One-way ANOVA

Three or more groups.

When should I use One-way ANOVA?

You are comparing a numerical measurement across three or more separate groups. One-way ANOVA tests them together, avoiding the inflated error rate you would get from running several t-tests.

What your data needs to look like

Three or more groups of measurements.

What One-way ANOVA assumes

Chavery checks each of these against your data before it runs the test, and says whether it held. It does not ask you to assert them.

Normality (Shapiro-Wilk)

The values are spread roughly symmetrically around their average, rather than bunched at one end or dominated by a few extreme readings. When this one fails, Chavery runs Kruskal-Wallis instead.

Equal variance (Levene's test)

The groups being compared are about equally spread out. A group that varies far more than the others makes the comparison of their averages unreliable. When this one fails, Chavery runs Kruskal-Wallis instead.

What Chavery offers instead, and when

• Kruskal-Wallis — when normality does not hold.

What Chavery does with it

It checks the assumptions first and says whether each one held. When an assumption fails it names the alternative test rather than running this one anyway.

Then it reports the statistic, the p-value, a confidence interval and an effect size, and writes the sentence you would put in your results chapter. The same numbers always give the same answer; nothing is generated by a language model.

Reporting it

A p-value on its own is not a result. Chavery reports the effect size beside it, because a difference can be statistically significant and too small to matter, and an examiner will ask which yours is. More on effect size.

Not sure this is the test you need? Work through the question Chavery asks and it will name the test your design calls for.

Related tests

• Independent t-test — Do two separate groups differ on average?
• Kruskal-Wallis — Three or more groups, without assuming normality.
• Mann-Whitney U — Two groups, without assuming normality.
• One-sample t-test — Is this group's mean different from a known value?
• Paired t-test — Before and after, in the same people.
• Welch's t-test — Two groups with unequal spread.
• Wilcoxon signed-rank — Before and after, without assuming normality.