One-way analysis of variance: paste each group's numbers, get the between/within decomposition, the F statistic and its exact p-value from the F distribution.
ANOVA answers "are all group means equal" in one test. Doing it with repeated t tests inflates the false-positive rate — three groups need three comparisons (14% chance of at least one spurious "significance" at α = 0.05), ten groups push it past 90%.
Frequently asked questions
What if the groups have very different variances?
Classical ANOVA assumes roughly equal variances. With clearly unequal spreads, a Welch-type ANOVA (or a non-parametric alternative) is safer; comparing the group standard deviations in the output table is the first check.
What does a significant F tell me?
Only that at least one group mean differs from the rest — not which one. Follow up with post-hoc pairwise comparisons that control the multiple-comparison error rate.
中文说明
单因素方差分析:逐组粘贴数据,得到组间/组内变异分解、F 统计量与来自 F 分布的精确 p 值。
ANOVA 用一个检验回答“各组均值是否全相等”。反复做 t 检验会放大假阳性——三组要比较三次(α = 0.05 下至少一次假“显著”的概率约 14%),十组超过 90%。
常见问题
各组方差差很多怎么办?
经典 ANOVA 假设方差大致相等。离散程度明显不一时,Welch 型 ANOVA(或非参数替代)更稳妥;先看输出表里各组标准差是最简单的检查。
F 显著说明什么?
只说明至少有一组均值与其余不同——不指明是哪一组。后续要做控制多重比较错误率的事后两两比较。