📚 Year 9 OCR Psychology: Formula and Law Quick Reference Handbook | Year 9 OCR 心理学：公式定理速查手册
Welcome to your Year 9 OCR Psychology Formula and Law Quick Reference Handbook. This guide brings together the essential psychological laws, models, and mathematical formulas you will meet in your first year of GCSE Psychology. From classic principles that explain behaviour to the descriptive statistics needed for research methods, each entry is presented with a clear English explanation followed by its Chinese equivalent. Use this handbook to revise key concepts, strengthen your AO2 application skills, and build confidence for end-of-topic tests.
欢迎使用 Year 9 OCR 心理学公式定理速查手册。本手册汇集了你在 GCSE 心理学第一年学习中会遇到的核心心理学定律、模型和数学公式。从解释行为的经典原理，到研究方法所需的描述性统计，每一个条目都先提供英文解释，再附上对应的中文说明。使用这本手册可以帮助你巩固关键概念，提升 AO2 应用能力，并为单元测验建立信心。
1. Yerkes-Dodson Law | 耶克斯–多德森定律
The Yerkes-Dodson Law states that performance increases with physiological or mental arousal up to an optimal point, after which further arousal leads to a decline in performance. The relationship is often drawn as an inverted U-shaped curve.
耶克斯–多德森定律指出，生理或心理唤醒水平的提高会促进表现，直至达到最佳唤醒点；超过该点后，继续上升的唤醒水平反而会导致表现下降。这种关系通常被绘制成一条倒 U 形曲线。
The position of the optimal arousal level depends on task difficulty. For simple or well-learned tasks, peak performance occurs at relatively high arousal. For complex or unfamiliar tasks, peak performance occurs at lower arousal levels.
最佳唤醒水平的位置取决于任务难度。对于简单或高度熟练的任务，最佳表现出现在较高的唤醒水平上；对于复杂或陌生的任务，最佳表现则需要较低的唤醒水平。
| Task Type 任务类型 | Optimal Arousal 最佳唤醒 | Performance 表现 |
|---|---|---|
| Simple / well-learned 简单/熟练 | High 高 | Best at high arousal 高水平最佳 |
| Complex / new 复杂/新任务 | Low to moderate 中低 | Best at lower arousal 较低水平最佳 |
This law is used to explain why a little stress before an exam can sharpen focus, but extreme anxiety harms memory recall.
这一定律可用于解释为什么考前适度的压力能提升专注力，而过度的焦虑却会损害记忆提取。
2. Miller’s Law (The Magical Number Seven) | 米勒定律（神奇数字 7±2）
Miller’s Law states that the capacity of short-term memory is approximately seven items, plus or minus two (7±2). George Miller (1956) proposed that people can hold about seven chunks of information in their working memory at any one time.
米勒定律指出，短时记忆的容量大约为 7±2 个项目。乔治·米勒（1956）提出，人们一次能在大脑中保持约七个组块的信息。
A ‘chunk’ can be a single digit, a letter, a word, or even a meaningful unit such as ‘BBC’ or ‘2024’. By grouping information into larger chunks, we can expand the amount of material held in short-term memory.
“组块”可以是一个数字、一个字母、一个词语，也可以是一组有意义的单位，例如 “BBC” 或 “2024”。通过将信息组成更大的组块，我们可以扩展短时记忆中的信息量。
This law helps explain why phone numbers are often broken into segments and why acronyms make revision notes easier to remember.
这一定律解释了为什么电话号码通常被分成几段，以及为什么首字母缩略词能让复习笔记更容易记住。
3. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus discovered that memory for newly learned information decays rapidly at first, then levels off over time. The forgetting curve can be approximated mathematically by the equation:
赫尔曼·艾宾浩斯发现，新学信息的记忆会先快速衰退，然后随时间的推移逐渐趋于平缓。遗忘曲线可以用以下方程近似描述：
R = e–t/S
where R is memory retention, t is time elapsed, and S is the relative strength of the memory trace. The key finding is that the steepest drop occurs within the first hour after learning.
其中 R 代表记忆保持量，t 代表经过的时间，S 代表记忆痕迹的相对强度。最关键的发现是，遗忘最急剧的阶段发生在学习后的第一个小时内。
Ebbinghaus also measured ‘savings’ when relearning material. The percentage of time saved when relearning compared to the original learning time reflects how much information remained in long-term memory.
艾宾浩斯还测量了重新学习时的“节省量”。重新学习所节省的时间百分比，反映了有多少信息留在了长时记忆中。
This curve underpins the importance of regular revision: reviewing material at spaced intervals flattens the forgetting curve significantly.
这条曲线支撑了定期复习的重要性：间隔重复复习可以显著拉平遗忘曲线。
4. Weber’s Law | 韦伯定律
Weber’s Law describes the relationship between a physical stimulus and the just noticeable difference (JND) – the smallest change in a stimulus that can be detected. The law states that the JND is a constant proportion of the original stimulus intensity:
韦伯定律描述了物理刺激与最小可觉差（JND）之间的关系。最小可觉差是指能被觉察到的刺激最小变化量。定律表明，最小可觉差与原始刺激强度的比例是一个常数：
ΔI / I = k
ΔI is the change in stimulus intensity, I is the original intensity, and k is the Weber fraction, which varies across sensory modalities.
