📚 Year 11 AQA Psychology: Key Formulas & Theorems Quick Reference Handbook | Year 11 AQA 心理学：公式定理速查手册
This quick reference handbook compiles the essential formulas, statistical concepts and core theoretical principles you will encounter in AQA GCSE Psychology (Year 11). It is designed to support your study of research methods, memory, perception, social influence and development. Each entry is presented as a bite-sized pair of English and Chinese explanations to help you master the content efficiently.
本速查手册汇集了 AQA GCSE 心理学（Year 11）中必考的核心公式、统计概念与重要理论原理，涵盖研究方法、记忆、感知、社会影响和发展等领域。每一条目均以中英双语简要对照的形式呈现，帮助你在短时间内高效掌握这些必背内容。
1. Mean Formula & Application | 平均值公式及应用
The mean is a measure of central tendency that summarises a set of scores. In the formula, the symbol Σ (sigma) means 'sum of', x represents each individual score, and n is the total number of scores.
平均值是一种集中趋势度量，用来概括一组分数。公式中，符号 Σ（西格玛）表示“求和”，x 代表每一个单独的分数，n 是分数的总个数。
Mean = Σx / n
平均值 = Σx / n
rked example: For the scores 4, 7, 9, 12, 18, the mean is (4+7+9+12+18) ÷ 5 = 50 ÷ 5 = 10.
计算示例：对于分数 4、7、9、12、18，平均数 = (4+7+9+12+18) ÷ 5 = 50 ÷ 5 = 10。
2. Median, Mode & Range | 中位数、众数与极差
The median is the middle value when all scores are arranged in ascending order. If there is an even number of scores, the median is the average of the two middle numbers.
中位数是将所有分数从小到大排列后中间位置的那个数值。如果分数的个数为偶数，则中位数是中间两个数的平均值。
The mode is the most frequently occurring score in a data set. A set may have one mode (unimodal), more than one mode (multimodal) or no mode at all.
众数是数据集中出现频率最高的分数。一组数据可能有一个众数（单模式）、多个众数（多模式）或没有众数。
The range is a simple measure of dispersion. It is calculated by subtracting the smallest score from the largest score.
极差是一种最简单的离散程度度量，计算方法是用最大值减去最小值。
Range = highest score – lowest score
极差 = 最高分 – 最低分
3. Percentage & Proportion Calculation | 百分比与比例计算
A proportion compares a part to the whole and is often expressed as a fraction or decimal. To convert a proportion into a percentage, multiply by 100.
比例是部分与整体之间的比较，通常用分数或小数表示。要将比例转换成百分数，只需乘以 100。
Percentage (%) = (part / whole) × 100
百分数 (%) = (部分 / 总体) × 100
17 out of 50 participants recall a word correctly, the percentage is (17 ÷ 50) × 100 = 34%.
例如，如果 50 名被试中有 17 人能正确回忆一个词语，百分数为 (17 ÷ 50) × 100 = 34%。
When working with experimental data, you also use proportions to express the ratio of participants showing a particular behaviour. Always remember to express percentages to an appropriate number of decimal places as required by the exam.
在处理实验数据时，你也会需要用比例来表示表现出某种行为的被试占比。考试时务必按照题目要求保留合适的小数位数。
4. Normal Distribution Characteristics | 正态分布特征
A normal distribution produces a bell-shaped symmetrical curve. In a perfect normal distribution, the mean, median and mode are all located at the highest point of the curve.
正态分布会形成一条对称的钟形曲线。在完全的正态分布中，平均数、中位数和众数全部位于曲线最高点处。
The curve is symmetric around the centre, meaning 50% of the scores lie on each side. The tails extend infinitely without touching the horizontal axis.
曲线以中心为对称轴左右对称，意味着各有 50% 的分数分布在每一侧。两端尾部无限延伸，但不会碰触横轴。
Most scores cluster around the middle, and the frequency of extreme high or low scores decreases as you move away from the centre. This property makes the normal curve a cornerstone for understanding later inferential statistics.
大多数分数聚集在中间，离开中心越远，极高或极低分数的频率就越低。这一特性使正态曲线成为理解后续推断统计的重要基础。
5. Scatter Graphs & Correlation | 散点图与相关
A scatter graph visualises the relationship between two co-variables by plotting one variable on the x-axis and the other on the y-axis. Each point represents a single participant or observation.
散点图将两个协变量分别画在 x 轴和 y 轴上，从而直观地呈现二者之间的关系。图中每一个点代表一名被试或一次观测。
A positive correlation means that as one variable increases, the other also increases. A negative correlation means that as one variable increases, the other decreases.
正相关表示一个变量增大时，另一个变量也增大。负相关则表示一个变量增大时，另一个变量减小。
Zero correlation occurs when there is no clear pattern between the two variables; the points appear randomly scattered. Correlation does not imply causation.
零相关是指两个变量之间没有明显的规律，各点呈随机分布。相关关系并不代表因果关系。
Correlation coefficients (e.g. r) fall between -1 and +1. The closer the coefficient is to +1 or -1, the stronger the relationship.
