📚 GCSE Cambridge Psychology: Quick Reference to Formulae and Laws | GCSE 剑桥心理学：公式定理速查手册
This quick‑reference handbook brings together the essential statistical tools and core theoretical laws that appear throughout the Cambridge GCSE Psychology syllabus. Whether you are analysing data from a practical investigation, revising the mechanisms of memory, or checking the principles behind classical conditioning, the formulas and models here provide a concise summary of what you need to apply in exam questions and coursework. Each entry is presented as a clear rule, equation or flow diagram that you can learn, understand and use with confidence.
这本速查手册汇集了剑桥 GCSE 心理学课程中涉及的基本统计工具和核心理论定律。无论你是在分析实践研究数据、复习记忆的运作机制，还是核对经典条件作用背后的原理，这里列出的公式与模型都能为你提供简洁的总结，帮助你轻松应对考试题目和课程作业。每一条都以清晰的规则、方程式或流程图的形式呈现，方便学习、理解和灵活运用。
1. Mean, Median, Mode and Range | 平均值、中位数、众数与范围
Measures of central tendency and spread are the first formulas you need when handling raw data. The mean is calculated by dividing the sum of all values by the number of values; the median is the middle score in an ordered list; the mode is the most frequently occurring value; and the range shows how far the data spread from the smallest to the largest score.
集中趋势和离散程度的测量是处理原始数据时首先需要掌握的公式。平均值等于所有数值之和除以数值的个数；中位数是排序后位于中间位置的数值；众数是出现频率最高的数值；范围则显示数据从最小值到最大值的分布宽度。
Mean = Σx / n
The Greek letter Σ (sigma) means ‘ r example, if five participants score 4, 6, 7, 8 and 10, the mean is (4+6+7+8+10) ÷ 5 = 7.
希腊字母 Σ（西格玛）表示“求和”。将所有分数 (x) 相加，再除以参与者人数 (n)。例如，五名参与者的分数是 4, 6, 7, 8, 10，则平均值为 (4+6+7+8+10) ÷ 5 = 7。
Median = middle value after arranging scores in order
With an odd number of scores, the median is the central number. With an even number, it is the mean of the two middle numbers. The median is unaffected by extreme outliers, making it useful when a distribution is skewed.
当数据个数为奇数时，中位数即排序后的中间数；若为偶数，则是中间两个数的平均值。中位数不受极端异常值影响，因此在数据分布偏斜时非常有用。
Mode = most frequent value
A data set may have one mode (unimodal), two modes (bimodal) or none if all values occur equally often. The mode is the only measure of central tendency that can be used with nominal (category) data.
一组数据可能有一个众数（单峰）、两个众数（双峰），或当所有数值出现频率相同时没有众数。众数是唯一可用于名义（类别）数据的集中趋势测量。
Range = highest value – lowest value
Although quick to compute, the range is heavily influenced by a single extreme score. Psychologists therefore often report the interquartile range as a more robust measure of spread.
计算虽然快捷，但范围很容易受到单个极端值的影响。因此，心理学家常报告四分位距，作为更稳健的离散程度指标。
2. Percentage, Ratio and Proportion | 百分比、比与比例
When you want to describe how much of a sample falls into a certain category, or to compare the frequency of two groups, you need percentages, ratios and proportions. These three tools transform raw frequencies into meaningful, standardised numbers that can be compared across studies.
当你需要描述样本中有多大比例属于某个类别，或比较两个组的频率时，就需要用到百分比、比和比例。这三种工具能把原始频数转换成有意义的标准化数字，便于在不同研究之间进行比较。
Percentage = (part ÷ whole) × 100%
8 out of 30 participants recalled a word correctly. The percentage is (18 ÷ 30) × 100 = 60% Percentages are particularly helpful for presenting results in bar charts and pie charts.
假设 30 名参与者中有 18 人正确回忆了一个单词，那么百分比为 (18 ÷ 30) × 100 = 60%。百分比特别适合在柱状图和饼图中呈现结果。
Ratio = comparison of two quantities, written a : b
A ratio shows the relative size of two groups, for example the number of boys to girls in a study. If a sample has 10 boys and 15 girls, the boy‑to‑girl ratio is 10 : 15, which simplifies to 2 : 3.
比表示两个数量的相对大小，例如研究中男生与女生的人数比。若样本包含 10 名男生和 15 名女生，则男女生比为 10 : 15，可简化为 2 : 3。
Proportion = part ÷ whole
A proportion is simply a decimal fraction of the total. The proportion of correct recalls in the earlier example is 0.6. Proportions are used when calculating probability or effect sizes.
