Welch's t-test

Welch's t-test is a two-sample test of whether the means of two independent groups differ, which does not assume equal variances and uses Welch-Satterthwaite approximate degrees of freedom.

웰치 t검정은 등분산을 가정하지 않고 웰치-새터스웨이트 근사 자유도를 사용하여 두 독립 집단의 평균이 다른지를 검정하는 두 표본 검정이다.

How do I compare two group means when their variances or sample sizes differ?

두 집단의 분산이나 표본 크기가 다를 때 평균을 어떻게 비교하나요?

Welch's t-test compares the means of two independent groups without assuming equal population variances, adjusting the degrees of freedom to the variance and size of each group. Many methodologists recommend it as the default two-group test because it loses little power when the variances are in fact equal.

When to use Welch's t-test

• Two independent groups with unequal variances or unequal sample sizes
• A default two-group mean comparison without a variance pretest
• Approximately normal outcomes within each group, or reasonably large groups

When to use something else

• More than two groups: use Welch's ANOVA followed by Games-Howell post hoc tests
• Ordinal outcomes or strongly skewed data in small samples: use the Mann-Whitney U test

Assumptions and requirements

• Exactly two independent groups; a grouping variable with more levels is rejected (use Welch's ANOVA)
• Independent observations
• Continuous outcome, approximately normal within each group or with large groups

What the analysis reports

• Welch t statistic with Welch-Satterthwaite degrees of freedom
• Two-sided p-value
• Mean of each group
• Cohen's d (pooled standard deviation)
• Normality check for each group and box plot by group
• Mean difference with confidence interval

How to report it

A Welch's t-test showed that [outcome] was significantly higher in [group A] (M = [value]) than in [group B] (M = [value]), t([df]) = [value], p = [value], d = [value].

Related methods

• Independent Samples t test
• Mann-Whitney U Test
• Games-Howell Post Hoc Test

Run Welch's t-test on Quorant