📚 IGCSE Psychology: Formulas and Key Theories Quick Reference | IGCSE 心理学：公式与关键理论速查手册
This quick reference handbook brings together the essential formulas, statistical measures, and the key theoretical frameworks (often referred to as ‘theorems’ in the context of psychological laws) that you need for your CIE IGCSE Psychology course. Every concept is explained in English immediately followed by its Chinese translation, so you can build understanding in both languages. Keep this guide handy for revision, and remember that in psychology, knowing how to apply these formulas and theories is just as important as memorising them.
这份速查手册汇总了 CIE IGCSE 心理学课程所需的基本公式、统计指标以及关键理论框架（在心理学定律语境中常被称为“定理”）。每个概念先用英文解释，紧接着是中文译文，帮助你用双语理解。复习时请随时查阅，并记住：在心理学中，知道如何应用这些公式和理论与你记住它们同样重要。
1. Research Methods and Statistical Formulas | 研究方法与统计公式
In any psychology study, researchers collect numerical data that must be summarised. The three most common measures of central tendency tell us where the centre of the data lies.
在任何心理学研究中，研究人员都会收集需要总结的数字数据。三种最常见的集中趋势测量值可以告诉我们数据的中心位于何处。
Mean = Σx / n
The mean (average) is calculated by adding up all the scores (Σx) and dividing by the total number of scores (n). It is sensitive to extreme values.
平均数的计算方法是将所有分数相加 (Σx)，再除以分数的总数 (n)。它对极端值很敏感。
The median is the middle value when all scores are arranged in order. If there is an even number of scores, the median is the average of the two middle numbers. It is not affected by outliers.
中位数是将所有分数从小到大排序后位于中间的值。如果分数总数为偶数，中位数就是中间两个数值的平均数。它不受极端值影响。
The mode is the most frequently occurring score in a data set. A set can have more than one mode. It is the only measure of central tendency that can be used with nominal (category) data.
众数是数据集中出现次数最多的分数。一个数据集可以有多个众数。它是唯一能用于称名数据（分类数据）的集中趋势测量值。
Spread or dispersion is described by the range.
数据的离散程度用全距（范围）来描述。
Range = Highest score – Lowest score
The range is quick to calculate but only considers two values, so a single extreme score makes it misleading.
全距计算简便，但只考虑两个数值，因此一个极端分数就会使其产生误导。
When comparing frequencies, we often express parts as a percentage of the whole.
比较频数时，我们常用百分比来表示部分占整体的多少。
Percentage = (Part / Whole) × 100%
In an experiment, the independent variable (IV) is the factor deliberately manipulated by the researcher. The dependent variable (DV) is the factor measured to see if the IV has had an effect.
在实验中，自变量 (IV) 是研究者有意操纵的因素。因变量 (DV) 是为观察自变量是否产生影响而测量的因素。
Extraneous variables are any other variables that might affect the DV, and they must be controlled so they do not become confounding variables.
额外变量是任何可能影响因变量的其他变量，必须加以控制，以免成为混淆变量。
There are three main experimental designs. In an independent groups design, different participants take part in each condition. In a repeated measures design, the same participants do all conditions. A matched pairs design uses different but closely matched participants in each condition.
主要有三种实验设计。在独立组设计中，不同的参与者分别接受不同的实验条件。在重复测量设计中，相同的参与者接受所有实验条件。配对组设计则是在每个实验条件下使用不同但高度匹配的参与者。
2. Key Theories of Memory | 记忆的关键理论
Atkinson and Shiffrin (1968) proposed the Multi-Store Model of Memory (MSM). It describes three separate stores: sensory memory, short-term memory (STM) and long-term memory (LTM).
Atkinson 和 Shiffrin（1968）提出了记忆的多存储模型 (MSM)。该模型描述了三个独立的存储系统：感觉记忆、短时记忆 (STM) 和长时记忆 (LTM)。
Information enters sensory memory, where it is held briefly. If attention is paid to it, the information passes into STM. Through maintenance rehearsal (repetition), it can then be transferred to LTM.
信息首先进入感觉记忆，在此短暂停留。如果加以注意，信息就会进入短时记忆。通过维持性复述（重复），信息便能转入长时记忆。
on of about 18-30 seconds. LTM has potentially unlimited capacity and a lifetime duration.
感觉记忆的容量极大，但持续时间仅为几毫秒至两秒。短时记忆的容量有限，为 7±2 个组块，持续时间约 18-30 秒。长时记忆的容量可能无限，并可持续终生。
Baddeley and Hitch (1974) developed the Working Memory Model (WMM), which replaced the idea of a single STM. The central executive acts as an attentional controller and allocates tasks to two slave systems: the phonological loop (deals with auditory and verbal information) and the visuospatial sketchpad (deals with visual and spatial information). A later addition, the episodic buffer, integrates information from these systems and links to LTM.
