๐Ÿ“Š Analysis of Variance

ANOVA

Compare means across multiple groups simultaneously. Includes full ANOVA table, effect size (ฮทยฒ), and Tukey HSD post-hoc tests. Supports one-way and two-way designs.

Groups โ€” enter each group on a separate row
ANOVA Table

SS Between (groups):

SSB = ฮฃแตข nแตข(xฬ„แตข โˆ’ xฬ„..)ยฒ SSW = ฮฃแตข ฮฃโฑผ (xแตขโฑผ โˆ’ xฬ„แตข)ยฒ F = (SSB/dfB) / (SSW/dfW) where dfB = kโˆ’1, dfW = Nโˆ’k

Effect size (eta-squared):

ฮทยฒ = SSB / SST

Tukey HSD critical difference:

HSD = q(ฮฑ, k, dfW) ร— โˆš(MSW/nโ‚•)
Design Setup

Enter data for a balanced two-way ANOVA. Each cell may contain multiple replicates (comma-separated). Leave empty cells blank for equal replication.

Two-Way ANOVA Table

For balanced design with a levels of A, b levels of B, n reps per cell:

SS_A = bn ร— ฮฃแตข(xฬ„แตข. โˆ’ xฬ„..)ยฒ SS_B = an ร— ฮฃโฑผ(xฬ„.โฑผ โˆ’ xฬ„..)ยฒ SS_AB = n ร— ฮฃแตข ฮฃโฑผ (xฬ„แตขโฑผ โˆ’ xฬ„แตข. โˆ’ xฬ„.โฑผ + xฬ„..)ยฒ SS_err = ฮฃแตข ฮฃโฑผ ฮฃโ‚– (xแตขโฑผโ‚– โˆ’ xฬ„แตขโฑผ)ยฒ