SPSS command: SPSS ONEWAY
One-way ANOVA in your browser
One-way ANOVA tests whether the mean of a scale variable differs across three or more groups of a single factor.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS ONEWAY procedure on your device, with the variance-robust Welch and Brown-Forsythe tests, η² and ω² effect sizes, polynomial trend contrasts and seven post hoc methods.
- Whether at least one group mean differs from the others (the omnibus F test), not which one.
- Whether the equal-variance assumption is credible, via Levene's test based on the mean and on the median.
- How large the group effect is: η², ε², and fixed- and random-effects ω² with confidence intervals.
- Which specific pairs differ, after correcting for multiple comparisons (Tukey HSD, Bonferroni, Šidák, Scheffé, LSD, Games-Howell, Dunnett, Hochberg's GT2, Gabriel, Tamhane's T2, Dunnett's T3 and C), and homogeneous subsets from S-N-K, Tukey's-b, Duncan, R-E-G-W F or Q and the Waller–Duncan k-ratio t test.
- Whether means rise or fall in a linear, quadratic or cubic trend across ordered groups.
When to use it
Use it when
- One continuous outcome (satisfaction score, spend, task time) compared across three or more independent groups.
- Each case belongs to exactly one group, such as region, plan tier or experimental arm.
- Group sizes are unequal or variances differ — read the Welch test and Games-Howell instead of the classical F and Tukey.
Use something else when
- Only two groups: use the independent-samples t test, which reports the same p value plus a confidence interval for the difference.
- Two or more factors or a covariate: use GLM Univariate for factorial ANOVA or ANCOVA.
- The same people measured repeatedly: use repeated-measures ANOVA or the Friedman test.
- Ordinal ratings or heavily skewed data with small groups: use the Kruskal-Wallis test.
How to run it in Crosstabs
- 01
Open your data
Open a .sav, CSV or Excel file in the workspace and switch to Statistics mode. The file is read in your browser.
- 02
Choose One-Way ANOVA
In the Compare means group, pick One-Way ANOVA (ONEWAY).
- 03
Set the Dependent list and Factor
Tick one or more scale variables in the Dependent list, then choose the grouping variable as the Factor.
- 04
Pick statistics
Under Statistics, tick Descriptive, Homogeneity of variance test, Welch, Brown-Forsythe and Estimate effect size for overall tests; optionally choose Polynomial contrasts up to cubic.
- 05
Add post hoc comparisons
Under Post hoc comparisons, choose Tukey HSD for equal variances or Games-Howell when they differ; for a control group pick Dunnett and set its control category and test direction.
- 06
Read and export
Results update as you change options. Missing values are excluded analysis by analysis by default; a declared frequency weight replicates cases.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
36 synthetic users split evenly across three onboarding flows (product tour, checklist, video); the outcome is minutes to finish setup. Values are drawn from normal distributions with a fixed seed, so every build produces the same file.
| Flow | N | Mean | Std. Deviation | 95% CI lower | 95% CI upper |
|---|---|---|---|---|---|
| Checklist | 12 | 10.74 | 1.31 | 9.91 | 11.57 |
| Tour | 12 | 11.14 | 3.41 | 8.97 | 13.31 |
| Video | 12 | 9.14 | 2.59 | 7.50 | 10.78 |
| Total | 36 | 10.34 | 2.66 | 9.44 | 11.24 |
| Item | Levene Statistic | df1 | df2 | Sig. |
|---|---|---|---|---|
| Based on Mean | 6.633 | 2 | 33 | .004 |
| Based on Median | 6.277 | 2 | 33 | .005 |
| Item | Sum of Squares | df | Mean Square | F | Sig. |
|---|---|---|---|---|---|
| Between Groups | 26.88 | 2 | 13.44 | 2.011 | .150 |
| Within Groups | 220.59 | 33 | 6.68 | ||
| Total | 247.47 | 35 |
| Item | Statistic | df1 | df2 | Sig. |
|---|---|---|---|---|
| Welch | 2.001 | 2 | 18.91 | .163 |
| Brown-Forsythe | 2.011 | 2 | 24.12 | .156 |
| (I) Flow | (J) Flow | Mean Difference (I−J) | Std. Error | Sig. | 95% CI |
|---|---|---|---|---|---|
| Checklist | Tour | −0.40 | 1.055 | .924 | −2.99 to 2.19 |
| Checklist | Video | 1.60 | 1.055 | .297 | −0.99 to 4.19 |
| Tour | Checklist | 0.40 | 1.055 | .924 | −2.19 to 2.99 |
| Tour | Video | 2.00 | 1.055 | .156 | −0.59 to 4.59 |
| Video | Checklist | −1.60 | 1.055 | .297 | −4.19 to 0.99 |
| Video | Tour | −2.00 | 1.055 | .156 | −4.59 to 0.59 |
* The mean difference is significant at the .05 level.
