📚 AQA Year 9 Psychology Formula & Theorem Quick Reference Handbook | Year 9 AQA 心理学公式定理速查手册
Welcome to your go-to Psychology 'formula sheet'. While Psychology is not a subject of equations like Physics, it is built on robust models, laws, and statistical recipes that explain human behaviour. This handbook collects the essential formulas, theorems, and quick-reference models you will need for the AQA Year 9 course, covering memory, perception, social influence, development, research methods, and more. Use it as a revision companion to cement your understanding of how the mind works.
欢迎使用这本心理学“公式手册”。虽然心理学不像物理那样充满方程式，但它建立在解释人类行为的坚实模型、定律和统计方法之上。本手册汇集了 AQA Year 9 课程所需的核心公式、定理与速查模型，涵盖记忆、知觉、社会影响、发展、研究方法等。将它作为你的复习伙伴，夯实你对心智运作方式的理解。
1. Descriptive Statistics: Mean, Median, Mode & Range | 描述性统计：平均数、中位数、众数与极差
The 'big four' of descriptive statistics allow us to summarise a data set with a single value. The mean is calculated by adding all scores and dividing by the number of scores. The median is the middle value when data are ordered. The mode is the most frequently occurring score. The range (a measure of dispersion) is the difference between the highest and lowest scores.
描述性统计的“四大件”使我们用单一数值概括数据集。平均数：将所有分数相加后除以分数个数。中位数：将数据排序后位于中间的值。众数：出现频率最高的分数。极差（一种离散度指标）：最高分与最低分之间的差值。
Mean = (Σx) / n | Range = Highest score - Lowest score
se these to spot patterns and compare conditions, but must watch out for outliers that skew the mean.
在一项研究中，若记忆测试分数为 5、8、8、12、15，则平均数 = (5+8+8+12+15)/5 = 9.6；中位数 = 8；众数 = 8；极差 = 15-5=10。心理学家用它们发现规律和比较条件，但必须注意会拉偏平均数的异常值。
2. Percentage Change & Ratio | 百分比变化与比率
Original value] × 100. Ratios, such as the number of participants who conformed to the total, are expressed as a simplified relationship (e.g., 3:1). Always state whether a result represents an increase or a decrease.
许多心理学研究追踪随时间或组间的变化。百分比变化公式：[(新值 - 原值) / 原值] × 100。比率（例如从众参与者人数与总人数之比）表示为约简的关系（如 3:1）。务必说明结果是增加还是减少。
Example: In a replication of Asch' had 8 conformers out of 20, the percentage increase in conformity is [(12-8)/8] × 100 = 50%. This is a quick 'effect size' snapshot.
示例：在重复阿希实验时，20名参与者中有12人至少从众一次，从众比率为 12:8，约简为 3:2。若原研究有8人从众，则从众的百分比增幅为 [(12-8)/8] × 100 = 50%。这是快速了解“效应大小”的缩影。
3. The Multi-Store Memory Model (Atkinson & Shiffrin) | 多存储记忆模型（阿特金森和谢弗林）
This foundational 'formula' rows are controlled by attention and rehearsal. Without attention, sensory information decays rapidly; without rehearsal, STM items are displaced or decay. The model is linear and highlights how information is transferred.
这个记忆的基础“公式”提出，信息流经三个固定的存储库：感觉登记 → 短时记忆（STM） → 长时记忆（LTM）。箭头由注意和复述控制。缺乏注意，感觉信息迅速消退；缺乏复述，短时记忆项目会被替代或消退。该模型是线性的，突出了信息如何传递。
±2 items, duration: 18-30 sec) → Rehearsal → LTM (capacity: unlimited, duration: lifetime)
The '7±2 items' is Miller's magic number – a vital 'constant' for STM capacity. Maintenance rehearsal loops keep information in STM, while elaborative rehearsal transfers it to LTM by linking it to existing knowledge.
