🔗 相关系数计算器Correlation Coefficient Calculator

使用说明与常见问题How-to & FAQ

「相关系数计算器」是什么？What is the Correlation Coefficient Calculator tool?

输入成对的 (x, y) 数据，计算皮尔逊相关系数 r、决定系数 r²、斯皮尔曼等级相关系数 ρ 和协方差，并给出相关强度的常用描述。Enter paired (x, y) data to get the Pearson correlation coefficient r, r², Spearman's rank correlation ρ and the covariance, with a common description of the strength.

如何使用「相关系数计算器」？How do I use the Correlation Coefficient Calculator tool?

在「相关系数计算器」中，填写上方字段等参数，结果会随输入实时计算并显示在下方。In the Correlation Coefficient Calculator: Fill in the fields above; results are recalculated instantly as you type.

皮尔逊和斯皮尔曼有什么区别？Pearson or Spearman?

皮尔逊 r 衡量线性关系，对异常值敏感；斯皮尔曼 ρ 用数据的名次计算，衡量单调关系（不一定是直线），对异常值更稳健。并列值取平均名次。Pearson r measures a linear relationship and is sensitive to outliers; Spearman's ρ uses ranks, measures any monotonic relationship and is more robust. Ties get the average rank.

r 和 r² 的含义？What do r and r² mean?

r 在 −1 到 1 之间，符号表示方向，绝对值表示线性关系的紧密程度。r² 是 y 的变化中能被 x 的线性关系解释的比例。r runs from −1 to 1; the sign gives the direction and the size how tightly the points follow a line. r² is the share of the variation in y explained by a linear relationship with x.

工具会算 p 值吗？Does it give a p-value?

不会。显著性检验取决于样本量和前提假设，这里只给描述性统计。No. Significance depends on the sample size and assumptions; this tool gives descriptive statistics only.

计算精度如何？How precise are the results?

「相关系数计算器」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 Correlation Coefficient Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「相关系数计算器」免费吗？需要注册吗？Is the Correlation Coefficient Calculator free? Do I need an account?

「相关系数计算器」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 Correlation Coefficient 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.