One way ANOVA

One-way ANOVA is a test that compares the means of a continuous outcome across three or more independent groups defined by a single categorical factor.

일원분산분석(One-way ANOVA)은 하나의 범주형 요인으로 구분된 세 개 이상의 독립 집단 간에 연속형 결과변수의 평균이 다른지를 검정하는 방법이다.

How do I test whether three or more group means differ?

세 개 이상 집단의 평균이 다른지 어떻게 검정하나요?

One-way analysis of variance (ANOVA) tests whether the means of a continuous outcome differ across three or more independent groups by comparing between-group variance to within-group variance. It fits when one categorical factor defines the groups and residuals are roughly normal with similar variances.

When to use One way ANOVA

• One continuous outcome compared across three or more independent groups
• Experimental conditions defined by a single factor with several levels
• Comparing average scores across categories such as regions or education levels

When to use something else

• Group variances are clearly unequal: use Welch's ANOVA with Games-Howell post hoc tests
• The outcome is ordinal or strongly non-normal in small samples: use the Kruskal-Wallis test

Assumptions and requirements

• Independent observations
• Approximately normal residuals within each group
• Homogeneity of variances across groups (checked with Levene's test)

What the analysis reports

• F statistic with between- and within-group degrees of freedom
• p-value
• Group means and standard deviations
• Effect size such as eta squared or omega squared
• Post hoc pairwise comparisons such as Tukey HSD

How to report it

A one-way ANOVA revealed a significant effect of [factor] on [outcome], F([df1], [df2]) = [value], p = [value], η² = [value].

Related methods

• Welch's ANOVA
• Kruskal-Wallis Test
• Tukey HSD Post Hoc Test

Run One way ANOVA on Quorant