Reporting ANOVA Results in SPSS
Naming the Effect Size and the Follow-Ups
Reporting ANOVA results in SPSS starts with an F statistic that carries both degrees of freedom and turns on a naming problem: the effect size SPSS prints must be labeled correctly, and every follow-up comparison must state its adjustment.
IN SHORT
The Parts of an ANOVA Write-Up, in Order
An ANOVA report gives the F statistic with both degrees of freedom and an exact p-value, a named effect size, the group means with their standard deviations, and the follow-up comparisons with their adjustment. In a factorial design the interaction is reported first, because its presence changes how the main effects are read. For reporting ANOVA results in SPSS, the values come from the ANOVA table of One-Way ANOVA or the Tests of Between-Subjects Effects table of Univariate, and labels differ slightly between releases. In-house PhD-level statisticians at OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, prepare ANOVA write-ups from the output or check existing drafts against it.
In This Guide
MODEL SUPPORT
Pages for the Model Behind the Report
A covariate changes what the F test refers to, and a design still undecided changes the whole write-up.
One-Way ANOVA
Means of three or more independent groups compared, with the assumption checks and the follow-ups planned for your design.
ANCOVA
A group comparison adjusted for a baseline measure or covariate, reported with adjusted means and their intervals.
BEFORE YOU REPORT IT
Choices the F Sentence Depends On
Each choice below changes the wording or a figure of the F sentence, which is why none can wait until the tables are open.
Which Effect Size Eta squared, partial eta squared and omega squared answer slightly different questions. Choose one in advance, name it in the sentence and keep it for every effect.
Equal or Unequal Variances If spread differs clearly across groups, Welch's F replaces the standard F and the follow-ups are chosen to match. Equal group sizes do not justify assuming equal variances.
Planned or Post Hoc Comparisons set out in the analysis plan are reported as contrasts, and those chosen after seeing the means as post hoc, each with the adjustment that was used.
One Factor or Several In a factorial design the interaction comes first. A significant interaction leads to simple effects, and the main effects are then described with care or not at all.
IN SPSS
Assembling the Sentence From the Tables
The run and the assumption checks are covered in One-Way ANOVA in SPSS: Checks and Reporting, so this guide starts from the printed tables.
Take the F, df and Sig.
From the ANOVA table of One-Way ANOVA, or the factor row of Tests of Between-Subjects Effects, take F, the effect df, the error df and Sig.
Check: The error df is the number of cases minus the number of groups or cells in the model, so it should match the sample used. A smaller figure points to cases lost to missing values.
Take the Effect Size and Name It
Take Partial Eta Squared from Tests of Between-Subjects Effects when Estimates of effect size is ticked, and name it in the text.
Watch: In a one-way design partial eta squared equals eta squared, yet the output label stays Partial Eta Squared. In a factorial design the two differ, so values from different studies are not interchangeable.
Take Means and Standard Deviations
Take the mean, Std. Deviation and N of each group from the Descriptive Statistics table, or from Descriptives under Options in One-Way ANOVA.
Tip: Put the group means with their standard deviations and n in a table, because the F sentence alone shows no direction for any difference between the groups.
Take the Welch Line Where Variances Differ
If variances differ, take the Welch statistic with df1, df2 and Sig. from the Robust Tests of Equality of Means table (One-Way ANOVA, Options).
Watch: The second degrees of freedom of Welch’s F is not a whole number. It is reported as printed, to one or two decimals, and not rounded to an integer.
Take the Follow-Up Comparisons
From the Multiple Comparisons table, take the Mean Difference (I-J), Std. Error, Sig. and 95% Confidence Interval of each pair, and name the adjustment.
Check: Confirm that the pairs reported are those the adjustment covered. Tukey’s HSD adjusts all pairs, whereas a Bonferroni correction applied by hand to a few comparisons states how many there were.
Order the Lines and Match the Rows
Put the interaction line first in a factorial design, then the effects it allows. In a one-way design begin with the F line. Match each value to its row in the output.
Check: Read the sentence against the table of means. The direction of every difference named in the text should be visible there, and each should be one that the follow-up comparisons supported.
READING THE OUTPUT
Where Each ANOVA Output Value Goes in the Report
One-Way ANOVA and the Univariate procedure print overlapping quantities under different labels, so each row names its source.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| F, df and Sig. | ANOVA table, or Tests of Between-Subjects Effects | F(effect df, error df) = ___, with p; a printed .000 becomes p < .001 |
| Partial Eta Squared | Tests of Between-Subjects Effects, with effect size estimates requested | Named as partial eta squared; in a one-way design it equals eta squared |
| Eta-squared, epsilon-squared and omega-squared, with 95% CI | ANOVA Effect Sizes table of One-Way ANOVA, in recent releases | The measure reported is named, with its interval |
| Corrected Model and Intercept rows | Tests of Between-Subjects Effects | Not reported as effects; the Intercept row tests whether the grand mean is zero |
| Welch statistic, df1 and df2 | Robust Tests of Equality of Means | Reported in place of the standard F when variances clearly differ |
| Mean Difference (I-J) and 95% Confidence Interval | Multiple Comparisons | The difference for each pair with its adjusted interval, and the adjustment named |
| Mean and Std. Deviation per group | Descriptives or Descriptive Statistics | The means table; the F sentence alone shows no direction |
| Interaction row, for example A * B | Tests of Between-Subjects Effects, factorial designs | Reported first; simple effects follow if it is present |
| Levene’s statistic | Tests of Homogeneity of Variances | Informs the Welch decision but does not make it alone |
REPORTING
An ANOVA Sentence, a Means Table and a Named Effect Size
The sentence carries the test, the table carries the direction, and the note carries the effect-size name and the adjustment.