Baddeley 和 Hitch（1974）提出了工作记忆模型 (WMM)，取代了单一的短时记忆概念。中央执行器作为注意控制器，将任务分配给两个子系统：语音回路（处理听觉和言语信息）和视空间画板（处理视觉和空间信息）。后来增加的情景缓冲区将这些系统的信息整合起来，并与长时记忆相连。
Forgetting in STM is often explained by trace decay (memory fades with time) or displacement (new information pushes out old items). In LTM, interference theory suggests that forgetting occurs because similar memories compete, either proactively (old memories disrupt new ones) or retroactively (new memories disrupt old ones).
短时记忆中的遗忘通常用痕迹消退（记忆随时间淡化）或替代（新信息挤出旧信息）来解释。在长时记忆中，干扰理论认为遗忘是由于相似记忆相互竞争所致，分为前摄干扰（旧记忆干扰新记忆）和倒摄干扰（新记忆干扰旧记忆）。
3. Perception: Theories and Constancies | 知觉：理论与恒常性
Gibson’s direct theory of perception argues that we extract information directly from the environment without the need for thought or inference. The optic array provides all the cues we need, such as texture gradient and motion parallax.
Gibson 的直接知觉理论认为，我们能直接从环境中提取信息，无需思维或推论。光阵列提供了所有所需线索，如纹理梯度和运动视差。
In contrast, Gregory’s constructivist theory suggests perception is an active process where the brain constructs a hypothesis about what we see using top-down processing. This explains why visual illusions trick us: we make incorrect inferences based on past experience.
与之相反，Gregory 的建构主义理论则认为知觉是一个主动过程，大脑运用自上而下的加工构建关于所见事物的假设。这就解释了为何视错觉会欺骗我们：我们基于过往经验做出了错误的推断。
Perceptual constancies allow us to perceive objects as stable even when the retinal image changes. Size constancy means we perceive an object as the same size even if its distance from us changes. Shape constancy means we recognise a door as a rectangle even when it opens and casts a trapezoidal image on the retina. Colour constancy helps us recognise colours under different lighting conditions.
知觉恒常性使我们能在视网膜影像变化时依旧感知到物体的稳定。大小恒常性意味着即使物体与我们的距离改变，我们仍感知到其大小不变。形状恒常性意味着即便门被打开并在视网膜上投射出梯形影像，我们仍将其识别为矩形。颜色恒常性则帮助我们在不同光照条件下识别颜色。
Famous illusions include the Muller-Lyer illusion, where lines of equal length appear different because of arrowheads, and the Ponzo illusion, where the top line seems longer due to converging lines creating a depth cue.
著名的错觉包括缪勒-莱耶错觉（箭头使等长线条看起来不等）和彭佐错觉（汇聚的线条提供了深度线索，使上方线条看起来更长）。
4. Social Influence: Conformity and Obedience | 社会影响：从众与服从
Conformity is a change in behaviour or belief to fit in with a group. Asch (1951) conducted a famous line-judgement study where a naive participant was placed in a group of confederates who deliberately gave wrong answers. About 75% of participants conformed at least once, and the overall conformity rate was approximately 37%.
从众是指为融入群体而改变行为或信念。Asch（1951）进行了一项著名的线条判断实验：一名不知情的被试被安排在一群故意给出错误答案的假被试中。大约 75% 的被试至少从众过一次，整体从众率约为 37%。
Factors increasing conformity include a larger group size (up to about 4-5 people), a unanimous majority, and a difficult or ambiguous task. Having a dissenting ally dramatically reduces conformity.
增加从众的因素包括较大的群体规模（大约超过 4-5 人）、多数人的一致性以及困难或模糊的任务。而有一个与之持异议的同伴则会显著降低从众率。
Obedience refers to following a direct order from an authority figure. Milgram (1963) recruited participants to act as ‘teachers’ in a memory experiment, instructing them to administer increasingly severe electric shocks to a ‘learner’ (a confederate). A staggering 65% of participants delivered the maximum 450-volt shock, even when the learner appeared to be in pain.
服从是指遵从权威人物下达的直接命令。Milgram（1963）招募被试在一项记忆实验中扮演“老师”，要求他们对“学生”（实际上是假被试）实施不断增强的电击。令人震惊的是，65% 的被试施加了最高 450 伏的电击，即使“学生”表现出痛苦。
Obedience was highest when the authority was close by and wearing a lab coat, when the victim was at a distance, and when the task was framed as contributing to scientific progress.
当权威人物近距离在场并身着实验室白大褂、受害者距离较远、以及任务被说成是为科学进步做贡献时，服从程度最高。
Deutsch and Gerard (1955) proposed a dual-process model of conformity: normative social influence (we conform to be accepted and liked) and informational social influence (we conform because we believe others have more accurate knowledge).
Deutsch 和 Gerard（1955）提出了从众的双重过程模型：规范性社会影响（我们为被接纳和喜欢而从众）和信息性社会影响（我们因相信他人拥有更准确的知识而从众）。
5. Developmental Psychology: Piaget's Stage Theory | 发展心理学：皮亚杰的阶段理论
Jean Piaget’s theory of cognitive development describes how children’s thinking becomes increasingly sophisticated. He proposed four invariant stages, each characterised by different cognitive abilities.
