📝 原始分计算器（由 z 分数、百分位或 T 分数反推）Raw Score Calculator (From a z-Score, Percentile or T-Score)

使用说明与常见问题How-to & FAQ

「原始分计算器（由 z 分数、百分位或 T 分数反推）」是什么？What is the Raw Score Calculator (From a z-Score, Percentile or T-Score) tool?

由 z 分数、百分位数或 T 分数加上均值和标准差，反推原始分 x = μ + z·σ；也可以反过来由原始分求 z 分数、T 分数和百分位（正态分布）。本地处理。Finds the raw score x = μ + z·σ from a z-score, a percentile or a T-score together with the mean and standard deviation, or goes the other way from a raw score to its z-score, T-score and percentile under a normal distribution. Processed locally.

如何使用「原始分计算器（由 z 分数、百分位或 T 分数反推）」？How do I use the Raw Score Calculator (From a z-Score, Percentile or T-Score) tool?

在「原始分计算器（由 z 分数、百分位或 T 分数反推）」中，填写「已知」、「z 分数」、「百分位 %」、「T 分数」、「原始分」等参数，结果会随输入实时计算并显示在下方。In the Raw Score Calculator (From a z-Score, Percentile or T-Score): Fill in "Known", "z-score", "Percentile %", "T-score", "Raw score"; results are recalculated instantly as you type.

由 z 分数怎么求原始分？How do I get a raw score from a z-score?

原始分 x = μ + z·σ。例如均值 100、标准差 15、z = 1.5，则 x = 100 + 1.5 × 15 = 122.5。x = μ + z·σ. With mean 100, standard deviation 15 and z = 1.5, x = 100 + 1.5 × 15 = 122.5.

由百分位怎么求？How about from a percentile?

先用标准正态分布的反函数把百分位换成 z，再代入公式。第 90 百分位对应 z ≈ 1.2816，所以上例约为 119.2。这假设分数服从正态分布。Convert the percentile to z with the inverse standard normal, then use the formula. The 90th percentile is z ≈ 1.2816, giving about 119.2 above. This assumes scores are normally distributed.

T 分数是什么？What is a T-score?

T 分数是均值 50、标准差 10 的标准分：T = 50 + 10z。T = 60 表示高于平均 1 个标准差。A T-score is a standard score with mean 50 and standard deviation 10: T = 50 + 10z. T = 60 is one standard deviation above average.

能举个计算实例吗？Can you show a worked example?

例如在「原始分计算器（由 z 分数、百分位或 T 分数反推）」中填 已知 = z 分数，z 分数 = 0，均值 μ = 100，标准差 σ = 15，结果区显示：原始分：100；公式：x = μ + z·σ = 100 + 0 × 15；T 分数（50 + 10z）：50；百分位（正态）：50 %；高于此分的比例：50 %For example, entering Known = z-score, z-score = 0, Mean μ = 100, Standard deviation σ = 15 in the Raw Score Calculator (From a z-Score, Percentile or T-Score) gives: Raw score: 100; Formula: x = μ + z·σ = 100 + 0 × 15; T-score (50 + 10z): 50; Percentile (normal): 50 %; Share scoring higher: 50 %

哪些输入会被检查？Which inputs are validated?

「原始分计算器（由 z 分数、百分位或 T 分数反推）」会检查这些输入——「z 分数」、「百分位 %」、「T 分数」、「原始分」、「均值 μ」：所选方式用到时必须填写；「标准差 σ」：必须填写，须大于 0；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Raw Score Calculator (From a z-Score, Percentile or T-Score) checks its inputs — "z-score", "Percentile %", "T-score", "Raw score", "Mean μ": required when the chosen option uses it; "Standard deviation σ": required, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「原始分计算器（由 z 分数、百分位或 T 分数反推）」的设置：「已知」可选 z 分数、百分位、T 分数、原始分（反求）（默认 z 分数）；「z 分数」默认 1.5；「百分位 %」默认 90；「T 分数」默认 60；「原始分」默认 115；「均值 μ」默认 100；「标准差 σ」默认 15。每次生成结果都按当前设置处理。Settings in the Raw Score Calculator (From a z-Score, Percentile or T-Score) — "Known": z-score, Percentile, T-score, Raw score (reverse) (default z-score); "z-score" default 1.5; "Percentile %" default 90; "T-score" default 60; "Raw score" default 115; "Mean μ" default 100; "Standard deviation σ" default 15. The result always uses the current settings.

计算精度如何？How precise are the results?

「原始分计算器（由 z 分数、百分位或 T 分数反推）」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 Raw Score Calculator (From a z-Score, Percentile or T-Score) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「原始分计算器（由 z 分数、百分位或 T 分数反推）」免费吗？需要注册吗？Is the Raw Score Calculator (From a z-Score, Percentile or T-Score) free? Do I need an account?

「原始分计算器（由 z 分数、百分位或 T 分数反推）」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 Raw Score Calculator (From a z-Score, Percentile or T-Score) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.