📚 Year 10 CAIE Psychology: Formula & Theorem Quick Reference Handbook | Year 10 CAIE 心理学：公式定理速查手册
This handbook collects the essential formulas, laws, and must-know theoretical models that you need to master for the CAIE IGCSE Psychology syllabus. Use it as a rapid revision tool to anchor your understanding of research methods, descriptive statistics, and the core theorems that shape every topic from memory to social influence.
本手册汇集了 CAIE IGCSE 心理学大纲要求掌握的关键公式、定律和核心理论模型。您可以将其作为快速复习工具，巩固对研究方法、描述统计以及贯穿各个主题（从记忆到社会影响）的核心定理的理解。
1. Core Research Variables and Operationalisation | 核心研究变量与操作化
The independent variable (IV) is the factor the researcher deliberately manipulates or changes. It is the presumed cause in an experiment.
自变量（IV）是研究者故意操纵或改变的因素，是实验中被认为是原因的那个变量。
The dependent variable (DV) is the factor that is measured. It is the outcome that may change as a result of the manipulation of the IV.
因变量（DV）是被测量的因素，是可能随着自变量的操纵而发生改变的结果变量。
Operationalisation means defining variables in precise, measurable terms so that the experiment can be conducted clearly and replicated. For example, 'aggression' could be operationalised as the number of times a child hits a doll.
操作化指的是用精确、可测量的术语定义变量，使实验能够清晰进行并得以重复。例如，“攻击性”可以操作化定义为儿童击打娃娃的次数。
Extraneous variables are unwanted factors that could influence the DV if not controlled. When an extraneous variable systematically changes with the IV, it becomes a confounding variable and ruins the internal validity of the study.
额外变量是不必要的、如果未受控制就会影响因变量的因素。如果额外变量随着自变量系统性地变化，它就会变成混淆变量，破坏研究的内部效度。
2. Experimental Designs at a Glance | 实验设计速查
Independent groups design uses different participants in each condition of the IV. The main strength is no order effects, but a weakness is that participant variables may differ between groups.
独立组设计在自变量的每种条件下使用不同的被试。其主要优点是没有顺序效应，但缺点是被试变量可能在组间存在差异。
Repeated measures design uses the same participants in all conditions. This eliminates individual differences, but order effects (practice, fatigue, boredom) must be controlled, usually by counterbalancing.
重复测量设计在所有条件下使用同一批被试，消除了个体差异，但必须控制顺序效应（如练习、疲劳、厌倦），通常采用平衡法来解决。
Matched pairs design uses different but similar participants who have been matched on a variable relevant to the study, such as IQ. It reduces participant variables without order effects, but matching is difficult and time-consuming.
匹配对设计使用不同的、但在与实验相关的变量上（如智商）进行过匹配的相似被试。它减少了个体差异变量且无顺序效应，但匹配过程困难且耗时。
3. Sampling Methods | 抽样方法
Random sampling: every member of the target population has an equal chance of being chosen. This is the best way to achieve a representative sample, but it is often difficult to carry out fully.
随机抽样：目标人群中的每一个体都有均等机会被选入样本。这是获得代表性样本的最佳方法，但通常难以完全实施。
Opportunity sampling: researchers select participants who are readily available at the time of the study. It is quick and inexpensive, but the sample is likely to be biased because it only reflects those who were accessible.
机会抽样：研究者选取研究时最容易接触到的人作为被试。这种方法快捷且成本低，但样本可能存在偏差，因为它只反映了那些可接触到的人群。
Volunteer sampling: participants self-select, e.g. by responding to an advertisement. Such samples may be highly motivated but are often unrepresentative because they attract a certain type of person.
志愿者抽样：被试通过自我选择参与，例如回应广告。这类样本可能积极性很高，但往往不具代表性，因为它们只吸引特定类型的人。
Stratified sampling: the researcher identifies subgroups (strata) in the population and then selects random samples from each stratum in proportion to their size. This helps to ensure that all key groups are represented.