“7±2 个项目”是米勒的魔法数字——短时记忆容量的关键“常数”。维持性复述循环把信息保留在短时记忆中，而精细复述通过将信息与已有知识相连接，将其转移至长时记忆。
4. The Working Memory Model (Baddeley & Hitch) | 工作记忆模型（巴德利和希奇）
The Working Memory Model (WMM) challenges the idea of a single STM store. It is a multi-component 'system' with a Central Executive, Phonological Loop, Visuo-Spatial Sketchpad, and Episodic Buffer. Think of the Central Executive as the manager that distributes attention, while the slave systems handle verbal and visual data.
工作记忆模型（WMM）挑战了单一短时记忆库的观点。它是一个包含中央执行器、语音回路、视空画板和情节缓冲器的多组件“系统”。中央执行器如同分配注意力的管理者，而从属系统处理言语和视觉数据。
| Component | Function (Formula role) | Capacity |
| Central Executive | Supervisory attentional controller; decides what to process | Limited, flexible |
| Phonological Loop | Holds speech-based information; inner voice and inner ear | ~2 seconds of speech |
| Visuo-Spatial Sketchpad | Manipulates visual and spatial images | 3-4 objects |
| Episodic Buffer | Integrates information across domains into episodes; links to LTM | Limited |
This model explains how we can perform two tasks simultaneously if they use different slave systems (e.g., listening to music while drawing), because no single store is overloaded. It is a more dynamic 'equation' for immediate memory than the multi-store model.
该模型解释了若两项任务使用不同的从属系统（例如边听音乐边画画），我们能同时执行，因为没有单个存储库过载。与多存储模型相比，这是一个更动态的即时记忆“方程式”。
5. Ebbinghaus Forgetting Curve & Interference ‘Formula’ | 艾宾浩斯遗忘曲线与干扰“公式”
Hermann Ebbinghaus plotted the rate at which we forget nonsense syllables over time – a curve that drops steeply in the first hour and then levels off. The forgetting 'formula' is not an equation but a graphical law: without repetition, retention drops to about 40% after one day. Re-learning takes less time, which gave us the 'savings score': Savings = (Original learning time - Relearning time) / Original learning time × 100.
赫尔曼·艾宾浩斯绘制了我们忘记无意义音节随时间变化的速率曲线——该曲线在最初一小时内急剧下降，然后趋于平缓。遗忘“公式”不是方程，而是一条图形定律：没有重复，一天后记忆保持量降至约40%。再学习耗时更短，由此产生了“节省分数”：节省量 = (原学习时间 - 再学习时间) / 原学习时间 × 100。
Two other forgetting 'theorems' are proactive interference (old learning disrupts new) and retroactive interference (new learning disrupts old). They act like a competitive formula: similar memories interfere most. For example, learning French vocabulary may retroactively interfere with previously learned Spanish if not consolidated.
另外两个遗忘“定理”是前摄干扰（旧学习干扰新学习）和倒摄干扰（新学习干扰旧学习）。它们像竞争公式：相似的记忆干扰最大。例如，学习法语词汇可能会倒摄干扰之前学过的西班牙语，若未得到巩固。
6. Serial Position Curve & the Primacy-Recency Formula | 序列位置曲线与首因-近因公式
imacy effect) and at the end (recency effect), while middle items are recalled worst. This 'U-shaped' f(serial position), determined by rehearsal (long-term memory for primacy) and STM availability (recency). If a delay is introduced after learning, the recency effect disappears.
记忆清单时，开头项目（首因效应）和末尾项目（近因效应）的回忆率最高，而中间项目回忆最差。这条“U形”曲线可用序列位置公式表达：回忆概率 = f(序列位置)，由复述（长时记忆支持首因）和短时记忆可用性（近因）决定。若学习后引入延迟，近因效应便消失。
Practically, if you are given a 20-word list, you are likely to remember words 1-3 (primacy) and words 18-20 (recency), but struggle with words 9-11. This pattern provides evidence for separate STM and LTM stores. The formula also explains why cramming right before a test helps with recency, but only deep encoding secures long-term recall.