比例即部分除以整体的一个小数。在上例中，正确回忆的比例为 0.6。在计算概率或效应量时常用比例。
3. The Law of Effect and Operant Conditioning | 效果律与操作条件作用
Edward Thorndike’s Law of Effect states that behaviours followed by satisfying consequences are more likely to be repeated, while those followed by annoying consequences are weakened. B. F. Skinner built on this idea to create the principles of operant conditioning, using reinforcement and punishment to shape voluntary behaviour.
爱德华·桑代克的效果律指出，带来满意结果的行为更可能被重复，而带来恼人结果的行为会被削弱。斯金纳在此基础上发展出操作条件作用原理，运用强化和惩罚来塑造自愿行为。
Positive reinforcement: R → S⁺ → ↑R
A pleasant stimulus (S⁺, e.g. praise or a token) is added after a behaviour (R), making that response more frequent in the future. Skinner called this a ‘reinforcer’ because it strengthens the behaviour.
在行为 (R) 之后加入令人愉快的刺激（S⁺，如表扬或代币），使得该反应在将来更频繁地出现。斯金纳称之为“强化物”，因为它能强化行为。
Negative reinforcement: R → S⁻ removed → ↑R
An unpleasant stimulus (S⁻, e.g. a loud noise or nagging) is removed following the desired behaviour. Notice that negative reinforcement still increases the behaviour – it is not punishment.
在期望行为出现后，移除令人不快的刺激（S⁻，如噪音或唠叨）。注意，负强化同样会增加该行为，这并非惩罚。
Positive punishment: R → S⁺ (aversive) → ↓R
An aversive stimulus is added after an undesired behaviour, reducing its occurrence. Negative punishment involves removing a pleasant stimulus (e.g. taking away a phone) to weaken a behaviour.
正惩罚是在不良行为后添加厌恶刺激，从而减少该行为。负惩罚则是移除愉快刺激（如没收手机）来削弱行为。
The effectiveness of reinforcement depends on schedules: continuous reinforcement produces rapid learning but quick extinction, while partial (variable) schedules create more durable behaviour. These concepts are directly tested in the Cambridge GCSE topic on learning.
强化的效果取决于强化程序：连续强化导致快速学习但也容易消退，而部分（可变）强化程序则能形成更持久的行为。这些概念在剑桥 GCSE 心理学的“学习”专题中会直接考查。
4. Classical Conditioning Formulae | 经典条件作用公式
Ivan Pavlov’s discovery of classical conditioning can be summarised as a series of stimulus–response relationships. By pairing a neutral stimulus with an unconditioned stimulus that naturally triggers a reflex, the neutral stimulus eventually becomes a conditioned stimulus that elicits the same response. The notation below captures this learning pathway.
巴甫洛夫发现的经典条件作用可概括为一系列“刺激—反应”关系。通过将中性刺激与能自然引发反射的无条件刺激反复配对，中性刺激最终会变成能引起相同反应的条件刺激。以下符号化表示捕捉了这一学习路径。
Before conditioning: UCS → UCR
The unconditioned stimulus (UCS), such as food, naturally produces an unconditioned response (UCR), such as salivation. A neutral stimulus (NS), like a bell, produces no relevant response.
无条件刺激（UCS），如食物，天然引发无条件反应（UCR），如分泌唾液。中性刺激（NS），如铃声，则不会引起相关反应。
During conditioning: NS + UCS → UCR
The neutral stimulus is presented just before the UCS repeatedly. The organism continues to produce the UCR because the UCS is still present.
中性刺激在无条件刺激之前出现，反复配对。由于 UCS 依然存在，生物体持续产生 UCR。
After conditioning: CS → CR
Once learning has taken place, the neutral stimulus becomes a conditioned stimulus (CS) that alone elicits a conditioned response (CR), which is similar to the original UCR. In Pavlov’s experiment, the bell (CS) alone made the dogs salivate (CR).
一旦学习发生，中性刺激变为条件刺激（CS），单独出现就能引发条件反应（CR），后者与最初的 UCR 相似。在巴甫洛夫的实验中，单独铃声（CS）就能让狗分泌唾液（CR）。
Classical conditioning is essential for understanding phobias, systematic desensitisation and aversion therapy, all of which feature in the Cambridge GCSE psychology specification.
经典条件作用对于理解恐惧症、系统脱敏疗法和厌恶疗法至关重要，这些内容均出现在剑桥 GCSE 心理学大纲中。
5. Social Learning Theory: ARRM Process | 社会学习理论：注意、保持、再现、动机
Albert Bandura proposed that we learn not only through direct reinforcement but also by observing and imitating others. His four‑stage mediational process – attention, retention, reproduction and motivation – acts as a rule that must be met for observational learning to occur. The famous Bobo doll experiments demonstrated this sequence.