分层抽样：研究者识别出人群中的子群体（层），然后按比例从每一层中随机抽取样本。这有助于确保所有关键群体都被代表到。
4. Descriptive Statistics: Central Tendency and Dispersion | 描述统计：集中趋势与离散程度
The mean is the arithmetic average. It uses all data points but can be distorted by extreme outliers. The formula is:
平均数是算术平均数，它利用了所有数据点，但容易被极端异常值扭曲。计算公式为：
Mean = Σx ÷ n
式中 Σx 是所有分数的总和，n 是分数的个数。
The median is the middle value when scores are arranged in order. For an even number of scores, it is the average of the two middle numbers. The median is not affected by extreme scores, making it useful for skewed data.
中位数是将分数按顺序排列后位于中间位置的那个值。如果分数个数为偶数，则是中间两个数的平均值。中位数不受极端分数影响，适用于偏态数据。
The mode is the most frequently occurring score. A data set can have one mode, more than one mode (bimodal/multimodal), or no mode if all scores occur equally often.
众数是出现频率最高的分数。一组数据可以有一个众数、多个众数（双峰/多峰），或没有众数（如果所有分数出现次数相同）。
The range is the simplest measure of dispersion. It is the difference between the highest and lowest values.
全距是最简单的离散程度测量指标，即最高值与最低值之差。
Range = Maximum value − Minimum value
全距易受异常值影响，只能提供关于数据分布的有限信息。
5. Percentage Change, Ratios and Proportions | 百分比变化、比率与比例
Percentage change is used to measure how much a quantity has increased or decreased relative to its original value. It is a fundamental tool for comparing results before and after an intervention.
百分比变化用于衡量数量相对于原始值增加或减少了多少，是比较干预前后结果的基本工具。
% Change = [(New value − Old value) ÷ Old value] × 100
如果结果为正值表示增长，负值表示降低。
A ratio compares the sizes of two or more quantities. For instance, if in a study 15 participants were conformist and 45 were non-conformist, the ratio of conformists to non-conformists can be expressed as 15:45, which simplifies to 1:3.
比率用于比较两个或多个数量的大小。例如，在一项研究中如果有 15 名从众者和 45 名非从众者，从众者与非从众者的比率可以表示为 15:45，化简为 1:3。
tion or decimal. In the same example, the proportion of conformists is 15/60 = 0.25 (or 25%).
比例将整体的一部分表示为分数或小数。在上述例子中，从众者所占比例为 15/60 = 0.25（即 25%）。
6. Memory Laws and Models | 记忆定律与模型
Miller' er (1956) proposed that the capacity of short-term memory (STM) is about 7 ± 2 items. This 'magic number' at explains why we can hold only so many chunks of information at once. Chunking helps expand functional capacity by grouping bits into meaningful units.
米勒定律：乔治·米勒（1956）提出短时记忆（STM）的容量约为 7 ± 2 个组块。这个“魔法数字”解释了为什么我们一次只能保存有限数量的信息。组块化通过将信息比特组合为有意义的单元，帮助扩展功能性容量。
The Multi-Store Model (Atkinson and Shiffrin, 1968) describes memory as a flow of information through three separate stores: sensory register, Short-Term Memory, and Long-Term Memory. Information moves from STM to LTM through rehearsal. The model emphasises capacity, duration and coding differences between stores.
多存储模型（阿特金森和希夫林，1968）将记忆描述为信息流经三个独立仓库的过程：感觉登记、短时记忆和长时记忆。信息通过复述从短时记忆转入长时记忆。该模型强调了各仓库在容量、持续时间与编码方式上的差异。
Long-Term Memory is divided into episodic (personal experiences), semantic (facts) and procedural (skills) memory, as suggested by Tulving. This distinction is crucial for understanding different types of amnesia.
图尔文提出长时记忆可分为情景记忆（个人经历）、语义记忆（事实）和程序性记忆（技能）。这一区分对于理解不同类型的失忆症至关重要。
7. Key Theorems of Social Influence | 社会影响关键定理
Asch's Conformity Paradigm (1951, 1955): In unambiguous line-judgement tasks, about 75% of participants conformed to an obviously wrong majority at least once. The key factors affecting conformity are group size (conformity increased up to 3-4 confederates and then leveled off), unanimity (conformity plummeted if there was just one dissenter), and task difficulty.
