A p-value tells you whether a difference is statistically significant. It does not tell you whether that difference is big, small, or worth caring about. That is the job of an effect size — and it is the number examiners, reviewers, and journal editors increasingly expect to see next to every p-value in your results section.
In this tutorial, you will learn the two effect sizes you will use most often in SPSS: Cohen’s d for comparing means, and eta-squared for ANOVA. You will see exactly where to click to get each one, how to read the output, and how to report both in APA style (7th edition).
Why p-values alone are not enough
Imagine two studies. Both compare exam scores between two teaching methods, and both find a statistically significant difference with p = .03. In the first study, the average difference is 12 marks. In the second, it is 1 mark. The p-values look the same, but the findings are very different in practical terms.
This happens because a p-value is heavily influenced by sample size. With a large enough sample, even a tiny difference becomes “significant.” An effect size solves this problem: it measures the size of the difference or association in standardised units, largely independent of sample size. Reporting it lets your reader judge practical importance, not just statistical significance.
Two rules to remember throughout this tutorial: always report an effect size alongside a p-value, never instead of one — the two answer different questions. And an effect size is a descriptive summary of your data; it does not need a significance test of its own.
Cohen’s d: the effect size for comparing two means
Cohen’s d expresses the difference between two group means in standard deviation units. A d of 1.00 means the two means differ by one full standard deviation. A d of 0.50 means they differ by half a standard deviation.
How to interpret Cohen’s d
The conventional benchmarks, suggested by Jacob Cohen and still widely used as rough guides, are: d = 0.20 — small effect; d = 0.50 — medium effect; d = 0.80 — large effect.
Treat these as starting points, not verdicts. What counts as “large” depends on your field. In education research, a d of 0.40 might be an important result. In a drug trial, a much larger effect might be expected. Always interpret d in the context of your study, and report the actual means and standard deviations alongside it so readers can judge for themselves. Note that Cohen’s d can also be negative, depending on which group you subtract from which. The sign simply tells you the direction of the difference; the size of the effect is the absolute value.
Getting Cohen’s d in SPSS: independent-samples t-test
Suppose you want to compare test scores between a control group and an intervention group. Here is the click-by-click route in recent versions of SPSS:
1. Go to Analyze > Compare Means > Independent-Samples T Test.
2. Move your outcome variable (for example, Test Score) into the Test Variable(s) box.
3. Move your grouping variable (for example, Group) into the Grouping Variable box, then click Define Groups and enter the two group codes.
4. Click the Options button, or look for the effect size option in the main dialog, and make sure “Estimate effect sizes” is ticked. In newer SPSS versions this appears as a checkbox in the main dialog.
5. Click OK.
SPSS produces two tables: the familiar Independent Samples Test table and a new Independent Samples Effect Sizes table. In the effect sizes table, look at the row labelled “Cohen’s d” and the column “Point Estimate.” That value is your effect size. The table also gives a 95% confidence interval for d, which you should report if your institution or journal asks for it.
Getting Cohen’s d for a paired-samples t-test
For before-and-after designs, the route is similar:
1. Go to Analyze > Compare Means > Paired-Samples T Test.
2. Move your two paired variables (for example, Score Before and Score After) into the Paired Variables box.
3. Tick “Estimate effect sizes” if it is shown as an option.
4. Click OK.
The Paired Samples Effect Sizes table again gives Cohen’s d as a point estimate. Be aware that SPSS standardises the mean difference by the standard deviation of the differences for paired designs, so a paired d is not directly comparable to an independent-samples d from a different study. Report which design you used so readers are not misled.
Paste-ready SPSS syntax for Cohen’s d
If you prefer syntax, or you want a reproducible record of exactly what you ran, use the following. Replace the variable names with your own:
* Independent-samples t-test with Cohen’s d.
T-TEST GROUPS=Group(1 2)
/MISSING=ANALYSIS
/VARIABLES=TestScore
/CRITERIA=CI(.95)
/ES DISPLAY(TRUE).
* Paired-samples t-test with Cohen’s d.