ΔI 是刺激强度的变化量，I 是原始强度，k 是韦伯分数，不同感觉通道的 k 值不同。
For example, if you are holding a 100 g weight, you might need to add 2 g to notice a difference (k = 0.02). If you were holding a 500 g weight, you would need to add about 10 g to detect the change. This principle applies to brightness, loudness, and even price perception.
例如，当你托着 100 克的重量时，可能需要增加 2 克才能察觉变化（k = 0.02）。如果托着 500 克，则需要增加大约 10 克才能感知不同。这一原理适用于亮度、响度，甚至价格感知。
5. Descriptive Statistics: Mean | 描述统计：平均数
The mean is the arithmetic average of a set of scores. It is calculated by adding all values together and dividing by the number of values.
平均数是一组分数的算术平均值。计算方法是把所有数值相加，再除以数值的个数。
Mean = Σx / n
Σx (sigma x) represents the sum of all data values, and n is the total number of values. The mean is sensitive to extreme scores (outliers), which can pull it up or down.
Σx（西格玛 x）代表所有数据值的总和，n 是数值的总个数。平均数对极端值（离群值）敏感，这些值会将它拉高或拉低。
Example: If five students scored 12, 15, 18, 20, and 25 in a memory test, the mean is (12+15+18+20+25) ÷ 5 = 90 ÷ 5 = 18.
示例：若五名学生在记忆测试中的得分分别为 12、15、18、20 和 25，平均数为 (12+15+18+20+25) ÷ 5 = 90 ÷ 5 = 18。
6. Descriptive Statistics: Median | 描述统计：中位数
The median is the middle value when a data set is arranged in ascending order. It splits the distribution into two equal halves and is unaffected by outliers.
中位数是将数据集按升序排列后位于中间位置的数值。它将分布分成相等的两半，且不受离群值影响。
When the number of scores is odd, the median is the single middle value. When the number is even, the median is the mean of the two middle numbers.
当数据的个数为奇数时，中位数是唯一的中间值；当个数为偶数时，中位数是中间两个数值的平均数。
Example (odd): With reaction times of 210, 230, 245, 260, 300 ms, the median is 245 ms. Example (even): With times 200, 220, 240, 260 ms, the median is (220+240) ÷ 2 = 230 ms.
示例（奇数）：反应时 210、230、245、260、300 毫秒，中位数为 245 毫秒。示例（偶数）：反应时 200、220、240、260 毫秒，中位数为 (220+240) ÷ 2 = 230 毫秒。
7. Descriptive Statistics: Mode and Range | 描述统计：众数与范围
The mode is the most frequently occurring value in a data set. A set can have one mode (unimodal), two modes (bimodal), or more. If no value repeats, there is no mode. Unlike mean and median, the mode can be used with nominal (category) data.
众数是数据集中出现频率最高的数值。一组数据可以有一个众数（单峰）、两个众数（双峰）或更多。如果没有数值重复，则没有众数。与平均数和中位数不同，众数可用于名义（类别）数据。
The range measures the spread of the data. It is calculated as:
范围衡量数据的离散程度。计算公式为：
Range = Highest value – Lowest value
A small range indicates that scores are clustered closely together; a large range suggests high variability. Range is quick to compute but easily distorted by a single extreme value.
范围小说明分数紧密聚集在一起；范围大则表明变异性高。范围计算简便，但容易被单一极端值扭曲。
8. Percentage Change | 百分比变化
Percentage change is a useful formula in psychological research, especially when comparing before-and-after measurements, such as memory recall before and after an intervention, or calculating the ‘savings’ score in Ebbinghaus-style studies.
百分比变化是心理学研究中有用的公式，尤其用于比较干预前后的测量值，例如干预前后的记忆回忆量，或计算艾宾浩斯式研究中的“节省”分数。
Percentage Change = (New Value – Original Value) ÷ Original Value × 100%
A positive result indicates an increase, while a negative result indicates a decrease. For example, if a participant recalled 15 words originally and 21 words after using a mnemonic, the percentage change is (21 – 15) ÷ 15 × 100% = 40% improvement.
结果为正值表示增长，负值表示减少。例如，某参与者在采用记忆术之前回忆了 15 个词，之后回忆了 21 个词，则百分比变化为 (21 – 15) ÷ 15 × 100% = 40% 的提升。
In Ebbinghaus’s savings method, the percentage of time saved when relearning a list compared to the original learning time is calculated similarly. This formula also appears in social influence studies when reporting changes in conformity or obedience rates.
在艾宾浩斯的节省法中，重新学习一个词表相比原学习时间所节省的时间百分比，也可以用类似方式计算。该公式还出现在社会影响研究中，用于报告从众率或服从率的变化。
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