How to use this calculator
Enter each group’s observations on its own line. The calculator tests whether all group means are equal and, if not, which pairs differ.
Formulas
TreatmentsSSTr = Σni(ȳi − ȳ)², df = a − 1
ErrorSSE = SST − SSTr, df = N − a
TestF0 = MSTr/MSE
Worked example
Tensile strength of paper at four hardwood concentrations (the default; Montgomery Example 13-1)
- Group means 10.00, 15.67, 17.00 and 21.17; grand mean 15.96.
- SSTr = 382.79 (df 3), SSE = 130.17 (df 20), so MSTr = 127.60 and MSE = 6.51.
- F0 = 19.61, P = 3.6 × 10⁻⁶: hardwood concentration affects strength.
Frequently asked questions
What does ANOVA assume?
Independent observations, normal errors and equal variances in every group. Check with residual plots.
Why not just do t-tests on every pair?
Many t-tests inflate the chance of a false positive. ANOVA tests all means at once; LSD comparisons then follow only if it rejects.