SC QUALITY GUILDOne-way ANOVA
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Paste up to six groups of data and get the single-factor ANOVA table, the F test with an exact p value, group means with confidence intervals and a check on equal variances.
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Q-BotClick for an explanation of this tool.For educational use. This page is a study aid. The method behind it has far more depth and detail than one page and one tool can cover, and what you see here is not everything the method offers or everything this site offers. For full understanding and application, use the governing standards and texts, and seek further education, training or qualified advice. Results depend on the data you enter, so check them before relying on them.
What one-way ANOVA tests
Analysis of variance compares the means of three or more groups defined by one factor, such as four picking methods, three suppliers or five fixtures. The null hypothesis is that all the group means are equal; the alternative is that at least one differs. Running a t test on every pair instead inflates the overall chance of a false alarm: with four groups there are six pairs, and at α = 0.05 each, the chance of at least one false positive is far above 5 percent.
Reading the ANOVA table
- SS between (treatment, factor) measures how far the group means sit from the grand mean, weighted by group size. SS within (error) is the variation of the observations around their own group mean. They add to SS total.
- Degrees of freedom: k − 1 between, N − k within, N − 1 total, where k is the number of groups and N the number of observations.
- Mean squares are SS divided by df. F = MS between ÷ MS within. If the group means are equal, F is about 1; a large F says the differences between groups are big compared with the noise inside them.
- Compare the p value with α, or F with the critical F for (k − 1, N − k) df. R² = SS between ÷ SS total is the share of variation the factor explains.
Assumptions
The observations are independent, each group is roughly normal, and the groups have about the same variance. ANOVA is fairly tolerant of non-normality when the groups are of similar size, and less tolerant of unequal variances, especially when the group sizes differ too. The tool runs Levene's test (median version, also called Brown–Forsythe) on the absolute deviations from each group median. If it flags unequal variances, Welch's ANOVA is the usual alternative.
Common traps
- A significant F does not say which means differ. Follow up with a multiple-comparison method such as Tukey's, or look at the interval plot as a first guide.
- The group intervals here use the pooled standard deviation, the way most statistics packages draw them. Overlapping intervals do not prove the means are equal.
- One-way ANOVA handles one factor. Two factors at once, with a possible interaction, need a two-way ANOVA or a designed experiment.
On the Green Belt exam
Expect to complete a partly filled ANOVA table (find a missing df, MS or F), state the hypotheses, compare F with a critical value and say what the result means for the process. Knowing that F is a ratio of two variance estimates answers many of these questions.