An ANOVA table partitions variation into model and residual components, converts each component to a mean square, and compares them with an F statistic. Read the rows and degrees of freedom before the p-value. A significant omnibus F says that the fitted group or term structure explains variation beyond the residual reference; it does not identify which means differ or how important the differences are.[NIST/SEMATECH (2012)]
The anatomy of the table
| Column | Reading job |
|---|---|
| Source or term | Names the group effect, factor, interaction, covariate, or residual component. |
| Sum of squares (SS) | Amount of variation assigned to that source under the chosen ANOVA type. |
| df | Independent information associated with the source. |
| Mean square (MS) | SS divided by its df. |
| F | Term mean square divided by an appropriate error mean square. |
| p-value | Tail probability for that F under the null model and assumptions. |
The residual row is not background clutter. Its mean square supplies the denominator for many F tests, and its df governs the reference distribution. R’s summary.aov documentation shows the standard term-by-term table and notes that unbalanced designs require particular care.[R Core Team (2026)]
A worked reading
Suppose the group row reports SS = 84, df = 2, MS = 42, F = 6.00, p = .004, while residual MS = 7. The arithmetic is F = 42/7 = 6. The defensible conclusion is that the data provide evidence that not all modeled group means are equal under the ANOVA assumptions.
It is not yet correct to say every group differs from every other group. The omnibus test can be driven by one contrast. Read planned contrasts or a justified post-hoc procedure next.
Why ANOVA reports F instead of t
A t test compares one signed contrast with its standard error. An omnibus ANOVA can evaluate variation among more than two means at once, so it uses a nonnegative variance ratio. For a simple two-group comparison under matching assumptions, the tests are linked: F with one numerator degree of freedom equals t². The t-test output guide covers the signed two-group table.
This section does not turn the page into a general “which test should I choose?” tutorial. It explains why the artifact in front of you contains F rather than t.
Main effects and interactions
In a factorial table, a main-effect row averages over the other factor. An interaction asks whether one factor’s effect changes across levels of another. If an interaction is substantively important, a main effect alone can hide the pattern. Examine estimated means or simple effects that match the interaction; do not interpret the two rows as independent stories.
The sum-of-squares type matters in unbalanced designs because terms can share explanatory variation. Record whether the output uses sequential, partial, or another definition before comparing tables.
Read post-hoc output after the omnibus test
Tukey’s honest-significant-difference output commonly lists each pair, its estimated difference, confidence limits, and multiplicity-adjusted p-value.[R Core Team (2026)] Read the group order, interval, and adjustment method. A pairwise interval crossing 0 remains compatible with no mean difference under that procedure.
Post-hoc significance does not supply effect magnitude. Use eta squared and partial eta squared or an appropriate contrast effect size with uncertainty. For a categorical count table rather than means, use chi-square output interpretation.
Assumptions remain outside the p-value column
The usual fixed-effects ANOVA relies on an appropriate mean structure, independent observations, and an error model suitable for the design. Check residual patterns, variance behavior, and design features. A small omnibus p-value does not certify those assumptions.
A defensible reporting sentence
“The omnibus group effect was F(2, 57) = 6.00, p = .004. Multiplicity-adjusted pairwise intervals identified the named contrast, and effect size with uncertainty was reported separately.”