T-TEST PAIRS=ScoreBefore WITH ScoreAfter (PAIRED)
/CRITERIA=CI(.95)
/MISSING=ANALYSIS
/ES DISPLAY(TRUE).
The /ES DISPLAY(TRUE) subcommand is what tells SPSS to produce the effect sizes table. If you are using an older SPSS version that does not support it, you can still compute d by hand from the group means and pooled standard deviation shown in the Group Statistics table.
Eta-squared: the effect size for ANOVA
Eta-squared is the effect size most often reported with ANOVA. It tells you what proportion of the total variation in your outcome variable is explained by your grouping factor. An eta-squared of 0.12, for example, means that 12% of the variance in scores is associated with group membership.
Partial eta-squared: the value SPSS actually gives you
Here is a common source of confusion. SPSS reports partial eta-squared, not eta-squared, in its ANOVA tables. The two are related but not identical: eta-squared divides the effect sum of squares by the total sum of squares, while partial eta-squared divides the effect sum of squares by the effect sum of squares plus the error sum of squares, leaving out variance explained by other factors.
In a one-way ANOVA with a single factor, eta-squared and partial eta-squared are the same number. In factorial ANOVA or ANCOVA, they differ, and partial eta-squared will be larger. The important rule is simple: report the value SPSS gives you, and label it correctly as partial eta-squared. Do not call it eta-squared when it is partial eta-squared, and vice versa.
How to interpret partial eta-squared
The conventional benchmarks, again from Cohen, are: 0.01 — small effect; 0.06 — medium effect; 0.14 — large effect. As with Cohen’s d, use these as rough guides only. In a tightly controlled experiment, a small partial eta-squared might still matter. In a noisy field study, a medium effect might be a strong result. Context beats cut-offs.
Getting eta-squared in SPSS: one-way ANOVA
1. Go to Analyze > Compare Means > One-Way ANOVA.
2. Move your outcome variable into the Dependent List box and your grouping variable into the Factor box.
3. Click Options, and tick “Estimates of effect size” under the Statistics section.
4. Click Continue, then OK.
In the ANOVA table, a new column appears on the right: “Partial Eta Squared.” That is your effect size for the overall group difference.
Getting partial eta-squared in SPSS: factorial ANOVA and ANCOVA
For designs with two or more factors, or a covariate, use the General Linear Model route:
1. Go to Analyze > General Linear Model > Univariate.
2. Move your outcome variable into the Dependent Variable box, your grouping variables into Fixed Factor(s), and any covariate into the Covariate(s) box.
3. Click Options, and tick “Estimates of effect size” under Display.
4. Click Continue, then OK.
The Tests of Between-Subjects Effects table now includes a Partial Eta Squared column for every effect: each main effect, each interaction, and the covariate. Report the value for the effect you are describing, not just the largest one in the table.
Paste-ready SPSS syntax for eta-squared
* One-way ANOVA with eta-squared.
ONEWAY TestScore BY Group
/STATISTICS DESCRIPTIVES
/ES DISPLAY(TRUE)
/MISSING ANALYSIS.
* Factorial ANOVA / ANCOVA with partial eta-squared.
UNIANOVA TestScore BY Group Method WITH PretestScore
/METHOD=SSTYPE(3)
/PRINT=ETASQ DESCRIPTIVE
/CRITERIA=ALPHA(.05)
/DESIGN=Group Method Group*Method PretestScore.
The /PRINT=ETASQ subcommand is what produces the partial eta-squared column in the General Linear Model output.
How to interpret the output: a worked example
Suppose you run an independent-samples t-test comparing exam scores for students taught with two methods. Your output shows a mean of 72 for Method A and 64 for Method B, with p = .012 and Cohen’s d = 0.68. Here is how to read that together: the p-value (p = .012) says the difference is unlikely to be due to chance alone; Cohen’s d (d = 0.68) says the difference is just over two-thirds of a standard deviation — a medium-to-large effect by conventional benchmarks; and the means themselves (72 vs 64) say the difference is 8 marks in real terms.