In ANOVA APA format the F statistic carries both degrees of freedom, F(___, ___) = ___, with an exact p-value and a named effect size, followed by the means and standard deviations that show which groups differed. The frame below is for one factor with three groups, and a factorial design reports the interaction before the main effects. The effect size is named every time, for example partial η² = ___. Reporting post hoc tests in APA style means giving each difference with its interval and the adjustment used, not a significance flag alone.
A one-way ANOVA showed [a statistically significant / no statistically significant] effect of [factor] on [outcome], F(___, ___) = ___, p = ___, partial η² = ___. [Where variances differed: Welch’s F(___, ___) = ___, p = ___.] [Group A] (M = ___, SD = ___) differed from [Group B] (M = ___, SD = ___) by ___, 95% CI [___, ___], adjusted p = ___ using the [Tukey / Bonferroni] adjustment. [Group C] did not differ significantly from [Group A], ___, 95% CI [___, ___], adjusted p = ___.
| Table 1. Means, Standard Deviations and Pairwise Differences for [Outcome] | |||
|---|---|---|---|
| Group | n | M (SD) | Difference from [Reference], 95% CI |
| [Group A] | ___ | ___ (___) | Reference |
| [Group B] | ___ | ___ (___) | ___ [___, ___] |
| [Group C] | ___ | ___ (___) | ___ [___, ___] |
| Note. F(___, ___) = ___, p = ___, partial η² = ___. Differences and intervals are adjusted by [method]. | |||
Eta squared divides the effect sum of squares by the total, partial eta squared divides it by the effect plus error, and omega squared, or partial omega squared in a factorial model, reduces the upward bias of the matching eta measure. In a one-way design the first two are equal, so SPSS output labeled Partial Eta Squared can be named eta squared in a single-factor study. In a factorial design they differ, and partial values across the effects of one model do not add up to the total variance. Whichever measure is chosen is named in the text and the note, and omega squared is computed from the table where the release does not print it.
COMMON MISTAKES
Labels and Table Rows That Misreport an ANOVA
Setting the sentence beside the Tests of Between-Subjects Effects table and the Multiple Comparisons table exposes each of these in turn.
Partial Label Dropped in a Factorial Model In a model with two or more factors, partial eta squared reported as plain eta squared overstates each effect's share of the total variance, because the other factors are removed from its denominator.
Partial Values Added Into a Total Partial eta squared values from one factorial model share no common denominator, so their sum can exceed 1. They are reported effect by effect and never totaled as the variance the design explains.
Corrected Model F Quoted as the Effect The Corrected Model row tests all terms together. In a one-way model it matches the factor row, but in a factorial model it does not, and quoting it as one factor's effect reports the wrong hypothesis.
Only One df Given An F statistic with a single df hides the error df, which shows how many cases the analysis used. Both degrees of freedom belong in the parentheses after F, with the exact p-value.
Benchmarks Borrowed Across Measures Labels such as small or large, set for eta squared, are often applied to partial values from factorial models, where the same number means something different. Any label is tied to the measure and to the field.
Standard F Where Welch Was Needed With clearly unequal spread across groups the standard F can mislead, above all when group sizes differ. Welch's F and a matching follow-up are reported instead.
Unsure whether your draft says eta squared or partial eta squared? Independent Statistical Review compares each value in the paragraph with the printed tables.
FREQUENTLY ASKED QUESTIONS
Effect Size Labels, Welch Wording and Pairwise Effects
The effect size SPSS prints has a fixed label, a Welch result needs wording of its own, and each pair carries an effect size of its own.
Which effect size does SPSS print for ANOVA?
Partial eta squared in the Univariate procedure, when Estimates of effect size is ticked under Options. In a one-way design it equals eta squared and may be named as such. Recent releases add an ANOVA Effect Sizes table to One-Way ANOVA, with eta-squared, epsilon-squared, omega-squared and intervals; otherwise omega squared is computed from the sums of squares.
How is a Welch result worded when the standard F is printed too?
Only the row fixed in the plan is reported, named as Welch’s F with its fractional second df. Quoting both and choosing by the p-value is a selective choice. The effect sizes SPSS prints come from the standard sums of squares, so the sentence names the measure and does not imply an adjustment for unequal variances.
Which effect size goes beside each pairwise difference?
The mean difference with its adjusted interval is itself the effect size for a pair, in the units of the outcome. A standardized difference can be added where a field expects one, with the standardizer named, such as the pooled SD or the root mean square error. Multiple Comparisons prints no standardized value, so it is computed and labeled.
Which part of an ANOVA report does OnlineSPSS prepare?
The F sentence, the table of means and the follow-up wording can each be prepared from the saved output, or a draft of them checked against it, by an in-house PhD-level statistician at OnlineSPSS. Results Reporting & Interpretation covers this work, and what the group differences mean for your field is for the researcher to judge.
How do you protect my research data and confidentiality?
Your data and project details are handled confidentially, and project information is not published. Researcher names and institutions are not used publicly without permission. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, such as the dataset or the output you have, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Is Your ANOVA Effect
Size Named Correctly?
A reviewer reads the F sentence, the effect-size label and the adjustment together. A check of the draft against its output follows that same reading, row by row.
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