📚 Year 9 Cambridge Psychology: Quick Reference Guide to Formulas and Principles | Year 9 剑桥心理学：公式定理速查手册
Psychology may seem like a subject full of abstract theories and famous case studies, but a surprising number of its core ideas can be expressed as crisp formulas, laws and mathematical principles. This revision handbook gathers the essential 'formulas' you need for Year 9 Cambridge Psychology, covering everything from basic psychophysics to memory capacity and social dynamics. Use it to rapidly revisit key equations, constants and predictive models while preparing for your assessments.
心理学或许看起来像是一门充满抽象理论和著名案例研究的学科，但它许多核心思想其实都可以用清晰的公式、定律和数学原理来表达。这本复习手册汇集了你在 Year 9 剑桥心理学中所需的关键“公式”，涵盖从基础心理物理学到记忆容量和社会动力学的内容。在备考时用它快速回顾关键方程、常数和预测模型吧。
1. Weber’s Law | 韦伯定律
Weber’s Law states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus. The formula is written as:
韦伯定律指出，两个刺激之间的最小可觉差（JND）与原始刺激的强度成正比。其公式写作：
ΔI / I = k
Here, ΔI represents the increment in intensity needed to detect a change, I is the original intensity, and k is the Weber fraction – a constant that differs for each sense. For example, the Weber fraction for lifted weights is around 0.02 (1/50). This means if you are holding 100 grams, you will just notice a difference when 2 grams are added.
此处，ΔI 表示察觉变化所需增加的强度，I 是原始强度，k 是韦伯分数——每种感觉道特有的常数。例如，提起重量的韦伯分数约为 0.02（1/50）。这意味着当你拿着 100 克物体时，增加 2 克你才能刚好察觉出差异。
The table below gives common Weber fractions tested in Cambridge psychology courses:
下表列出了剑桥心理学课程中常见的韦伯分数：
| Sense (感觉道) | Weber Fraction (k) 韦伯分数 | Practical Meaning 实际含义 |
|---|---|---|
| Visual brightness (视觉亮度) | ~0.0167 (1/60) | A light must change by 1/60th of its intensity to be noticed |
| Pitch of sound (音高) | ~0.003 (1/333) | Very small changes in frequency are detectable |
| Saltiness (咸味) | ~0.2 (1/5) | A large change in salt is required to taste a difference |
| Lifted weights (提起的重量) | ~0.02 (1/50) | Adding 2 g to 100 g is just noticeable |
Weber’s Law helps explain why we fail to notice a single candle added to a brightly lit room but easily notice that same candle in the dark.
韦伯定律有助于解释为什么我们在灯火通明的房间里察觉不到多加一支蜡烛，但在黑暗中却很容易注意到同一支蜡烛。
2. Fechner’s Law | 费希纳定律
Fechner built on Weber’s work to describe the numerical relationship between physical stimulus intensity and our subjective sensation. Fechner’s Law is usually shown as:
费希纳在韦伯研究的基础上描述了物理刺激强度与主观感觉之间的数量关系。费希纳定律通常表示为：
S = k log I
S is the sensation magnitude, I is the physical intensity of the stimulus, and k is a constant that depends on the sensory modality. The formula tells us that sensation grows as the logarithm of stimulus intensity, not in direct proportion. In practice, doubling the physical intensity of a light does not double its perceived brightness; instead, the perceived increase is much smaller.
其中，S 表示感觉量，I 是刺激的物理强度，k 是一个依赖于感觉通道的常数。这个公式告诉我们，感觉是按刺激强度的对数增长的，而非正比关系。实际上，将灯光的物理强度加倍并不会使感知亮度翻倍，反而感觉到的增加要小得多。
Fechner’s Law is fundamental to understanding why our perception compresses a wide range of physical energies into a manageable sensory experience.
费希纳定律是理解为何我们的感知能将广泛的物理能量压缩为可控感觉体验的基础。
3. Miller’s Magic Number 7 ± 2 | 米勒的神奇数字 7 ± 2
George Miller’s (1956) classic paper argued that the capacity of short-term memory (STM) is limited to about 7 items, plus or minus 2. The central principle can be stated as:
乔治·米勒（1956）的经典论文指出，短时记忆（STM）的容量仅限于约 7 个项目，加减 2。其核心原则可表述为：
STM span = 7 ± 2 chunks
A 'chunk' is any meaningful unit, such as a digit, letter, word, or even a familiar grouping. By reorganising individual items into larger chunks, we can dramatically increase the amount of information recalled. For example, the sequence 'FBI CIA IBM' is far easier to remember than 'FBICIAIBM'.
“组块”可以是任何有意义的单元，如一个数字、字母、单词，甚至是熟悉的组合。通过将单个项目重新组织成更大的组块，我们可以大幅增加回忆的信息量。例如，序列“FBI CIA IBM”比“FBICIAIBM”容易记忆得多。
This concept lays the groundwork for later models of working memory and explains why phone numbers are broken into segments. The exact number varies between individuals, but the principle of limited capacity remains central to memory theory.
