it essential for t-tests, ANOVA post-hoc comparisons, and meta-analyses.
Essential Components for APA Reporting
When reporting Cohen's d in APA 7th edition format, include:
- Effect size value: Cohen's d to two decimal places
- Direction: which group scored higher
- 95% confidence interval: [lower, upper] when available
- Interpretation: small, medium, or large per Cohen's benchmarks
- Context: alongside the corresponding t or F statistic
Cohen's d Benchmarks
Cohen (1988) proposed these widely used interpretation guidelines:
| d | Interpretation | Meaning | |-----|---------------|---------| | 0.20 | Small effect | Difference is real but difficult to see with the naked eye | | 0.50 | Medium effect | Difference noticeable to a careful observer | | 0.80 | Large effect | Difference obvious and substantial |
Additional reference points used in recent literature:
| d | Interpretation | |-----|---------------| | < 0.20 | Negligible | | 0.20-0.49 | Small | | 0.50-0.79 | Medium | | 0.80-1.19 | Large | | ≥ 1.20 | Very large |
Important: These are general guidelines, not rigid cutoffs. A d of 0.30 in clinical research may be practically significant if the outcome is life-threatening. Always interpret effect sizes in the context of your field.
How Cohen's d Is Calculated
For Independent Samples t-Test
d = (M1 - M2) / SDpooled
Where SDpooled = √[(SD12 + SD22) / 2]
For Paired Samples t-Test
d = Mdiff / SDdiff
Some researchers use the pre-test SD or the average of both SDs as the standardizer. Specify which formula you used.
Converting From t
d = 2t / √df (for equal group sizes)
d = t √(1/n1 + 1/n2) (for unequal group sizes)
Reporting Cohen's d With Independent Samples t-Test
Basic Template
The treatment group (M = X.XX, SD = X.XX) scored significantly higher than the control group (M = X.XX, SD = X.XX), t(df) = X.XX, p = .XXX, d = X.XX.
Complete Example
Scenario: Comparing exam scores between a tutored group (n = 30) and a non-tutored group (n = 30).
Students who received tutoring (M = 82.40, SD = 8.50) scored significantly higher on the final exam than students who did not receive tutoring (M = 74.60, SD = 9.20), t(58) = 3.43, p = .001, d = 0.88, 95% CI [0.34, 1.41]. The effect size indicated a large difference between groups.
Reporting Cohen's d With Paired Samples t-Test
Complete Example
Scenario: Pre-post anxiety scores for 25 participants.
Anxiety scores decreased significantly from pre-test (M = 45.80, SD = 10.20) to post-test (M = 38.50, SD = 9.80), t(24) = 4.12, p < .001, d = 0.82, 95% CI [0.38, 1.26]. This represents a large effect.
Reporting Cohen's d in ANOVA Post-Hoc Comparisons
When conducting pairwise comparisons after a significant ANOVA, report d for each pair:
Bonferroni-corrected post-hoc comparisons revealed that Group A (M = 78.30) scored significantly higher than Group C (M = 65.10), p < .001, d = 1.12. The difference between Group A and Group B (M = 73.50) was not significant, p = .089, d = 0.41. Group B scored significantly higher than Group C, p = .003, d = 0.72.
Cohen's d vs. Other Effect Sizes
| Effect Size | Used With | Range | When to Use | |------------|-----------|-------|-------------| | Cohen's d | Two-group comparisons | 0 to ∞ | t-tests, pairwise comparisons | | η2p | ANOVA (3+ groups) | 0 to 1 | Overall F-test effect | | r | Correlations, Mann-Whitney U | -1 to 1 | Nonparametric tests | | Odds ratio | Logistic regression | 0 to ∞ | Binary outcomes |
Use Cohen's d for pairwise comparisons and η2p for the overall ANOVA effect.
Common Mistakes to Avoid
1. Omitting the Effect Size Entirely
APA 7th edition requires effect sizes. Never report only t and p values without d.
2. Using Wrong Benchmarks
Cohen's benchmarks (.20, .50, .80) apply to d, not to r or η2. Each effect size has its own benchmarks.
3. Not Specifying the Formula
For paired designs, different formulas yield different d values. State which standardizer you used (pooled SD, pre-test SD, or SD of differences).
4. Ignoring Confidence Intervals
A point estimate of d = 0.50 is less informative than d = 0.50, 95% CI [0.05, 0.95]. Include CIs when your software provides them.
5. Over-Interpreting Small Samples
Effect sizes from small samples have wide confidence intervals. A d of 1.20 from n = 10 per group is much less reliable than d = 0.50 from n = 200 per group.
Try It With Your Own Data
Calculate Cohen's d automatically with our free t-test calculator, which provides the effect size, 95% confidence interval, and a ready-to-copy APA results sentence. For ANOVA post-hoc comparisons, use our one-way ANOVA calculator.