Now suppose an ANOVA comparing three teaching methods gives F(2, 87) = 5.42, p = .006, partial eta-squared = 0.11. The reading is: the F-test says the three group means are not all equal; partial eta-squared (.11) says group membership accounts for about 11% of the variance in scores — a medium-to-large effect; and the F-test alone does not say which groups differ — you still need post-hoc tests to find out, and you can report Cohen’s d for the pairwise comparisons that matter.
Notice the pattern: the test statistic answers “is there a difference?”, the effect size answers “how big is it?”, and the means answer “what does it look like in real units?” A complete results section gives the reader all three.
Reporting in APA style (7th ed.)
APA style (7th edition) expects effect sizes to be reported alongside test statistics. The general pattern is: test statistic, degrees of freedom, p-value, effect size — in that order, in the same sentence.
For an independent-samples t-test with Cohen’s d: Students taught with Method A (M = 72.40, SD = 8.10) scored significantly higher than students taught with Method B (M = 64.20, SD = 9.30), t(58) = 2.58, p = .012, d = 0.68.
For a one-way ANOVA with partial eta-squared: Teaching method had a significant effect on exam scores, F(2, 87) = 5.42, p = .006, partial eta-squared = .11.
A few APA formatting points to get right: report effect sizes to two decimal places, just like p-values. Use the Greek letter for eta-squared, with a subscript p for partial eta-squared. Do not put a leading zero before the decimal point for values that cannot exceed 1, so write partial eta-squared = .11, not 0.11. Cohen’s d can exceed 1, so it keeps its leading zero where applicable (d = 0.68). If you report a confidence interval for Cohen’s d, place it after the point estimate: d = 0.68, 95% CI [0.15, 1.20]. Name the effect size you are reporting — writing “the effect size was .11” without saying which one forces the reader to guess.
One common mistake is reporting the effect size for the wrong effect. In a factorial ANOVA, each factor and interaction has its own partial eta-squared. Make sure the value in each sentence matches the effect that sentence is about.
Key Takeaways
- A p-value tells you whether a difference is significant; an effect size tells you whether it is big. Report both, every time.
- Use Cohen’s d when you compare two means (t-tests). Rough benchmarks: 0.20 is small, 0.50 is medium, 0.80 is large.
- Use (partial) eta-squared with ANOVA. Rough benchmarks: .01 is small, .06 is medium, .14 is large.
- In SPSS, tick “Estimate effect sizes” for t-tests and “Estimates of effect size” for ANOVA — or use the /ES and /PRINT=ETASQ syntax options.
- SPSS reports partial eta-squared, not eta-squared. Label it correctly, especially in factorial designs.
- In APA style, report the test statistic, degrees of freedom, p-value, and effect size together, and always give the group means and standard deviations too.
Frequently asked questions
Do I need an effect size if my result is not significant?
Yes. A non-significant result with a large effect size tells a very different story from a non-significant result with a tiny one. The first may mean your study lacked power; the second suggests there really is little or no effect. Reporting the effect size lets readers tell the difference.
Can I convert between Cohen’s d and eta-squared?
Approximate conversions exist, but they are only valid in simple two-group designs, and they are rarely needed. The cleaner approach is to report the effect size that matches your analysis: d for t-tests, eta-squared for ANOVA. If a journal asks for a specific measure, convert it and say that you did.
Why does SPSS give me partial eta-squared instead of eta-squared?
Because in general linear models with several factors, partial eta-squared is the standard summary for each individual effect, independent of the other effects in the model. In a one-way ANOVA the two values are identical, so nothing is lost. Just label the value correctly.
What if my SPSS version has no effect size option?
Versions of SPSS before 27 do not include the built-in effect size output for t-tests. You can still compute Cohen’s d by hand: subtract one group mean from the other and divide by the pooled standard deviation, both of which appear in the Group Statistics table. For ANOVA, eta-squared can be computed from the sums of squares in the ANOVA table.
Should I report Cohen’s d or Hedges’ g?
SPSS reports both Cohen’s d and Hedges’ g in its effect sizes table. Hedges’ g applies a small correction for sample size and is slightly more accurate with small samples. Either is acceptable, but pick one, name it, and use it consistently throughout your paper.
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