📚 Cambridge IGCSE Psychology Formulas & Theorems Quick Reference | 剑桥IGCSE心理学公式定理速查手册
This quick reference guide compiles essential formulas, laws, and key theoretical models for Cambridge IGCSE Psychology. It is designed to help you review statistical computations, foundational laws of behaviour and perception, and influential process models that appear frequently in exam questions.
本速查手册汇编了剑桥 IGCSE 心理学中必不可少的公式、定律和关键理论模型，帮助你高效复习统计计算、行为与知觉的基本定律以及常考的加工过程模型。
1. Descriptive Statistics Formulas | 描述性统计公式
Descriptive statistics summarise raw data. The most commonly required calculations in IGCSE Psychology are the mean, median, mode, range, and percentage change.
描述性统计用于汇总原始数据。IGCSE 心理学中最常要求的计算是平均数、中位数、众数、全距和百分比变化。
The mean is the arithmetic average and is found by summing all the scores and dividing by the number of scores.
平均数是算术平均值，计算方法是将所有分数相加再除以分数的个数。
Mean = Σx / N
The median is the middle value when scores are arranged in order. If there are two middle values, take their mean.
中位数是将分数按顺序排列后居于中间的值。如果有两个中间值，则取它们的平均数。
The mode is the most frequently occurring score in a data set.
众数是数据集中出现频率最高的分数。
The range is a simple measure of dispersion, calculated as the difference between the highest and lowest scores.
全距是简单的离散程度度量，由最高分减去最低分得出。
Range = Maximum value – Minimum value
Percentage change is used to compare before-and-after measures. Use the formula:
百分比变化用于比较前后测结果，公式如下：
Percentage change (%) = [(New value – Original value) / Original value] × 100
2. Yerkes-Dodson Law | 耶克斯-多德森定律
The Yerkes-Dodson Law states that performance increases with physiological or mental arousal, but only up to an optimal point. Beyond that level, further increases in arousal lead to a decline in performance.
耶克斯-多德森定律指出，生理或心理唤醒水平升高会提高表现，但只到最佳点为止。超过该水平后，进一步增加唤醒反而会导致表现下降。
The relationship is often depicted as an inverted-U curve. The optimal arousal level is lower for difficult or complex tasks and higher for simple, well-rehearsed tasks.
这一关系常被描绘为倒U曲线。困难或复杂任务的最佳唤醒水平较低，而简单、熟练任务的最佳唤醒水平较高。
Example: An athlete may perform best when moderately anxious before a familiar race, but a student tackling a new, difficult problem may need a calmer state to think clearly.
例如：运动员在熟悉的比赛前感到适度焦虑时可能发挥最佳，而面对全新难题的学生则需要更平静的状态才能思路清晰。
3. Weber's Law | 韦伯定律
Weber's Law is a principle of psychophysics stating that the just noticeable difference (JND) between two stimuli is a constant proportion of the original stimulus intensity.
韦伯定律是心理物理学的一条原理：两个刺激之间的最小可觉差（JND）与原始刺激强度呈恒定比例。
The law is expressed as:
该定律表达为：
ΔI / I = k
where ΔI is the change needed to produce a JND, I is the initial intensity, and k is a constant that varies between sensory modalities. For example, for loudness, k is approximately 0.1, meaning a 10 % change in sound intensity is needed to notice a difference.
其中 ΔI 是产生最小可觉差所需的变化量，I 是初始强度，k 是随感觉模态不同而异的常数。例如，对于响度，k 约为 0.1，意味着声音强度变化约 10% 才能被察觉。
4. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus discovered that memory loss follows a predictable pattern. His forgetting curve shows a rapid drop in retention shortly after learning, which then flattens over time.
赫尔曼·艾宾浩斯发现记忆丧失遵循可预测的规律。他的遗忘曲线显示，学习后短期保持率迅速下降，随后随时间推移趋于平缓。
The most dramatic forgetting occurs within the first hour, and after about a day, roughly 70% of initially learned nonsense syllables was forgotten unless rehearsed. The rate of forgetting then slows significantly.
最剧烈的遗忘发生在最初一小时内，若不加复习，约一天后最初学会的无意义音节约 70% 被遗忘。之后遗忘速率明显减慢。
This finding underlines the importance of spacing revision and revisiting material before the steep part of the curve takes effect.
这一发现强调了间隔复习、在曲线陡降生效前重温材料的重要性。
5. Gestalt Laws of Perceptual Organization | 格式塔知觉组织定律
Gestalt psychologists proposed that the human brain organises sensory input according to certain innate laws. These principles help explain why we perceive unified wholes rather than fragmented parts.
格式塔心理学家提出，人脑根据某些先天定律组织感觉输入。这些原理有助于解释为何我们知觉到的是统一的整体而非支离的局部。
Law of Proximity: Objects that are physically close together tend to be grouped as a single unit.
接近律： 在空间上接近的物体容易被知觉为一个整体。
Law of Similarity: Items that look similar in shape, colour, or size are perceived as belonging to the same group.
相似律： 在形状、颜色或大小上相似的物体被知觉为属于同一组。
Law of Closure: The brain tends to fill in missing gaps in incomplete figures, allowing us to see a complete shape.
闭合律： 大脑倾向于将不完整图形的缺口补全，使我们能看见完整的形状。
Law of Continuity: Lines and patterns are perceived as following the smoothest possible path rather than making abrupt changes in direction.
