📚 Year 7 Cambridge Psychology: Formula & Theorem Quick Reference Handbook | 剑桥七年级心理学公式定理速查手册
Welcome to the Year 7 Cambridge Psychology quick reference guide. This handbook collects the essential laws, principles, and theorems that shape the study of the mind and behaviour. Each entry presents a straightforward explanation in English and Chinese, together with simple symbolic formulas where applicable. Use it to strengthen your revision, build cross-language understanding, and deepen your grasp of foundational psychology.
欢迎使用剑桥七年级心理学速查手册。本手册汇集了塑造心智与行为研究的关键定律、原理和定理。每个条目用英文和中文提供清晰的解释，并在适当之处附上简洁的符号公式。用它来巩固复习、建立双语理解，并加深对心理学基础知识的掌握。
1. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law describes the relationship between arousal and performance. Performance improves as arousal increases, but only up to an optimal point; beyond that, further arousal leads to a decline in performance. The shape of this relationship is an inverted U.
耶克斯-多德森定律描述了唤醒水平与表现之间的关系。表现随唤醒提高而改善，但只到最佳点为止；超过该点后，唤醒继续增加反而会导致表现下降。这一关系呈倒 U 形。
Performance = f(arousal) (inverted-U curve)
For simple tasks, a higher arousal level often yields the best results. For complex or difficult tasks, a lower arousal level is more effective. This principle helps explain why anxiety can help us focus on a simple drill but disrupt performance during a challenging problem-solving task.
对于简单任务，较高的唤醒水平通常能带来最佳结果；对于复杂或困难的任务，较低的唤醒水平更有效。这条原理有助于解释为何焦虑能帮助我们在简单练习中集中注意，却会扰乱复杂问题解决任务的表现。
2. Weber’s Law | 韦伯定律
Weber’s Law states that the size of a just noticeable difference (JND) in a stimulus is a constant proportion of the original stimulus intensity. It applies to many sensory dimensions, such as brightness, loudness, and weight.
韦伯定律指出，刺激的恰可觉察差异（JND）的大小与原始刺激强度成固定比例。它适用于亮度、响度和重量等多种感觉维度。
ΔI / I = k
Here, ΔI is the smallest change in stimulus intensity that can be detected, I is the original intensity, and k is the Weber fraction, a constant specific to each sense modality. For example, the JND for lifting weights is about 2% of the original weight, so a 100 g weight might require an increase of about 2 g to notice a difference.
其中，ΔI 是可觉察的最小刺激强度变化量，I 是原始强度，k 是韦伯分数，是每种感觉通道特有的常数。例如，举重感觉的 JND 约为原重量的 2%，所以对于 100 克的重量，大约需要增加 2 克才能察觉到差异。
3. Ebbinghaus Forgetting Law | 艾宾浩斯遗忘定律
Hermann Ebbinghaus discovered that memory for newly learned information declines rapidly at first and then levels off over time. The forgetting curve illustrates this exponential decline in retention.
赫尔曼·艾宾浩斯发现，新学信息的记忆起初迅速下降，随后随时间推移趋于平缓。遗忘曲线展示了保持量的指数式衰减。
Retention (%) ≈ 100 – k log(t)
In a simplified form, retention decreases in a logarithmic fashion, which means the absolute loss of memory is greatest soon after learning. Frequent review sessions and active recall can dramatically reduce this forgetting, a fact that underpins spaced repetition study techniques.
简化的形式表明，保持量以对数形式下降，也就是说，记忆的绝对损失在学习后不久最大。经常复习和主动回忆能大幅削弱这种遗忘，这正是间隔重复学习法的依据。
4. Thorndike’s Law of Effect | 桑代克效果律
Edward Thorndike’s Law of Effect states that behaviours followed by satisfying consequences are more likely to be repeated, while behaviours followed by unpleasant consequences are less likely to occur again. This principle is foundational to operant conditioning.
爱德华·桑代克的效果律指出，获得满意后果的行为更可能被重复，而伴随不愉快后果的行为则不太可能再次发生。该原理是操作性条件作用的基础。
Behaviour → Satisfying consequence → Behaviour strengthened
Thorndike illustrated this with cats in puzzle boxes: actions that led to escape and food were gradually stamped in, while unsuccessful actions were stamped out. The law highlights how consequences shape voluntary behaviour.