阿希从众范式（1951, 1955）：在明确的线段判断任务中，约 75% 的被试至少有一次屈服于明显错误的大多数。影响从众的关键因素是：群体规模（从众在 3 到 4 名合谋者时上升，之后趋于平缓）、一致性（只要有一名异议者，从众就急剧下降）和任务难度。
Milgram's Obedience to Authority (1963): 65% of participants administered what they believed were lethal shocks to a learner simply because an authority figure instructed them to. Obedience was shaped by proximity of the victim, proximity of the authority, and diffusion of responsibility.
米尔格拉姆的服从权威实验（1963）：65% 的被试仅仅因为权威人物的指令，就向学习者施加了他们以为致命的电击。受害者距离、权威人物距离以及责任扩散等因素调节着服从程度。
Bystander Apathy Effect (Latane and Darley): The likelihood of helping in an emergency decreases as the number of bystanders increases, due to diffusion of responsibility and pluralistic ignorance. The five-step decision model (notice, interpret as emergency, assume responsibility, know how to help, decide to help) explains when help will be offered.
旁观者冷漠效应（拉塔奈和达利）：在紧急情境下，旁观者人数越多，个体提供帮助的可能性越低，原因在于责任扩散和多数无知。五步决策模型（注意、解释为紧急、承担责任、知道如何帮助、决定帮助）解释了人们何时会施以援手。
8. Developmental Psychology Theories | 发展心理学理论
Piaget's Stages of Cognitive Development: Children progress through four invariant stages — sensorimotor (0-2 years, object permanence), pre-operational (2-7 years, egocentrism, centration), concrete operational (7-11 years, conservation, logical thinking about concrete objects) and formal operational (11+ years, abstract and hypothetical reasoning). The process is driven by assimilation, accommodation and equilibration.
皮亚杰认知发展阶段论：儿童依次经历四个不变的阶段——感知运动阶段（0-2 岁，客体永久性）、前运算阶段（2-7 岁，自我中心、集中化）、具体运算阶段（7-11 岁，守恒、对具体事物的逻辑思维）和形式运算阶段（11 岁以后，抽象和假设推理）。该过程由同化、顺应和平衡驱动。
Dweck's Mindset Theory: Individuals hold either a fixed mindset (believing intelligence is static) or a growth mindset (believing intelligence can be developed). Growth mindset fosters resilience and a love of learning, while fixed mindset leads to helplessness in the face of failure.
德韦克思维模式理论：个体持有固定型思维（认为智力是固定的）或成长型思维（认为智力可以发展）。成长型思维培养韧性和对学习的热爱，而固定型思维则导致面对失败时的无助。
Ainsworth's Strange Situation identified three attachment types: secure, insecure-avoidant and insecure-resistant. The key behaviours observed were separation anxiety, stranger anxiety and reunion behaviour. The caregiver's sensitivity hypothesis is the most influential explanation for these differences.
安斯沃斯特朗奇情境法识别出三种依恋类型：安全型、不安全-回避型和不安全-矛盾型。观察的关键行为是分离焦虑、陌生人焦虑和重聚行为。养育者的敏感性假设是解释这些差异最具影响力的理论。
9. Learning Theories and Conditioning Laws | 学习理论与条件作用定律
Classical Conditioning (Pavlov): A neutral stimulus becomes a conditioned stimulus (CS) after repeated pairing with an unconditioned stimulus (UCS) that naturally elicits an unconditioned response (UCR). Eventually the CS alone produces the conditioned response (CR). Key laws include acquisition, extinction, spontaneous recovery, generalisation and discrimination.
经典条件作用（巴甫洛夫）：中性刺激在与自然引发无条件反应（UCR）的无条件刺激（UCS）多次配对后，转变为条件刺激（CS）。最终，仅条件刺激就能引发条件反应（CR）。关键规律包括：习得、消退、自然恢复、泛化和分化。
Operant Conditioning (Skinner): Behaviour is shaped by its consequences. Reinforcement increases the likelihood of a behaviour; punishment decreases it. Positive means adding something, negative means removing something. The schedules of reinforcement (fixed/variable, interval/ratio) have profound effects on response rates and extinction resistance.
操作性条件作用（斯金纳）：行为由其后果塑造。强化增加行为发生的可能性，惩罚减少它。正强化指增加某物，负强化指移除某物。强化程式（固定/可变，间隔/比率）对反应速率和消退抵抗性有深远影响。
Social Learning Theory (Bandura): Learning occurs through observation, imitation and modelling of others, mediated by cognitive processes: attention, retention, reproduction and motivation. The Bobo doll experiments demonstrated that children imitate aggressive role models, especially when the model is rewarded (vicarious reinforcement).
