📚 Year 10 CIE Psychology: Formula & Theorem Quick Reference Guide | Year 10 CIE 心理学：公式定理速查手册
Welcome to your quick revision guide for psychological formulas and key theorems in the CIE IGCSE Psychology syllabus. This resource lets you quickly brush up on essential laws, statistical calculations, and conceptual models that underpin psychological research.
欢迎使用CIE IGCSE心理学课程公式和关键定理速查手册。本文帮助您快速复习心理学研究背后那些重要的定律、统计算法和概念模型。
1. Weber's Law | 韦伯定律
Weber's Law describes the relationship between the magnitude of a stimulus and the size of a just noticeable difference (JND). It states that the change needed for a person to detect a difference is a constant proportion of the original stimulus intensity. Expressed as: ΔI / I = k, where ΔI represents the smallest detectable change in intensity, I is the baseline intensity, and k is the Weber fraction.
韦伯定律描述了刺激强度与最小可觉差（JND）之间的关系。该定律指出，一个人察觉出差异所需的刺激变化量，与原始刺激强度之比为常数。表示为ΔI / I = k，其中ΔI表示可察觉的最小强度变化，I 是基线强度，k 是韦伯分数。
| Sensory Modality | 感觉通道 | Weber Fraction (k) | 韦伯分数 |
|---|---|
| Vision (brightness) | 视觉（亮度） | 1/60 |
| Hearing (pitch) | 听觉（音高） | 1/333 |
| Taste (salt) | 味觉（咸味） | 1/5 |
| Touch (pressure) | 触觉（压力） | 1/7 |
(k=1/7 for pressure) to notice an increase. The JND grows as the initial weight increases.
例如，如果您正拿着一个100克的砝码，大约需要再增加14克（触觉的 k=1/7）才能察觉到变化。差别阈限随着初始重量的增加而上升。
2. Fechner's Law | 费希纳定律
Building on Weber's work, Fechner's Law proposes that perceived sensation (S) increases as the logarithm of the physical stimulus intensity (I). The formula is S = k log I, where k is a constant that differs between senses. This law explains why doubling the light intensity does not double the perceived brightness.
在韦伯研究的基础上，费希纳定律提出，心理感觉量（S）随着物理刺激强度（I）的对数而增长。公式为S = k log I，其中 k 是随感觉通道而异的常数。该定律解释了为什么把光线亮度提高一倍，并不会使感知到的亮度也翻倍。
3. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law describes the relationship between arousal and performance. It is not a numerical formula but a principle: performance increases with arousal up to an optimal point, after which further arousal leads to a decline. This is often drawn as an inverted-U curve. The optimum arousal level depends on task complexity—simple tasks benefit from higher arousal, while complex tasks require lower arousal for best performance.
耶克斯-多德森定律描述了唤醒水平与表现之间的关系。它并非一个数值公式，而是一项原理：表现随着唤醒水平的提高而上升，达到最佳点之后，进一步唤醒则导致表现下降。通常用倒U型曲线来表示。最佳唤醒水平取决于任务难度——简单任务在高唤醒下表现更好，复杂任务则需要较低唤醒才能发挥最佳水平。
In exams, you may be asked to interpret an inverted-U graph or explain why a stressed student performs poorly on a difficult exam (too much arousal for a complex task).
在考试中，你可能会被要求解释倒U型曲线，或者说明为何焦虑的学生会在很难的考试中表现不佳（对于复杂任务而言，唤醒过高）。
4. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus studied memory retention using nonsense syllables. He found that forgetting occurs rapidly soon after learning and then levels off. The retention rate can be described by the equation R = e–t/S, where R is the proportion of material retained, t is time elapsed, and S is the relative strength of memory. In practice, this curve shows a dramatic drop within the first hour and a more gradual decline thereafter.
赫尔曼·艾宾浩斯使用无意义音节研究记忆保持量。他发现遗忘在学习后不久迅速发生，随后趋于平缓。记忆保持率可用方程R = e–t/S描述，其中R为保持材料的比例，t为经过的时间，S为记忆的相对强度。这条曲线展现了一小时内急剧下降、此后缓慢减退的特点。
This theorem underscores the importance of timely revision and spaced practice to counteract forgetting.
这一定理强调了
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