How to read it
The omnibus test gives F(2, 33) = 2.01, p = .150, with η² = 0.109 and ω² = 0.053. Levene's test based on the mean is significant (p = .004), so the variances differ and the Welch test is the one to report: p = .163. With 36 users the observed gap between flows (largest mean difference 2.00 minutes) is not distinguishable from chance, and no Tukey pair is significant — a reason to collect more data rather than to declare the flows equal.
Output tables explained
- Descriptives
- N, mean, standard deviation, standard error, 95% confidence interval, minimum and maximum per group and in total, plus the fixed-effects model row.
- Tests of Homogeneity of Variances
- Levene's statistic based on the mean and on the median. A small p value means the variances differ, so prefer Welch and Games-Howell.
- ANOVA
- Between- and within-groups sums of squares, degrees of freedom, mean squares, F and its significance; polynomial terms appear here when requested.
- Robust Tests of Equality of Means
- Welch and Brown-Forsythe F statistics with adjusted denominator degrees of freedom; both are asymptotically F distributed.
- ANOVA Effect Sizes
- Point estimates and confidence intervals for η², ε², and fixed- and random-effects ω². ε² and ω² are less biased than η² in small samples.
- Multiple Comparisons
- Every pair of groups with the mean difference, standard error, adjusted p value and confidence interval; Tukey HSD can also show homogeneous subsets.
Assumptions and notes
- Observations are independent and each case appears in one group only.
- Within each group the outcome is roughly normal; with 15–20 or more cases per group the F test is robust to moderate skew.
- The classical F and Tukey assume equal variances; Welch, Brown-Forsythe and Games-Howell do not.
- Under a sampling weight only weighted descriptives are shown: ordinary significance tests assume simple random sampling, so they are withheld.
How the results are validated
The ONEWAY engine is checked against SciPy 1.18 (f_oneway, tukey_hsd), statsmodels 0.15 (Brown-Forsythe) and pingouin 0.7 (Welch ANOVA, Games-Howell) on reference datasets, agreeing to a relative tolerance of 1e-9; frequency weights are tested to reproduce replicated cases exactly. The Waller–Duncan Bayesian t value agrees within 1e-7 with an independent R solution of the Waller–Kemp equation and with 30-digit mpmath quadrature over 81 combinations of k-ratio, groups, error df and F, and its homogeneous subsets match R agricolae::waller.test. Validation evidence
Questions
Should I report the classical F or the Welch test?
When group sizes are unequal or Levene's test is significant, report Welch's F and use Games-Howell for pairs. With equal sizes and similar variances both give nearly the same answer.
Which post hoc test should I choose?
Tukey HSD is the usual choice for all pairwise comparisons with equal variances. Games-Howell handles unequal variances, Dunnett compares each group with one control, and Bonferroni or Šidák suit a small number of planned comparisons.
What effect size should I report?
η² is the share of variance explained in the sample. ω² (fixed effects) corrects its upward bias and is the better estimate for the population; report it with its confidence interval.
Can I run several outcomes at once?
Yes. Put several variables in the Dependent list and each gets its own tables. Choose listwise missing-value handling if every test must use the same cases.
Is my data uploaded?
No. The workspace parses the file and runs ONEWAY in your browser; the data is not sent to Crosstabs servers.
Related procedures
- Independent-Samples T TestT-TEST GROUPS
- Kruskal-Wallis TestNPAR TESTS /K-W
- GLM UnivariateUNIANOVA
- Repeated Measures ANOVAGLM WSFACTOR
- MeansMEANS
- Bayesian One-Way ANOVABAYES ANOVA
- Free SPSS alternative: full coverage list
Run One-Way ANOVA on your own data
Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.
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