One-Way ANOVA
Test whether 3+ group means differ significantly. E.g., do three machines produce different dimensions? Do four suppliers provide equal material strength?
A process engineer suspects that parts produced by three different machines have systematic differences in outer diameter and needs statistical confirmation rather than gut feeling. One-way ANOVA compares multiple group means simultaneously, avoiding the α inflation caused by repeated t-tests, and is the standard method for equipment consistency verification. Quality engineers also use ANOVA to analyze the effect of different operators, shifts, or material lots on quality characteristics and identify significant sources of variation.
Measure outer diameter of 10 parts from each of three machines (mm): Machine A: mean 10.02, s = 0.08 Machine B: mean 10.15, s = 0.09 Machine C: mean 9.98, s = 0.07 ANOVA result: F = MS(between) / MS(within) = 4.35 p = 0.018 < 0.05 → Reject the null hypothesis; the three machines differ significantly in outer diameter → Run Tukey post-hoc tests to identify which groups differ
FAQFrequently Asked Questions
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Box Plot
Before running ANOVA, use a box plot to visualize each group's distribution and outliers for a quick check of between-group differences.
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ANOVA compares effects of categorical factors while regression quantifies relationships between continuous variables; both are often combined in DOE.
Open toolMann-Whitney U Test
If data are not normally distributed, use Mann-Whitney (two groups) or Kruskal-Wallis (multiple groups) as non-parametric alternatives to ANOVA.
Open tool