桑代克用迷箱中的猫来演示：能带来逃脱和食物的动作逐渐被印刻，而不成功的动作则被抹去。这一规律强调了后果如何塑造随意行为。
5. Classical Conditioning Formula | 经典条件作用公式
Ivan Pavlov demonstrated that a neutral stimulus, when repeatedly paired with an unconditioned stimulus eliciting a natural reflex, could eventually trigger a similar response on its own. The process follows a predictable sequence of associations.
巴甫洛夫证明，一个中性刺激若能反复与引发天生反射的非条件刺激配对呈现，最终就能独自引发相似的反应。这一过程遵循一组可预测的联结序列。
UCS → UCR
CS + UCS → UCR
CS → CR
UCS stands for unconditioned stimulus (e.g., food), UCR for unconditioned response (e.g., salivation), CS for conditioned stimulus (e.g., bell), and CR for conditioned response (e.g., salivation to the bell). The formula encapsulates the shift from a natural reflex to a learned association.
UCS 代表非条件刺激（如食物），UCR 代表非条件反应（如唾液分泌），CS 代表条件刺激（如铃声），CR 代表条件反应（如听到铃声流口水）。公式概括了从天然反射到习得联结的转变。
6. Operant Conditioning Principle | 操作性条件作用原理
B. F. Skinner expanded on the Law of Effect by showing that behaviours are controlled by their consequences, which can be positive reinforcement, negative reinforcement, or punishment. Each type of consequence has a distinct effect on the likelihood of the behaviour recurring.
斯金纳进一步发展了效果律，指出行为受后果的控制，后果可以是正强化、负强化或惩罚。每一类后果对行为再次发生的可能性都有不同的影响。
R → S^R+ (positive reinforcement) → ↑R
R → S^R- (negative reinforcement) → ↑R
R → S^P+ (positive punishment) → ↓R
Reinforcement always increases the frequency of a target behaviour. Positive reinforcement adds a pleasant stimulus, while negative reinforcement removes an unpleasant stimulus. Punishment decreases behaviour; positive punishment adds an aversive stimulus, and negative punishment removes a pleasant one.
强化总是增加目标行为的频率。正强化是添加愉快刺激，负强化则是移除不愉快刺激。惩罚会减少行为；正惩罚是施加厌恶刺激，负惩罚是撤除愉快刺激。
7. Atkinson-Shiffrin Multi-Store Model | 艾金森-谢夫林多存储模型
The multi-store model describes memory as a flow of information through three distinct stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Each store has a specific capacity and duration, and information moves between them through attention and rehearsal.
多存储模型将记忆描述为信息流经三个截然不同的存储库：感觉记忆、短时记忆和长时记忆。每个存储库都有特定的容量和持续时间，信息通过注意和复述在它们之间转移。
Sensory input → Sensory memory → Attention → STM → Rehearsal → LTM
Sensory memory holds abundant raw sensory data for a fraction of a second. If we pay attention, selected information enters STM, which can retain around 7±2 items for about 20 seconds. Elaborative rehearsal then transfers material into LTM, a vast and relatively permanent store, while information not rehearsed is quickly forgotten.
感觉记忆在不到一秒的时间内保存大量原始感觉数据。如果我们给予注意，部分信息便进入短时记忆，它能短暂保留约 7±2 个项目约 20 秒。通过精细复述，内容转入容量巨大且相对持久的长时记忆，而未经复述的信息则迅速被遗忘。
8. Piaget’s Adaptation Formula | 皮亚杰适应公式
Jean Piaget proposed that cognitive development occurs through the processes of assimilation and accommodation, which together lead to adaptation. When a child encounters new information, they either fit it into existing schemes or adjust their schemes to accommodate the new experience.
皮亚杰提出，认知发展通过同化与顺应两个过程实现，二者共同导致适应。当儿童遇到新信息时，他们要么将其纳入已有图式，要么调整图式以适应新经验。
Assimilation + Accommodation → Adaptation → Schema development
Assimilation involves interpreting a new object or event in terms of an existing schema, while accommodation means modifying a schema to incorporate novel aspects. The ongoing interplay pushes intellectual growth and helps children move through the sensorimotor, preoperational, concrete operational, and formal operational stages.