阿尔伯特·班杜拉提出，我们不仅通过直接强化学习，还通过观察和模仿他人来学习。他的四阶段中介过程——注意、保持、再现和动机，构成了观察学习发生所必须满足的法则。著名的波波玩偶实验验证了此序列。
Attention → Retention → Reproduction → Motivation → Learning
Attention: The observer must notice the model’s behaviour. Factors such as the model’s attractiveness, status or similarity to the observer increase attention.
注意：观察者必须注意到榜样的行为。榜样的吸引力、地位或与观察者的相似性等因素会增强注意。
Retention: The behaviour must be remembered. This involves forming a mental image or verbal description of the actions, which is influenced by the observer’s cognitive ability.
保持：行为必须被记住。这要求对动作形成心理表象或言语描述，受观察者认知能力的影响。
Reproduction: The observer must be physically and mentally able to reproduce the behaviour. Self‑efficacy – the belief in one’s own ability – plays a key role here.
再现：观察者必须在身体和心理上有能力重现该行为。自我效能感——对自己能力的信念——在此起关键作用。
Motivation: Direct reinforcement, vicarious reinforcement (seeing the model rewarded) or self‑reinforcement provides the incentive to imitate. Without motivation, the learned behaviour may never be performed.
动机：直接强化、替代强化（看到榜样得到奖励）或自我强化提供了模仿的动力。没有动机，习得的行为可能永远不会表现出来。
In exam answers, linking each stage to Bandura’s findings helps demonstrate applied knowledge.
在考试答案中，将每个阶段与班杜拉的研究发现联系起来，有助于展示应用性知识。
6. Miller’s Law (7 ± 2) | 米勒定律（7±2）
George Miller’s classic 1956 paper argued that the capacity of short‑term memory (STM) is approximately seven items, plus or minus two. This ‘magic number’ explains why we can hold a short list of digits or words in mind for a few seconds before it decays or is displaced.
乔治·米勒 1956 年的经典论文提出，短时记忆的容量大约为 7 个项目，上下浮动 2 个。这个“神奇数字”解释了为何我们能将一列短小的数字或单词保持几秒，之后就衰退或被挤掉。
STM capacity ≈ 7 ± 2 chunks
Miller used the term ‘chunk’ to describe a meaningful unit of information. Chunking allows us to extend STM’s capacity – for example, remembering the letters ‘IBMCIAFBI’ is easier if you group them as IBM, CIA, FBI. This insight is directly applied in exam revision strategies and cognitive interviews.
米勒用“组块”来描述有意义的信息单元。组块化可以扩展短时记忆的容量——例如，记住字母“IBMCIAFBI”，若分成 IBM、CIA、FBI 三个组块就更容易。这一洞见直接应用于考试复习策略和认知访谈中。
Research using serial‑position curves (primacy and recency effects) supports the idea that STM and LTM are separate stores, an assumption behind the multi‑store model.
利用序列位置曲线（首因效应和近因效应）开展的研究支持了短时记忆与长时记忆是独立存储器的观点——这也是多储存模型背后的假设。
7. Multi‑Store Model of Memory (Atkinson & Shiffrin) | 记忆的多重存储模型
The multi‑store model depicts memory as a flow of information through three distinct stores. Information enters via the sensory register, and if attention is paid it moves into STM. Through elaborative rehearsal, material can then be transferred into long‑term memory (LTM), from which retrieval is possible. The model can be written as a linear chain.
多重存储模型将记忆描述为信息流经三个独立存储器的过程。信息首先通过感觉登记器进入，若受到注意则移至短时记忆。通过精细复述，信息可转入长时记忆，并可从那里提取。该模型可以表示为一条线性链条。
Sensory Register → Attention → STM → Rehearsal → LTM
The sensory register holds a fleeting copy of environmental stimuli (iconic for vision, echoic for hearing). Most of this information decays within milliseconds unless attention selects it for further processing.
感觉登记器短暂保留环境刺激的复本（图像记忆负责视觉，回声记忆负责听觉）。除非注意力挑选其进入进一步加工，否则绝大部分信息在毫秒内衰退。
STM has a limited capacity (7±2 chunks) and a duration of about 18– items in STM but is less effective for transferring them to LTM than elaborative rehearsal – making meaningful connections with existing knowledge.
短时记忆容量有限（7±2 个组块），不经复述只能保持约 18–30 秒。维持性复述（简单重复）可将项目留在短时记忆中，但不如精细复述——与已有知识建立意义联系——那样有效地将信息转入长时记忆。
Examiners often ask you to evaluate this model; remember that it oversimplifies the passive nature of STM and does not fully account for the working memory model’s active processing.
