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Two-Way ANOVA Calculator: Full Table, F, and p-Value

Run a two-way or one-way ANOVA in your browser: sums of squares, df, mean squares, F, and p for every effect, with the balanced-design and interaction conventions stated on the page.

Paste a factorial grid and get the whole table at once: every sum of squares, its degrees of freedom, its mean square, its F, and its p. The calculator reads your cell counts, tells you whether it is estimating an interaction, and shows the conventions it applied so you can cite them.

Design

Paste your data and run the calculator to see the full ANOVA table.

F = MS_effect / MS_error; p = 1 - fCdf(F, df1, df2) How?

How this is calculated

Sums of squares use centered two-pass sums to stay stable. In one-way ANOVA the between-groups mean square is tested against the within-groups mean square. In two-way ANOVA every F ratio uses the error mean square as its denominator, because this is a fixed-effects model. The p is the upper-tail area of the F distribution; ANOVA is one-sided and is never two-tailed.

Formula: F = MS_effect / MS_error; p = 1 - fCdf(F, df1, df2)

See Sources below

Model, design, and the conventions this page applies

Design and model. This calculator runs fixed-effects ANOVA on balanced designs. Every F ratio uses the error mean square as its denominator. Random-effects and mixed models change that denominator and are out of scope here.

Balanced-design convention. Every cell holds the same number of observations, so the Type I, Type II, and Type III sums of squares are identical here and the choice among them does not arise. Unequal cell sizes are refused with a message that names the balanced-design requirement.

Interaction and replication. With two or more observations per cell the tool estimates the row-by-column interaction against pure error. With one observation per cell the design is a randomized complete block: there is no separable interaction, and the residual carries what an interaction would have measured. The tool detects which case you gave it and labels the table accordingly.

Effect size. Eta squared is reported per effect as its sum of squares divided by the total sum of squares. Partial eta squared and omega squared are not shown in this version.

Summary input. The one-way summary path reads a count, a mean, and a sample standard deviation per group, and uses the sample convention (divisor n minus 1) for the within-groups sum of squares.

What the F test does and does not check. ANOVA assumes independent observations, roughly normal residuals, and comparable variances across cells. This page reports the F test. It does not run the homogeneity or normality checks those assumptions call for.

Sources

  1. NIST/SEMATECH e-Handbook of Statistical Methods, 7.4.3.4 Are the means equal? (one-way F, resistor example). NIST/SEMATECH.
  2. anova2: Two-way analysis of variance (popcorn example). MathWorks.
  3. STAT 502: Analysis of Variance and Design of Experiments. Penn State Eberly College of Science.
  4. Two-way ANOVA without replication. GraphPad Prism Statistics Guide.

How we choose and check our formulas