社会学习理论（班杜拉）：学习通过观察、模仿和示范他人而进行，并受认知过程——注意、保持、再现和动机——的调节。波波玩偶实验表明，儿童会模仿攻击性榜样，尤其当榜样因行为获得奖励时（替代性强化）。
10. Biological Psychology Essentials | 生物心理学基础
Synaptic Transmission: An electrical impulse reaches the presynaptic terminal, triggering the release of neurotransmitters from vesicles into the synaptic cleft. These chemicals bind to receptors on the postsynaptic membrane, causing excitation or inhibition of the next neuron. Reuptake and enzymatic breakdown terminate the signal.
突触传递：电冲动到达突触前终扣，触发囊泡释放神经递质进入突触间隙。这些化学物质与突触后膜上的受体结合，导致下一个神经元的兴奋或抑制。回收和酶解会终止信号。
The Body's 'Fight or Flight' Response: When a threat is perceived, the amygdala sends a distress signal to the hypothalamus, which activates the sympathetic-adrenal-medullary (SAM) pathway. The adrenal medulla releases adrenaline and noradrenaline, producing the physiological changes that prepare the body for action (increased heart rate, dilated pupils, etc.).
身体的“战斗或逃跑”反应：当感知到威胁时，杏仁核向下丘脑发出求救信号，激活交感神经-肾上腺髓质（SAM）通路。肾上腺髓质释放肾上腺素和去甲肾上腺素，产生让身体准备行动的生理变化（心率加快、瞳孔放大等）。
11. Research Ethics and Quality Criteria | 研究伦理与质量标准
Ethical Guidelines: The British Psychological Society (BPS) sets out principles that must be followed: informed consent (participants should know what the study involves and agree to take part), right to withdraw (at any time without penalty), protection from harm (psychological or physical), confidentiality (data should not be traceable to individuals), and debriefing (after the study, the true nature is explained).
伦理准则：英国心理学会（BPS）制定了必须遵循的原则：知情同意（被试应了解研究涉及内容并同意参加）、随时退出的权利（不受惩罚）、免受伤害（心理或身体）、保密性（数据不能追踪到个人）以及事后解释（研究结束后说明真实目的）。
Research quality is judged by reliability (consistency of results) and validity (whether the study measures what it claims to measure). Internal reliability can be checked through split-half methods, while inter-rater reliability is key for observations. Internal validity is threatened by confounding variables and demand characteristics, while external validity concerns generalisability to other people (population validity) and settings (ecological validity).
研究质量通过信度（结果的一致性）和效度（研究是否测量了它声称要测量的东西）来评判。内部信度可通过分半法检查，观察研究则重视评分者间信度。内部效度受混淆变量和需求特征威胁，外部效度关心向其他人（人群效度）及其他情境（生态效度）的可推广性。
12. Key Overarching Principles in Psychology | 心理学关键总原则
Correlation does not imply causation. A correlation coefficient (r) describes the strength and direction of a relationship between two variables, but it cannot prove that one variable caused the change in the other. Hidden third variables may be responsible.
相关性不等于因果性。相关系数（r）描述了两个变量间关系的强度和方向，但不能证明一个变量引起了另一个变量的变化。可能存在隐藏的第三变量在起作用。
Nature versus nurture is a central debate concerning the relative contribution of genetic inheritance (nature) and environmental factors (nurture) to human behaviour. Most modern psychologists adopt an interactionist position, recognising that both influences are intertwined.
先天与后天之争是探讨基因遗传（先天）和环境因素（后天）对人类行为相对贡献的核心辩论。现代心理学家大多采取交互论立场，承认两种影响相互交织。
Reductionism versus holism: Reductionism seeks to explain behaviour by breaking it down into its simplest components (e.g. biological reductionism explains social behaviour at the level of neurotransmitters). Holism argues that the whole is more than the sum of its parts and behaviour can only be understood within its broader social and cultural context.
还原论与整体论：还原论试图通过将行为分解为最简单的组成部分来解释（例如生物还原论从神经递质层面解释社会行为）。整体论则主张整体大于部分之和，行为只有放在更广阔的社会与文化脉络中才能被理解。
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