相关系数（如 r）的取值范围在 -1 到 +1 之间。系数的绝对值越接近 1，说明关系越强。
6. Experimental Design Principles | 实验设计原理
The independent variable (IV) is the factor that the researcher deliberately manipulates or changes. The dependent variable (DV) is the factor that the researcher measures; it should be caused by the IV.
自变量（IV）是研究者有意操纵或改变的因素。因变量（DV）是研究者测量的因素，应由自变量所引起。
All other variables that could influence the DV must be controlled or held constant; these are called extraneous variables. If an extraneous variable systematically varies with the IV, it becomes a confounding variable.
所有可能影响因变量的其他变量都必须加以控制或保持恒定，这类变量称为额外变量。如果某个额外变量与自变量系统性共变，则演变为混淆变量。
Three standard experimental designs are used: independent groups (different participants in each condition), repeated measures (the same participants in all conditions), and matched pairs (different but matched participants in each condition).
标准的实验设计有三种：独立组设计（不同被试处在不同条件下）、重复测量设计（同一批被试经历所有条件）和配对组设计（不同但经过匹配的被试处在不同条件下）。
Counterbalancing is used in repeated measures designs to control for order effects such as practice or fatigue. Random allocation helps distribute participant variables evenly across conditions.
重复测量设计中需要用平衡抵消法来控制顺序效应，例如练习效应或疲劳效应。随机分配则有助于将被试变量均匀分散到各个实验条件中。
7. Ethical Principles (BPS Guidelines) | 伦理原则（英国心理学会指导方针）
Researchers must gain informed consent from participants, which means participants know the true nature of the study where possible and agree to take part. If full disclosure is not possible, presumptive consent or retrospective consent may be used.
研究者必须获得被试的知情同意，即在条件允许的情况下，被试了解研究的真实性质并同意参与。如果无法完全告知，可以采用预先同意或事后同意。
Deception should be avoided, but when essential it must be followed by a thorough debrief during which the true aims are revealed and support is offered. Participants must also be reminded of their right to withdraw at any time.
应避免欺骗；若欺骗在所难免，事后必须进行充分的情况说明，披露真实目的并提供支持。同时须提醒被试有权随时退出研究。
Protection from physical and psychological harm is paramount. The risk of harm should not be greater than the everyday risks participants would encounter in normal life.
保护被试免受身体伤害与心理伤害至关重要。研究带来的风险不应超过被试在日常生活里会遇到的常规风险。
Confidentiality must be upheld; data should normally be anonymised so individual participants cannot be identified. These principles form the 'ethical theorem' that guards all AQA specified research.
必须坚守保密原则；数据通常应当匿名化处理，以便无法识别出特定的被试。这些原则构成了保护所有 AQA 指定研究的“伦理定理”。
8. Multi-Store Model of Memory (Key Propositions) | 记忆多存储模型的核心论点
Atkinson & Shiffrin (1968) proposed that memory consists of three distinct stores: sensory register, short-term memory (STM) and long-term memory (LTM). Information flows linearly through these stores if attention and rehearsal are applied.
Atkinson 和 Shiffrin（1968）提出记忆由三个独立的存储系统构成：感觉登记器、短期记忆（STM）和长时记忆（LTM）。在注意和复述的作用下，信息会线性地流经这些存储系统。
Sensory register has a very large capacity but duration of less than half a second for visual information (iconic) and about two seconds for auditory information (echoic). Coding is modality-specific.
感觉登记器的容量非常大，然而视觉信息（映像记忆）的持续时间不足半秒，听觉信息（回声记忆）约持续两秒。编码方式取决于感觉通道。
Short-term memory holds approximately 5–9 items (Miller's magic number 7 ± 2) and codes mainly acoustically. Duration is about 18–30 seconds without rehearsal.
短期记忆大约能容纳 5–9 个项目（米勒的魔数 7 ± 2），并以听觉编码为主。在没有复述的情况下，持续时间约为 18–30 秒。
Long-term memory has potentially unlimited capacity and duration, and codes primarily semantically. Maintenance rehearsal keeps information in STM, while elaborative rehearsal transfers it into LTM.
长时记忆的容量和持续时间在理论上是无限的，主要采取语义编码。维持性复述让信息保留在STM中，而精细复述则将其转入LTM。
9. Visual Cliff Experiment (Perception Theorem) | 视崖实验（知觉定理）
Gibson and Walk (1960) constructed a 'visual cliff' – a glass-covered drop that appeared dangerous but was perfectly safe – to test depth perception in infants and young animals. The experiment is a classic demonstration of the nature–nurture debate.
Gibson 和 Walk（1960）搭建了一个“视崖”——一块用玻璃覆盖的、看上去危险的“悬崖”实则绝对安全——用于测试婴儿和幼小动物的深度知觉。该实验是先天与后天之争的经典例证。
Six-month-old infants were placed on one side and encouraged by their mother to crawl across the deep side. Most infants refused to cross, suggesting that depth perception is present by this age.