实际上，若给你一张20词的清单，你很可能记住词1-3（首因）和词18-20（近因），却难以记起词9-11。该模式为独立的短时与长时记忆存储提供了证据。此公式也解释了为什么考前抱佛脚有助于近因回忆，但只有深度编码才能保证长期记忆。
7. Asch's Conformity ‘Theorem’ & Variables | 阿希从众“定理”与变量
Solomon Asch's line-judgement experiments revealed a powerful social 'formula': conformity = f(group size, unanimity, task difficulty). About 75% majorities added little extra pressure. If the majority is unanimous, conformity soars, but a single dissenter reduces conformity sharply.
所罗门·阿希的线段判断实验揭示了一个有力的社会“公式”：从众 = f(群体规模，一致性，任务难度)。当同谋者给出明显错误答案时，约75%的参与者至少从众一次。从众率在多数派为3-4人时达到顶峰；更大的多数派几乎不增加额外压力。若多数派一致，从众率飙升；但仅一个异议者就能大幅降低从众。
| Variable | Effect on Conformity | Asch's finding (approx.) |
| Group size 1 vs 3 | Sharp increase | Conformity ~3% to ~32% |
| Unanimity broken | Drops dramatically | Fell to ~5% in some trials |
| Task difficulty high | Increases (people look to others for information) | Conformity trend rose |
This 'normative social influence' drives public compliance without private acceptance. The theorem reminds us that context can outweigh individual judgement.
这种“规范性社会影响”导致公开顺从而无私人接纳。该定理提醒我们，情境可以压倒个人判断。
8. Milgram's Obedience ‘Equation’ | 米尔格拉姆服从“方程”
Stanley Milgram measured the voltage a participant would administer to a 'learner' under authority pressure. The stark result: 65% went to the maximum 450 volts. The obedience 'equation' ersonal responsibility. When the authority figure was close (in the same room), obedience was high; when the victim was in the same room, obedience dropped. When participants had to force the learner's hand onto a shock plate, obedience fell to 30%.
斯坦利·米尔格拉姆测量了在权威压力下参与者对“学习者”施加的电压。惊人的结果：65%的人达到了最高450伏。服从“方程”可建模为：服从 = 权威接近度 × 受害者接近度 / 个人责任。当权威人物接近（同一房间），服从度高；当受害者在同一房间，服从度下降。当参与者必须将学习者的手按在电击板上时，服从率降至30%。
The agentic state theory explains this: individuals move into an agentic state where they see themselves as carrying out another's wishes. This transforms the equation – personal responsibility goes to zero, and obedience skyrockets. The proximity of the authority increases the legitimacy of the command, acting as a multiplier in the obedience formula.
代理状态理论解释了这一点：个体进入代理状态，视自己为他人的意志执行者。这改变了方程——个人责任归零，服从急剧上升。权威的接近度增强了命令的正当性，成为服从公式中的乘数。
9. Ainsworth's Strange Situation Classifications | 安斯沃斯的陌生情境分类
Mary Ainsworth developed a structured observation 'formula' to assess attachment type in infants (12-18 months). The procedure involves eight episodes of separations and reunions with the caregiver and a stranger. Three main attachment types emerge: Secure (Type B), Insecure-Avoidant (Type A), and Insecure-Resistant (Type C). The percentages serve as normative constants: ~70% secure, ~20% avoidant, ~10% resistant in middle-class US samples.
玛丽·安斯沃斯建立了一个结构化观察“公式”，评估12-18个月婴儿的依恋类型。程序包含与照看者和陌生人的八次分离与重聚。三种主要依恋类型出现：安全型（B型）、不安全-回避型（A型）和不安全-抵抗型（C型）。百分比可作为常模常数：美国中产样本中约70%安全型，20%回避型，10%抵抗型。
The key behavioural indicators – proximity seeking, exploration base, separation anxiety, and reunion behaviour – act as variables in the attachment 'equation'. A securely attached infant explores freely, shows distress on separation, and is easily comforted on reunion. This classification predicts later social and emotional development.
