首页Home › 数学工具Math

📊 单因素方差分析(ANOVA)计算器One-Way ANOVA Calculator

每行输入一组数据,计算单因素方差分析表:组间/组内平方和、自由度、均方、F 值、P 值和 η²,并给出各组均值与标准差。Run a one-way ANOVA with one group per line: get the full table — between/within sums of squares, degrees of freedom, mean squares, F, the p-value and η² — plus each group's mean and standard deviation.

各组数据(每行一组)Groups (one per line)

使用说明与常见问题How-to & FAQ

「单因素方差分析(ANOVA)计算器」是什么?What is the One-Way ANOVA Calculator tool?

每行输入一组数据,计算单因素方差分析表:组间/组内平方和、自由度、均方、F 值、P 值和 η²,并给出各组均值与标准差。Run a one-way ANOVA with one group per line: get the full table — between/within sums of squares, degrees of freedom, mean squares, F, the p-value and η² — plus each group's mean and standard deviation.

如何使用「单因素方差分析(ANOVA)计算器」?How do I use the One-Way ANOVA Calculator tool?

在「单因素方差分析(ANOVA)计算器」中,填写「显著性水平 α」等参数,结果会随输入实时计算并显示在下方。In the One-Way ANOVA Calculator: Fill in "Significance level α"; results are recalculated instantly as you type.

单因素方差分析检验什么?What does one-way ANOVA test?

检验三个或更多(也可两个)独立组的总体均值是否全部相等。原假设:所有组均值相等;P 值小于 α 时认为至少有一组不同。Whether the population means of two or more independent groups are all equal. The null hypothesis is that they are; a p-value below α suggests at least one differs.

公式是什么?What are the formulas?

SSB = Σ nᵢ(x̄ᵢ − x̄)²,SSW = ΣΣ (x − x̄ᵢ)²;MSB = SSB/(k−1),MSW = SSW/(N−k),F = MSB/MSW,P 值来自 F(k−1, N−k) 分布右尾;η² = SSB/SST。SSB = Σ nᵢ(x̄ᵢ − x̄)², SSW = ΣΣ (x − x̄ᵢ)²; MSB = SSB/(k−1), MSW = SSW/(N−k), F = MSB/MSW with the p-value from the right tail of F(k−1, N−k); η² = SSB/SST.

前提条件?What are the assumptions?

各组独立、近似正态、方差大致相等。若方差差异大,可考虑 Welch ANOVA;显著后可用 Tukey HSD 做两两比较。Independent groups, roughly normal data and similar variances. With unequal variances consider Welch's ANOVA; after a significant result use Tukey's HSD for pairwise comparisons.

计算精度如何?How precise are the results?

「单因素方差分析(ANOVA)计算器」使用 JavaScript 双精度浮点数(约 15–16 位有效数字);极大或极小的数值可能存在精度误差。The One-Way ANOVA Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「单因素方差分析(ANOVA)计算器」免费吗?需要注册吗?Is the One-Way ANOVA Calculator free? Do I need an account?

「单因素方差分析(ANOVA)计算器」完全免费,无需注册或安装,打开网页即可使用,手机和电脑都能用;输入的内容只在你的浏览器本地处理。The One-Way ANOVA Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.

相关工具Related tools

🚩 异常值计算器(IQR 法)Outlier Calculator (IQR Method)📐 平均变化率计算器Average Rate of Change Calculator⬛ 配方法计算器Completing the Square Calculator✳️ 离散卷积计算器Convolution Calculator⏫ 翻倍时间计算器Doubling Time Calculator🔺 等边三角形计算器Equilateral Triangle Calculator📐 余弦定理计算器Law of Cosines Calculator📏 正弦定理计算器Law of Sines Calculator🧊 正方体计算器Cube Calculator⬡ 正多边形计算器Regular Polygon Calculator⏢ 梯形计算器Trapezoid Calculator✖️ 竖式乘法计算器(列竖式)Long Multiplication Calculator

← 全部工具All tools