研究员将六个月大的婴儿放在视崖的一侧，鼓励他们爬过深侧的玻璃板。大多数婴儿拒绝爬过去，表明在这个月龄深度知觉已经出现。
Similarly, day-old chicks and kid goats avoided the deep side, implying that some degree of depth perception is innate. However, the infants had six months of experience, so learning cannot be ruled out entirely.
同样地，仅出生一天的小鸡和小山羊都会避开深侧，这意味着部分深度知觉是先天具备的。然而，婴儿已经有六个月的经历，因此不能完全排除学习的作用。
The visual cliff theorem: depth perception emerges from a combination of innate biological preparedness and early visual experience, supporting an interactionist perspective.
视崖定理：深度知觉源自先天生物准备与早期视觉经验的结合，从而支持一种交互论的观点。
10. Asch & Milgram: Social Influence Theorems | 阿希与米尔格拉姆：社会影响定理
Asch (1951) studied conformity using a line judgement task. Although the correct answer was obvious, about 37% of responses were conformist errors when confederates unanimously gave the wrong answer.
Asch（1951）使用线条判断任务研究从众行为。尽管正确答案显而易见，但在所有假被试一致给出错误答案的情况下，真正的被试约有 37% 的判答出现了从众错误。
Key factors affecting conformity are group size (conformity peaks at around three to four confederates), unanimity (even one dissenter reduces conformity dramatically), and task difficulty.
影响从众的关键因素有：团体规模（当假被试为三至四人时从众达到峰值）、一致性（哪怕仅有一个反对者都能大大降低从众率）以及任务难度。
Milgram (1963) investigated obedience in a staged learning task where participants were ordered to administer increasing electric shocks. Astonishingly, 65% of participants administered the maximum 450-volt shock.
Milgram（1963）在一项伪装的学习任务中考察了服从行为：参试者遵命实施逐渐升高的电击。令人震惊的是，65% 的参与者给出了最高 450 伏的电击。
Situational factors explaining obedience include the legitimacy of the authority figure, the proximity of the victim and the presence of rebellious peers. The findings reveal the powerful situational theorem of behaviour.
解释服从的情境因素包括：权威人物的正当性、受害者的接近程度以及是否存在反叛的同辈。这些发现揭示了行为的强大情境定理。
11. Classical & Operant Conditioning Formulas | 经典条件反射与操作条件反射公式
In classical conditioning (Pavlov), a neutral stimulus (NS) is repeatedly paired with an unconditioned stimulus (UCS) that naturally produces an unconditioned response (UCR). After pairing, the NS becomes a conditioned stimulus (CS) that elicits a conditioned response (CR).
在经典条件反射（巴甫洛夫）中，中性刺激（NS）反复与自然引发无条件反应（UCR）的无条件刺激（UCS）配对出现。配对之后，NS 变成条件刺激（CS），能够引出条件反应（CR）。
Extinction occurs when the CS is repeatedly presented without the UCS, and the CR weakens.
其公式化顺序为：NS + UCS → UCR；形成条件反射后 CS → CR。当 CS 多次单独出现而没有 UCS 相伴时，就会发生消退，CR 逐渐减弱。
In operant conditioning (Skinner), behaviours are shaped by consequences. Positive reinforcement adds a pleasant stimulus, negative reinforcement removes an unpleasant stimulus; both increase the likelihood of a behaviour.
在操作条件反射（斯金纳）中，行为的后果会对行为产生塑造作用。正强化是增加一个愉快的刺激，负强化是移除一个不愉快的刺激；两者均使行为发生的概率上升。
Punishment, by contrast, decreases the probability of a behaviour. Positive punishment adds something unpleasant; negative punishment takes away something pleasant.
惩罚则与此相反，会降低行为出现的概率。正惩罚是施加令人不快的刺激；负惩罚是移除令人愉快的事物。
12. Piaget's Stages of Cognitive Development | 皮亚杰认知发展阶段定理
Piaget theorised that children's intelligence progresses through four invariant stages, each characterised by qualitatively different kinds of thinking.
皮亚杰提出，儿童智力按顺序经历四个不变的阶段，每一阶段都有着质的不同思维类型。
The sensorimotor stage (0–2 years) involves learning through senses and actions; key achievement is object permanence – knowing that objects continue to exist when out of sight.
感知运动阶段（0–2 岁）通过感觉和动作来学习；核心成就是客体永恒性——知道物体即使不在眼前也依然存在。
Pre-operational stage (2–7 years) features symbolic thinking but is dominated by egocentrism (inability to see others' perspectives) and lack of conservation (understanding that quantity stays the same despite changes in appearance).
前运算阶段（2–7 岁）具备符号思维，但以自我中心（无法采纳他人视角）和缺乏守恒能力（不理解数量不随外观改变而改变）为主要特征。
Concrete operational stage (7–11 years) sees the emergence of logical reasoning about concrete events, mastery of conservation and decreased egocentrism. Formal operational stage (11+ years) allows abstract and hypothetical thinking.
具体运算阶段（7–11 岁）出现对具体事件的逻辑推理、掌握守恒能力且自我中心减弱。形式运算阶段（11 岁以上）使人能够进行抽象和假设性思维。
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