皮亚杰的认知发展理论描述了儿童思维如何变得越来越复杂。他提出了四个不变的阶段，每个阶段都有不同的认知能力特征。
In the sensorimotor stage (0-2 years), infants learn through senses and actions. The key achievement is object permanence – understanding that objects continue to exist even when out of sight.
在感觉运动阶段（0-2 岁），婴儿通过感官和动作进行学习。其关键成就是客体永久性——明白物体即使从视线中消失也依然存在。
The preoperational stage (2-7 years) is marked by symbolic thinking, but children are egocentric (unable to see others’ viewpoints) and lack conservation (understanding that quantity remains the same despite changes in shape or arrangement). They also show animism, attributing lifelike qualities to inanimate objects.
前运算阶段（2-7 岁）以象征性思维为标志，但儿童以自我为中心（无法从他人角度看问题）且缺乏守恒概念（不理解数量在形状或排列变化后仍保持不变）。他们还表现出泛灵论，给无生命物体赋予生命特征。
In the concrete operational stage (7-11 years), children become capable of logical reasoning about concrete events. They master conservation, classification and seriation, but struggle with abstract or hypothetical ideas.
具体运算阶段（7-11 岁）的儿童能够对具体事件进行逻辑推理。他们掌握了守恒、分类和序列化，但仍难以处理抽象或假设性概念。
During the formal operational stage (11+ years), adolescents develop the ability to think abstractly, scientifically, and hypothetically. They can engage in systematic problem-solving and philosophical reasoning.
在形式运算阶段（11 岁以上），青少年发展出抽象、科学和假设性思维的能力。他们能进行系统的问题解决和哲学推理。
Piaget used the concepts of schema (mental frameworks), assimilation (fitting new information into existing schemas), accommodation (adapting schemas to fit new information), and equilibration (balancing assimilation and accommodation) to explain learning.
皮亚杰用图式（心理框架）、同化（将新信息纳入已有图式）、顺化（调整图式以适应新信息）和平衡（平衡同化与顺化）等概念来解释学习过程。
Vygotsky emphasised social and cultural influences on development, introducing the zone of proximal development (ZPD) – the gap between what a child can do alone and what they can achieve with guidance. Scaffolding refers to the supportive assistance provided by a knowledgeable other within the ZPD.
维果茨基强调社会文化对发展的影响，提出了最近发展区 (ZPD)——儿童独自所能完成与在指导下所能达到的水平之间的差距。脚手架指的就是知识更丰富者在最近发展区内提供的支持性帮助。
6. Biopsychology: Neurons and Synaptic Transmission | 生物心理学：神经元与突触传递
A neuron is the basic building block of the nervous system. It consists of dendrites (receive signals), a cell body (soma), an axon (carries the electrical impulse), a myelin sheath (insulates and speeds up transmission), and terminal buttons (release neurotransmitters).
神经元是神经系统的基本构成单元。它由树突（接收信号）、细胞体、轴突（传导电冲动）、髓鞘（绝缘并加速传导）以及终扣（释放神经递质）组成。
When an action potential (electrical signal) reaches the end of the axon, it triggers the release of neurotransmitters from synaptic vesicles into the synaptic gap. These chemicals diffuse across the synapse and bind to specialised receptor sites on the postsynaptic neuron, causing either excitation (more likely to fire) or inhibition (less likely to fire).
当动作电位（电信号）传到轴突末梢，会触发突触小泡向突触间隙释放神经递质。这些化学物质扩散通过突触，与突触后神经元上特化的受体位点结合，引起兴奋（更可能发放冲动）或抑制（更不可能发放冲动）。
Any unused neurotransmitter is either taken back up into the presynaptic neuron (reuptake) or broken down by enzymes. Serotonin, dopamine, acetylcholine and gamma-aminobutyric acid (GABA) are examples of important neurotransmitters.
未被利用的神经递质要么被回收到突触前神经元（再摄取），要么被酶分解。血清素、多巴胺、乙酰胆碱和伽马-氨基丁酸 (GABA) 是几类重要的神经递质。
7. Learning Theories: Conditioning and Social Learning | 学习理论：条件作用与社会学习
In classical conditioning, Pavlov demonstrated that a neutral stimulus (NS) could become a conditioned stimulus (CS) that elicits a conditioned response (CR) after repeated pairing with an unconditioned stimulus (UCS), which naturally produces an unconditioned response (UCR).
在经典条件作用中，巴甫洛夫证明，中性刺激 (NS) 通过与能自然引发出无条件反应 (UCR) 的无条件刺激 (UCS) 反复配对后，可以变成引发条件反应 (CR) 的条件刺激 (CS)。
Extinction occurs when the CS is repeatedly presented without the UCS, and spontaneous recovery is the sudden reappearance of the CR after a rest period. Generalisation refers to responding to stimuli similar to the CS.
当条件刺激反复单独呈现而不伴随无条件刺激时，便会出现消退；自发恢复则是指休息一段时间后条件反应突然再次出现。泛化是指对与条件刺激相似的刺激也做出反应。
Operant conditioning, developed by Skinner, states that behaviour is shaped by its
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