此概念为后来的工作记忆模型奠定了基础，也解释了为什么电话号码会被分段书写。尽管具体数字因人而异，但容量有限这一原则始终是记忆理论的核心。
4. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus conducted the first systematic studies of memory and forgetting using nonsense syllables. He found that forgetting follows a predictable curve that can be approximated by:
赫尔曼·艾宾浩斯率先使用无意义音节对记忆和遗忘进行了系统研究。他发现遗忘遵循一条可预测的曲线，近似为：
Retention = e(-t / T)
Retention is the proportion of material still remembered after time t has elapsed, and T is a time constant. In plain terms, the curve drops steeply within the first 20 minutes to an hour, then levels off. Crucially, relearning forgotten material takes less time than the original learning, a phenomenon known as 'savings'.
Retention 表示在时间 t 过后仍记住的材料比例，T 为时间常数。简单来说，这条曲线在最初 20 分钟到 1 小时内急剧下降，随后趋于平缓。关键的是，重新学习已被遗忘的材料所需时间比原先学习更短，这一现象称为“节省”。
For revision, the forgetting curve highlights why spaced repetition and regular review sessions are necessary to shift knowledge into long-term memory.
就复习而言，遗忘曲线凸显了为何需要间隔重复和定期回顾，才能将知识转入长时记忆。
5. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law describes the relationship between arousal and performance. The general principle follows an inverted U-curve and can be summarised as:
耶克斯-多德森定律描述了唤醒水平与表现之间的关系。其一般原则呈倒 U 形曲线，可概括为：
Performance = f(Arousal); optimal at moderate levels
For simple or well-learned tasks, a higher level of arousal improves performance. However, for complex or newly learned tasks, lower arousal is better because excessive stress impairs concentration. A real-world example: a runner benefits from being highly alert at the start of a race, but a student solving difficult equations needs a calmer state to avoid mistakes.
对于简单或熟练掌握的任务，较高的唤醒水平能提升表现。但对于复杂或新学习的任务，较低的唤醒更有利，因为过度的压力会损害注意力集中。现实案例：赛跑者在起跑时高度警觉会获益，但解答难题的学生则需要更平静的状态以避免错误。
This law is used to optimise exam preparation: moderately challenging practice tests create an optimal level of arousal that matches the actual exam setting.
这一定律被用于优化备考：难度适中的练习测验能营造与实际考试环境相匹配的最佳唤醒水平。
6. Lewin’s Equation: B = f(P, E) | 勒温公式：B = f(P, E)
Kurt Lewin, a pioneer of social psychology, proposed that behaviour is always a function of the person and the environment. His famous equation is:
社会心理学先驱库尔特·勒温提出，行为总是个人与环境的函数。他著名的公式为：
B = f(P, E)
‘B’ stands for behaviour, ‘P’ represents the person (including personality, motivations, past experiences), and ‘E’ represents the physical and social environment. According to this view, you cannot explain a student’s aggression simply by labelling them as an 'aggressive person'; you must also examine the classroom climate or peer pressure.
“B”代表行为，“P”代表个人（包括个性、动机、过往经历），“E”代表物理与社会环境。根据此观点，你不能仅仅通过给一个学生贴上“攻击性强”的标签来解释其攻击行为，还必须审视课堂氛围或同伴压力。
This interactionist formula underpins many Year 9 topics, from conformity to bystander intervention.
这一交互论公式支撑着从众、旁观者干预等众多 Year 9 主题。
7. Classical Conditioning Formula | 经典条件作用公式
Pavlov’s discovery of classical conditioning follows a predictable sequence that can be written as a 'conditioning formula':
巴甫洛夫发现的经典条件作用遵循一个可预测的顺序，可写作“条件作用公式”：
NS + UCS → UCR
After conditioning: CS → CR
ion), CS = conditioned stimulus (the former NS), and CR = conditioned response (learned salivation to the bell). In short, a neutral stimulus gains the power to elicit a response after being paired repeatedly with an unconditioned stimulus.
NS = 中性刺激（如条件作用前的铃声），UCS = 无条件刺激（如食物），UCR = 无条件反应（如唾液分泌），CS = 条件刺激（即原先的 NS），CR = 条件反应（习得的对铃声的唾液分泌）。简而言之，中性刺激在与无条件刺激反复配对后，便获得了引发反应的能力。
Key phenomena derived from this formula include acquisition, extinction, spontaneous recovery, and stimulus generalisation, all of which appear in Cambridge exam questions.
由此公式衍生的关键现象包括习得、消退、自然恢复和刺激泛化，这些内容常出现在剑桥考试题目中。
8. Schedules of Reinforcement Principles | 强化程式原理
In operant conditioning, B.F. Skinner showed that the way reinforcements are delivered shapes response rates and extinction resistance. Although not a single equation, the relationship can be captured by comparing the main schedules:
在操作性条件作用中，斯金纳证明了强化物的发放方式会塑造反应速率与消退抗性。虽然并非单一方程，但可通过比较主要程式来把握其关系：
| Schedule (强化程式) | Rule (规则) | Response Pattern (反应模式) |
|---|---|---|
| Fixed Ratio (FR) 固定比率 | Reward after every nth response (e.g., FR5: reward every 5 correct answers) | High response rate with a brief pause after reinforcement |
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