连续律： 线条和图形被知觉为沿着最平滑的路径延伸，而非出现方向突然转折。
6. Classical Conditioning Formula | 经典条件作用公式
Classical conditioning, first described by Ivan Pavlov, follows a predictable sequence of stimulus-response associations. The basic formula can be written as:
经典条件作用由伊万·巴甫洛夫首次阐述，遵循可预测的刺激-反应联结序列。基本的公式可表示为：
Before conditioning: Unconditioned Stimulus (UCS) → Unconditioned Response (UCR)
条件作用前： 无条件刺激 (UCS) → 无条件反应 (UCR)
During conditioning: Neutral Stimulus (NS) + UCS → UCR
条件作用中： 中性刺激 (NS) + UCS → UCR
After conditioning: Conditioned Stimulus (CS) → Conditioned Response (CR)
条件作用后： 条件刺激 (CS) → 条件反应 (CR)
Pavlov' tion); NS (bell) + UCS (food) → UCR (salivation); eventually, CS (bell) → CR (salivation).
巴甫洛夫的经典实验：UCS（食物）→ UCR（唾液分泌）；NS（铃铛）+ UCS（食物）→ UCR（唾液分泌）；最终 CS（铃铛）→ CR（唾液分泌）。
7. Operant Conditioning Principles | 操作性条件作用原理
B.F. Skinner's operant conditioning explains how behaviour is shaped by consequences. The principles can be arranged into a simple matrix to show effects on behaviour.
斯金纳的操作性条件作用解释了行为如何受结果塑造。这些原理可排成简易矩阵以展示对行为的影响。
Positive reinforcement: Adding a desirable stimulus to increase the likelihood of a behaviour. E.g. giving praise for completing homework.
正强化： 添加一个合意的刺激以增加行为发生的可能性，例如完成作业后得到表扬。
Negative reinforcement: Removing an aversive stimulus to increase a behaviour. E.g. taking away a painful headache when you take a pill.
负强化： 移除一个厌恶刺激以增加行为，例如服药后消除头痛。
Positive punishment: Adding an unpleasant stimulus to decrease a behaviour. E.g. giving extra chores for breaking a rule.
正惩罚： 添加一个不愉快的刺激以减少行为，例如因违反规则被罚做额外家务。
Negative punishment: Removing a pleasant stimulus to decrease a behaviour. E.g. taking away a teenager's phone for bad language.
负惩罚： 移除一个愉快的刺激以减少行为，例如因说脏话没收青少年的手机。
In summary: Reinforcement increases behaviour; punishment decreases behaviour. 'Positive' means adding a stimulus; 'negative' means removing one.
总结：强化增加行为；惩罚减少行为。“正”指添加刺激，“负”指移除刺激。
8. Atkinson-Shiffrin Multi-Store Model of Memory | 阿特金森-希弗林记忆多存储模型
This influential model describes memory as a flow of information through three distinct structural stores. The sequence can be summarised as a processing chain:
这一极具影响力的模型将记忆描述为信息流经三个不同结构存储的过程。其序列可归纳为一条加工链：
→ Short-term memory (STM, limited capacity, approximately 7 ± 2 chunks, duration about 18– → through Rehearsal → Long-term memory (LTM, potentially unlimited capacity and duration).
感觉输入 → 感觉记忆（极短暂、容量大）→ 经注意 → 短时记忆（STM，容量有限，约 7±2 个组块，持续时间约 18–30 秒）→ 经复述 → 长时记忆（LTM，容量和持续时间理论上无限）。
Information in STM is lost by decay or displacement if not rehearsed. Rehearsal serves both to maintain items in STM and to transfer them to LTM.
若不进行复述，STM 中的信息会因衰退或取代而丢失。复述既能将项目维持在 STM 中，又能将其转入 LTM。
9. Piaget's Processes of Adaptation | 皮亚杰的适应过程
Jean Piaget's theory of cognitive development includes core mechanisms by which schemas (mental frameworks) are formed and modified. These processes resemble a balancing loop:
皮亚杰的认知发展理论中包含形成和调整图式（心理框架）的核心机制。这些过程类似于一个平衡回路：
Assimilation: Integrating new experiences into existing schemas without changing the schema. E.g. a child who knows 'dog' sees a sheep and calls it 'dog'.
同化： 将新经验纳入现有图式而不改变图式本身。例如，已知“狗”的儿童见到绵羊也称其为“狗”。
Accommodation: Altering existing schemas or creating new ones when new information cannot fit into existing schemas. E.g. the child learns the new label 'sheep'.
顺应： 当新信息无法被现有图式容纳时，改变现有图式或创建新图式。例如，儿童学会“绵羊”这一新标签。
Equilibration: The drive to balance assimilation and accommodation. Disequilibrium (cognitive conflict) occurs when current schemas cannot explain the world, motivating learning until a new equilibrium is reached.
平衡化： 调适同化与顺应并达到平衡的驱动力。当现有图式无法解释世界时，便产生不平衡（认知冲突），促使学习直至达到新的平衡。
10. Information Processing Model | 信息加工模型
roach compares the human mind to a computer. The core formula is Input → Process → Output.
作为认知心理学的基础模型，信息加工取向将人脑比作计算机。其核心公式为：输入 → 加工 → 输出。
Input: Sensory information is received from the environment, much like data entry.
输入： 从环境接收感觉信息，类似数据录入。
Process: The brain performs mental operations: encoding, comparing, decision-making, and storing information in memory. This stage may involve selective attention and executive functions.
加工： 大脑进行心理操作：编码、比较、决策及将信息存入记忆。此阶段可能涉及选择性注意和执行功能。
Output: The result of processing: a decision, a movement, a spoken word, or a retrieval of a stored memory.
输出： 加工的结果：一个决定、一个动作、一句言语或对存储记忆的提取。
This model underpins many IGCSE topics, such as decision-making, problem-solving, and memory, and it helps explain reaction times and errors as limitations in processing capacity.
该模型是许多 IGCSE 主题（如决策、问题解决和记忆）的基础，并有助于将反应时和错误解释为加工容量的限制。
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