关键行为指标——亲近寻求、探索基础、分离焦虑和重聚行为——构成依恋“方程”的变量。安全型依恋婴儿自由探索，分离时表现出痛苦，重聚时易于安抚。这一分类可预测后期的社交与情感发展。
10. Piaget's Stage Theory Formula | 皮亚杰阶段理论公式
nitive development unfolds through four invariant stages. Think of this as a developmental 'formula' ixed order, though the ages may vary slightly. The stages are characterised by distinct intellectual abilities and limitations.
让·皮亚杰提出认知发展依四个不变阶段展开。可将其视为一个发展“公式”：每个儿童按固定顺序经历感知运动 → 前运算 → 具体运算 → 形式运算，尽管年龄可能略有差异。各阶段以独特的智力能力和局限性为特征。
| Stage (Age approx.) | Key 'formula' feature | Example |
| Sensorimotor (0-2) | Object permanence develops; world through senses and actions | A hidden toy is searched for |
| Pre-operational (2-7) | Symbolic thought, egocentrism, lack of conservation | Child thinks taller glass has more liquid |
| Concrete Operational (7-11) | Logical reasoning about concrete events; conservation mastered | Understands mass remains same after shape change |
| Formal Operational (11+) | Abstract and hypothetical thinking; systematic problem-solving | Can solve algebraic equations and ponder morality |
Piaget's 'conservation of number' task is like an equation: children under 7 fail to recognise that quantity remains identical despite spatial rearrangement. This marks the difference between pre-operational and concrete operational thought.
皮亚杰的“数量守恒”任务如同一个等式：七岁以下儿童未能理解尽管空间重排，数量保持不变。这标志着前运算和具体运算思维的差异。
11. Research Design: The IV-DV-CV ‘Trinity’ | 研究设计：自变量-因变量-控制变量“三位一体”
Every experiment is built around a simple 'formula': manipulate the independent variable (IV), measure the dependent variable (DV), and control all other variables (CVs) to establish cause and effect. The IV is the factor you change; the DV is the outcome you record. Confounding variables are unwanted extras that might distort the IV-DV relationship.
每个实验都围绕一个简单“公式”构建：操纵自变量（IV），测量因变量（DV），并控制所有其他变量（CV）以确立因果关系。IV是你改变的因素；DV是你记录的结果。混淆变量是可能扭曲IV-DV关系的不必要额外因素。
Operationalising variables means turning abstract ideas into measurable steps. For example, 'memory' (DV) might be operationalised as the number of words correctly recalled from a list of 20. This brings precision to the formula. Standardised procedures are the constant 'terms' in the equation, ensuring every participant experiences the same setup.
变量操作化意味着将抽象概念转化为可测量的步骤。例如，“记忆”（DV）可操作化为从一份20词清单中正确回忆的单词数量。这为公式带来了精确性。标准化程序是方程中的常数“项”，确保每位参与者经历相同的设置。
12. Ethical Guidelines – The BPS ‘Code’ | 伦理准则 – BPS 守则
Psychological research must follow a set of ethical 'theorems' established by the British Psychological Society (BPS). The key principles can be remembered as the acronym C-C-D-I-W: Consent, Confidentiality, Deception (avoid unless necessary), Debrief, Right to Withdraw, and Protection from Harm. Any study involving humans must demonstrate how these were satisfied.
心理学研究必须遵循英国心理学会（BPS）制定的一套伦理“定理”。关键原则可用首字母缩写 C-C-D-I-W 记忆：知情同意、保密、欺骗（除非必要应避免）、事后解释、退出权利和免受伤害保护。任何涉及人类的研究都必须表明如何满足这些原则。
In practice, if deception is used, a full debrief must be given afterwards, restoring the participant's understanding and offering the right to withhold data. This acts as a balancing 'equation': the scientific benefit must outweigh any temporary discomfort, and no long-term harm is allowed. Ethical committees evaluate this balance before a study proceeds.
实践中，若使用了欺骗，必须随后提供全面的事后解释，恢复参与者的理解并提供数据撤销权。这扮演了一种平衡“方程式”：科学利益必须大于任何暂时不适，且不允许造成长期伤害。伦理委员会在研究开展前评估这种平衡。
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