Free calculator
One-way ANOVA calculator
Paste raw values for two or more independent groups (one list per group). This page runs a one-way between-subjects ANOVA: sum of squares, degrees of freedom, mean squares, F, and a p-value (upper tail of the F distribution), plus η² effect size. It is introductory statistics—not budget “variance” in finance, not post-hoc pairwise tests in v1, and not two-way or repeated-measures designs.
When to use this calculator
Quick omnibus checks for differences among several group means before you mirror the same structure in a workbook or stats package—transparent table, not a full SPSS replacement.
- Homework or self-study: read F, df, and p from a one-factor layout with independent groups.
- Sanity-check Sheets or Excel output (Data Analysis → ANOVA: Single Factor on English Excel) against the same pasted raw values.
- See η² as a simple effect-size line alongside p (still read assumptions in your course or methods doc).
- If you only have two groups, a two-sample t-test may be enough—this page still works, but the dedicated t-test tool may match your assignment wording better.
One-way ANOVA tests whether several group means all match a single grand mean (the null idea) or whether between-group differences explain meaningful extra variation. This page uses the classical independent-groups (between-subjects) layout with one factor (the group label).
Group means and the grand mean
Each group has its own mean; the grand mean is the mean of all observations pooled. SS_between measures how far group means sit from the grand mean, weighted by n in each group.
Sums of squares (between, within, total)
SS_total is variation of every point around the grand mean. SS_within is pooled within-group variation (each value around its own group mean). SS_between is what is left in the factor part of the story: SS_total = SS_between + SS_within in this balanced textbook identity.
Mean squares and the F ratio
Divide SS_between by (k−1) and SS_within by (N−k) to get MS_between and MS_within. The F statistic is MS_between ÷ MS_within (when the denominator is positive).
p-value (upper tail of F)
The p-value shown is P(F′ > F) for an F random variable with (k−1, N−k) degrees of freedom, matching the usual omnibus one-way table. It is not a per-pair “which mean wins” result—post-hoc tests are out of scope for this v1 page.
We do not run Levene or Bartlett homogeneity tests, Shapiro–Wilk normality panels, two-way layouts, repeated measures, Welch ANOVA, or Kruskal–Wallis—add those in software when your methods require them.
For two groups only, a t-test workflow may be what your prompt names first—open the t-test calculator for summary-statistic **t** and **p** without pasting all raw rows here.
For spread on a single list (variance, SD), use the standard deviation calculator instead of this group-mean page.
Google Sheets & Excel
There is no single-cell formula for the full one-way ANOVA table in basic Google Sheets or Excel the way there is for AVERAGE. In Microsoft Excel (English) with the Analysis ToolPak enabled, use Data → Data Analysis → Anova: Single Factor and select all group columns. Per-group means line up with =AVERAGE(range). If your Excel is not in English, use Formulas → Insert function to find AVERAGE / local names; the add-in path may read differently.
=AVERAGE(A2:A20)Use one AVERAGE per group range. Layout those ranges in separate columns (or blocks) the way Anova: Single Factor expects.
Data → Data Analysis → Anova: Single FactorEnable the Analysis ToolPak first (File → Options → Add-ins on many Windows installs). Then pick your group ranges. Google Sheets has no built-in one-way ANOVA in the core grid—use an add-on or external stats for full parity.
More tools in Statistics
Browse all toolsSlide 1 of 12
Frequently asked questions
What is one-way ANOVA?
Analysis of variance (ANOVA) generalizes a two-sample comparison to three or more independent groups. One-way means a single factor (the group label). The table splits variation into between and within group parts and forms an F ratio and p-value for the omnibus “any difference in means?” question.
What does “one-way” mean?
One-way = one categorical factor with several levels (your groups). It is not “one click” in the marketing sense; it is a single-factor design. Two-way ANOVA (two factors, interactions) is not implemented here in v1.
Isn’t this the same as a t-test?
With exactly two groups, the F from one-way ANOVA is related to a pooled two-sample t (the F is the square of t under common assumptions). With more than two groups, several separate t tests would inflate the Type I error rate; ANOVA is the standard omnibus first step before planned post-hoc work.
What assumptions does classical one-way ANOVA need?
Textbook independent-groups one-way ANOVA assumes independent observations, roughly normal group distributions (especially for small n), and equal variances across groups (homoscedasticity) for the usual F null. This page does not run diagnostic plots or tests in v1—it computes the table from your numbers and states the usual equal-variance story in the methodology so you can follow your course or software checks elsewhere.
Is this for “variance” in budgets or actuals vs plan?
No. Business “variance” often means actual vs budget or percent change. This page is statistical ANOVA on raw measurements in independent groups. For % change or plan gaps, use the percentage tools in the catalog instead.
How do I match this in Microsoft Excel?
On many Windows English installs, enable the Analysis ToolPak, then Data → Data Analysis → Anova: Single Factor, and point at each group column. Group means still match =AVERAGE on each range. Mac and non-English Excel builds differ—use your language pack names and add-in path.
What is η² (eta-squared)?
A simple effect-size summary for this table: η² = SS_between ÷ SS_total (a proportion of total sum of squares associated with the group factor). It is descriptive here—not a substitute for your instructor’s partial η² or ω² definitions in advanced courses.
Do you support two-way ANOVA or repeated measures?
Not in v1. Those designs need second factors, interaction rows, or subject repeated measures—bigger tables and more assumptions. Use a statistics package for those models.
Which group is different? Can I get Tukey HSD here?
An omnibus p only says some group means differ when it is small. It does not name which pair differs. Post-hoc tests such as Tukey HSD are not on this page in v1; export the data to software that supports them under your false-positive rules.
Can I type only n, mean, and SD for each group?
Not in v1—this tool expects raw values in each group box. Some textbooks teach ANOVA from summary statistics; that mode is a possible later enhancement. For now, type or paste the underlying numbers (or one representative list if you are just exploring the UI).
How do I run this in Google Sheets without add-ons?
The core product does not include a one-click one-way ANOVA the way Excel’s Data Analysis add-in can. You can still compute group means with AVERAGE, and you can use add-ons or a separate stats tool for a full table. This web page is meant to match the textbook SS / df / MS / F layout transparently.
Is this professional statistics or research advice?
No. It is a free educational helper. For preregistration, IRB, publication, or high-stakes decisions, follow your institution’s statistics guidance and a qualified expert.