同化指用已有图式解释新对象或新事件，顺应则意味着修改图式以纳入新特征。这种持续的相互作用推动着智力成长，并帮助儿童经历感知运动阶段、前运算阶段、具体运算阶段和形式运算阶段。
9. Bandura’s Reciprocal Determinism | 班杜拉交互决定论
Albert Bandura argued that personal factors, behaviour, and the environment all influence one another in a continuous, reciprocal loop. No single factor determines personality or action; instead, they function as interdependent elements.
班杜拉认为，个人因素、行为和环境三者以持续且相互的方式彼此影响。没有任何一个因素能单独决定人格或行动；它们作为相互依赖的成分共同运作。
B = f(P, E) and P ⇄ B ⇄ E
P represents personal characteristics such as cognitions and emotions, E stands for the external environment, and B for behaviour. For instance, a student who believes they can succeed in mathematics (P) will engage in more practice problems (B), which leads to better grades and encouraging feedback from teachers (E), further boosting self-belief.
P 代表认知和情绪等个人特征，E 代表外部环境，B 代表行为。例如，一名相信自己在数学上能成功的学生（P）会做更多练习题（B），进而获得更好的成绩和教师的鼓励（E），这又进一步增强自信心。
10. Zajonc’s Social Facilitation Law | 扎荣茨社会助长定律
Robert Zajonc proposed that the mere presence of others increases arousal, which strengthens the dominant response. On well-learned or simple tasks, the dominant response is usually correct, so performance improves. On unfamiliar or complex tasks, the dominant response is often incorrect, and performance worsens.
扎荣茨提出，他人在场仅凭存在就能提高唤醒水平，从而增强优势反应。对于熟练或简单的任务，优势反应通常是正确的，因此表现改善；对于不熟悉或复杂的任务，优势反应往往是错误的，表现反而变差。
Performance = f(audience, task complexity)
This law explains why a skilled basketball player may shoot better in front of a cheering crowd, while a learner driver may make more mistakes when watched. The underlying mechanism is a combination of increased physiological arousal and evaluation apprehension.
这一定律解释了为何熟练的篮球运动员在欢呼的观众面前投篮更准，而学车的驾驶员被注视时却可能犯更多错误。其背后机制是生理唤醒的提高和评价忧虑的共同作用。
11. Peak-End Rule | 峰值-终结定律
Daniel Kahneman and colleagues demonstrated that people judge an experience largely by its most intense point (the peak) and by how it ends, rather than by the average or sum of every moment. This heuristic affects memories of medical procedures, holidays, and many everyday events.
卡尼曼及其同事证明，人们评判一段体验主要依据其最强烈的时刻（峰值）和结尾时刻，而不是所有时刻的平均或总和。这一认知规则影响着人们对医疗程序、假期以及诸多日常事件的记忆。
Evaluated experience ≈ average (peak affect, end affect)
When a painful colonoscopy was extended with a less painful final minute, patients rated the entire procedure as less unpleasant, even though the total duration of pain was longer. The peak-end rule has powerful implications for designing positive customer experiences and improving wellbeing.
当一次痛苦的结肠镜检查被延长了一个不那么痛苦的最后一分钟时，患者对整个过程的评价反而更积极，尽管痛苦的总时长变长了。峰值-终结定律对设计积极的客户体验和改善幸福感具有重大的启发意义。
12. Stroop Effect Law | 斯特鲁效应定律
The Stroop effect describes the cognitive interference that occurs when the name of a colour is printed in a mismatched ink colour. Naming the ink colour takes longer and is more error-prone because reading the word is an automatic and dominant response that interferes with the controlled task of colour naming.
斯特鲁效应描述了当颜色名称用不匹配的墨水颜色印刷时发生的认知干扰。对墨水颜色命名更加费时且容易出错，因为阅读词语是自动且占优势的反应，会干扰有控制的颜色命名任务。
Word meaning ≠ Ink colour → Interference → Reaction time ↑
Participants presented with the word ‘RED’ written in blue ink struggle to say ‘blue’ quickly because the meaning ‘red’ intrudes. The Stroop effect has become a classic tool for studying selective attention and the limits of automatic processing, and it reminds us that some mental conflicts are very hard to suppress.
当看到用蓝墨水写的“红”字时，被试很难快速说出“蓝”，因为“红”的字义会闯入意识。斯特鲁效应已成为研究选择性注意和自动加工局限的经典工具，它提醒我们有些心理冲突很难被压制。
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