Three or more groups, one numeric outcome, and the question of whether any of them genuinely differ. What the test answers, how Quanta runs it, what every card on the result means, and how to report it in APA 7.
A one-way ANOVA compares the mean of one numeric outcome across three or more groups. Three teaching methods. Five role levels. Four clinic sites. Each person belongs to exactly one group.
You could compare the groups two at a time with t tests, but every additional test is another chance at a false alarm, and with five groups that is ten comparisons and a badly inflated error rate. ANOVA asks one question first: is anything going on among these groups at all.
The name describes the method. It splits the total spread in your outcome into the spread between group means and the spread within each group. The statistic it returns, F, is the first divided by the second, signal over noise. A large F means the gaps between groups tower over the ordinary scatter inside them.
An ANOVA that reaches significance tells you the groups are not all alike. It does not tell you which ones differ. That is what the post-hoc comparisons are for, and reporting the omnibus result as though it identified a specific difference is the most common error in this analysis.
Independence. One row per person, each person in one group. A property of your design, so no software can verify it.
Roughly normal within groups. The test tolerates moderate departures, particularly at larger sample sizes. Quanta does not stop you on a normality flag; it raises the flag and runs a nonparametric alternative alongside so you can see whether the conclusion depends on the assumption.
Similar spread across groups. This is the one that changes which test you should read. Quanta runs Levene and Brown-Forsythe and states each verdict in plain words. When variances are unequal, the Welch F is the version to report.
Where the outcome is ordinal, or the differences are driven by a few extreme values, Kruskal-Wallis is the nonparametric counterpart and Quanta reports it beside the ANOVA by default.
Lay the data out in long format. One row per person, one column holding the group label, one column holding the numeric outcome. If your groups currently sit in separate columns, reshape before you run.
Bring in the data. Import from CSV, Excel, SPSS .sav, Stata .dta, or a ReliCheck survey package. Quanta reports rows, columns, and missing cells as the file lands, so a bad import shows itself before it becomes a bad result.
Choose one numeric dependent variable and one categorical independent variable in the Setup panel on the right. A demographic, a status, a condition, or a grouped item response all work. The analysis reports Ready once the pair is valid, and results appear in the center.
Look before you test. Descriptives and Explore gives the mean, median, skewness, histogram, and box plot. Two minutes here catches the coding errors that no assumption test will flag.
Quanta returns the result as evidence cards in the order a results section is written. The run opens with the selected test, F with both degrees of freedom, p, and the number of cases used, including how many rows were dropped for a missing group.
Plain-language result. The finding in a sentence, the groups included with their sample sizes, and a practical-size line. It says whether a clear difference was detected, not merely whether p crossed a threshold.
Analysis decision. The variant that ran and why, the post-hoc method being used, and the sensitivity analysis Quanta ran alongside it. The reasoning is on the page rather than in your memory of what you clicked.
Descriptives. N, mean, standard deviation, standard error, 95% confidence interval, and range for every group, with a total row.
Homogeneity of variance. Levene and Brown-Forsythe with F, both degrees of freedom, p, and a plain sentence saying whether unequal variances were flagged.
Omnibus tests. The full between-groups, within-groups, and total table, and then the part that matters: Welch, Brown-Forsythe F*, and Kruskal-Wallis reported beside the classic F rather than hidden behind a menu. When every version agrees, you can report the result without hedging. When they disagree, you have learned something before a reviewer finds it.
A Bayes factor with the prior stated. BF10 with a JZS fixed-effects prior, r scale 0.5, and a plain sentence naming the strength of evidence. On a null result this is the difference between moderate evidence for no group differences, which is a finding, and not enough evidence to say, which is not.
Post-hoc comparisons. Tukey HSD, in the Tukey-Kramer form that handles unequal group sizes, with family-wise adjusted p values and 95% intervals from the studentized range distribution. Every pair, with mean difference, standard error, t, df, raw p, and adjusted p.
Effect sizes. Eta squared, omega squared, and the Kruskal epsilon squared, with an interpretation line. Omega squared is the less biased estimate and the one reviewers increasingly ask for.
Assumption warnings and the report-ready summary. Flags stated in sentences with a severity, then the finding in careful language with explicit guardrails: do not claim causation from a group comparison, do not claim which groups differ without post-hoc evidence, do not ignore assumption warnings when reporting significance.
Report F with both degrees of freedom, p, and an effect size. Name the variant if it was not the classic F.
A one-way ANOVA found no statistically significant difference in job performance across role levels, F(4, 245) = 1.94, p = .105, η² = .03. A Bayes factor indicated moderate evidence for no group differences, BF10 = 0.23.
State the post-hoc method and that p values were family-wise adjusted. An unadjusted pairwise comparison after a significant ANOVA undoes the protection the omnibus test just gave you.
When the omnibus test is not significant, do not report the pairwise comparisons as findings. Quanta writes that caution into the summary, and it is worth heeding.
Every result carries a ReliCheck Intelligence card with one action: explain this result in plain language. It runs entirely on your Mac with Apple Intelligence. No upload, no API key, nothing to configure. The model only explains the result Quanta has already computed and validated. It never computes a statistic, and it never applies a decision on your behalf.
From the action bar you can add the result to a report, copy the table, or copy the APA text. Exported reports carry the APA table, its note, and a caution specific to that analysis beneath it.
Quanta's t tests, ANOVA, and ANCOVA are validated against R's t.test, aov, and car, matched exactly. Tukey adjusted p values and intervals come from the studentized range distribution, validated against R. The engine is pure Swift with no R or Python at runtime. Full record on the validation page.
Compare Means is part of every Quanta subscription, $9.99 a month or $79.99 a year after the 30-day trial. One price for everyone. See pricing.
The analysis, the report builder, and the on-device explanations all work with the network off. Your dataset is never uploaded.
Independent-samples t test for exactly two groups · Kruskal-Wallis when the outcome is ordinal or badly skewed · ANCOVA to adjust for a covariate · the complete list on the analyses page.