What is three-factor (three-way) ANOVA?
Three-way ANOVA is a factorial analysis of variance for one numeric response and three categorical factors. A full three-factor model evaluates seven terms: the three main effects, the three two-factor interactions, and the three-factor interaction. It is also called three-factor factorial ANOVA or 3-factor ANOVA.
An interaction means that the association between one factor and the response may change across levels of another factor. When an interaction is important, interpret it before summarizing main effects. A statistically significant result is evidence about the fitted model, not proof of cause or practical importance.
When should I use a three-way ANOVA?
Use it when your study has one numeric outcome and three categorical explanatory factors, and the experimental units are independent. For example, a crop study might examine variety, irrigation treatment, and fertilizer treatment against yield. If you have only one factor, start with a one-way ANOVA; with two factors, use a two-way ANOVA.
Choose a model that matches how the experiment was conducted. Statloft's current three-way analysis is a full fixed-effects model; it does not account for blocks, repeated measurements, or random effects. For those designs, use a suitable blocked, repeated-measures, or mixed-effects method instead.
Format your data for three-factor ANOVA
Use one row per independent experimental unit or replicate. Include one numeric response column and three categorical columns, one for each factor. A small example:
| Yield | Variety | Irrigation | Fertilizer |
|---|---|---|---|
| 24.1 | V1 | Low | F1 |
| 27.8 | V1 | Low | F2 |
| 31.2 | V1 | High | F1 |
Include observations for every combination of factor levels, with replication so the model can estimate residual error. Statloft stops if combinations are missing or the residual error cannot be estimated, and flags unequal cell sizes for careful interpretation. Do not enter plant subsamples as independent replicates when they belong to the same experimental unit.
Run the free 3-factor ANOVA calculator
- Open the Statloft workspace and upload a CSV or XLSX file (up to 10 MB).
- Choose Three-way ANOVA, then select the numeric response and three different factor columns.
- Run the analysis and review the model terms, p-values, effect estimates, data checks, and assumptions.
- Export the formula-free Excel results workbook for review and reporting.
Assumptions and interpretation
- Experimental units are independent; repeated observations need a different model.
- Residuals are approximately normal and have similar variance across factor combinations.
- Every selected factor combination is observed, with replication to estimate error.
- Inspect interactions before interpreting main effects, and report the design and limitations.
Statloft also offers a free DMRT calculator for supported treatment-mean comparisons. Select the dataset scope carefully; DMRT is not a replacement for a model that accounts for blocks or repeated measurements.
Frequently asked questions
Is Statloft's three-factor ANOVA calculator free?
Yes. All analysis tools and Excel reports are free during the public beta; no account or payment details are required.
Can I use an Excel workbook?
Yes. Statloft accepts CSV and XLSX files up to 10 MB and reads the first worksheet. Keep the first row for column names and use one row per observation.
Does three-way ANOVA test interaction effects?
Yes. Statloft fits the full three-factor fixed-effects model and reports all three main effects, all three two-way interactions, and the three-way interaction.