考官常要求评价这一模型；记住它过度简化了短时记忆的被动性质，且不能完全解释工作记忆模型的主动加工过程。
8. Yerkes–Dodson Law | 耶克斯-多德森定律
The Yerkes–Dodson law describes the relationship between arousal and performance as an inverted U‑shaped curve. Performance improves as arousal increases up to an optimal point, after which further arousal leads to a decline in performance. This law is crucial for explaining phenomena such as exam anxiety and optimal sport performance.
耶克斯-多德森定律将唤醒与绩效的关系描述为一个倒 U 形曲线。当唤醒水平上升到最佳点时，绩效随之提高；超过该点后，进一步唤醒会导致绩效下降。这一定律对于解释考试焦虑和最佳运动表现等现象至关重要。
Performance ↑ as arousal ↑ → optimal point → Performance ↓ as arousal ↑ further
The optimal level of arousal depends on task difficulty. For simple or well‑learned tasks, a higher arousal level may be beneficial; for complex or novel tasks, the optimal arousal is lower. This ‘sub‑law’ helps psychologists design stress‑management interventions.
最佳唤醒水平取决于任务难度。对于简单或熟练的任务，较高的唤醒水平可能有利；而对于复杂或新异任务，最佳唤醒水平较低。这一“子定律”有助于心理学家设计压力管理干预方案。
Remember that over‑arousal can trigger the ‘catastrophe’ model in sports psychology, but for GCSE the inverted‑U hypothesis is sufficient to explain the basic law linking arousal to performance.
请记住，过度唤醒在运动心理学中可能引发“灾难”模型，但在 GCSE 阶段，倒 U 假设足以解释唤醒与绩效相关的基本定律。
9. Schema Theory and Memory Reconstruction | 图式理论与记忆重构
Frederic Bartlett argued that memory is not a passive recording but an active reconstruction based on pre‑existing mental frameworks called schemas. When we encode and retrieve information, our schemas fill gaps, rationalise unfamiliar details and even distort memories to make them more consistent with our cultural expectations.
弗雷德里克·巴特利特主张，记忆并非被动记录，而是基于已有心理框架——图式——的主动重构。当我们编码和提取信息时，图式会填补空白、合理化陌生细节，甚至歪曲记忆，使之更符合我们的文化期望。
Memory = original experience + schema‑based interpretation
In his classic study ‘The War of the Ghosts’, Bartlett asked British participants to recall a Native American folk story. Over repeated reproductions, the story became shorter, more coherent and contained elements familiar to Western culture (e.g. ‘canoes’ became ‘boats’). This demonstrated both ‘levelling’ (simplification) and ‘sharpening’ (emphasis on familiar details).
在其经典研究“鬼魂的战争”中，巴特利特要求英国参与者回忆一则美洲原住民民间故事。经过多次复述，故事变短、更连贯，且包含了西方文化熟悉的元素（例如“独木舟”变成了“小船”）。这展示了“削平”（简化）和“锐化”（强调熟悉的细节）。
Understanding schema theory helps explain why eyewitness testimonies can be unreliable and why leading questions influence recall – connecting directly to the cognitive psychology topic on memory.
理解图式理论有助于解释为何目击者证词可能不可靠，以及诱导性问题为何会影响回忆，这与“记忆”这一认知心理学主题直接相关。
10. Forgetting Curve (Ebbinghaus) | 遗忘曲线（艾宾浩斯）
Hermann Ebbinghaus investigated the rate at which we forget nonsense syllables over time. His forgetting curve shows a steep drop in memory retention within the first hour after learning, followed by a gradual levelling off. This pattern is not a precise mathematical formula at GCSE but a descriptive law of memory decay.
赫尔曼·艾宾浩斯研究了无意义音节的遗忘速率。他的遗忘曲线显示，在学习后的第一个小时内，记忆保持量急剧下降，随后逐渐趋于平缓。在 GCSE 层面，这一模式虽非精确数学公式，却是描述记忆衰退的定律。
Retention ∝ 1 / (time since learning)
Roughly, retention drops rapidly and then asymptotes. The greatest forgetting occurs soon after learning; this is why distributed practice (spacing out revision sessions) is far more effective than cramming. Re‑learning the material takes less time than original learning, a phenomenon called ‘savings’.
粗略而言，保持量随时间迅速下降并趋于稳定。最大幅度的遗忘发生在学习后不久；这解释了为何分散练习（间隔复习）远比突击学习有效。重新学习材料所需的时间比初次学习更少，该现象称为“节省”。
For GCSE, you are expected to draw and interpret the forgetting curve, explain the difference between decay and interference theories, and apply Ebbinghaus’s insights to practical study skills.
在 GCSE 中，你需要能够绘制和解释遗忘曲线，区分衰退理论和干扰理论，并将艾宾浩斯的洞见应用于实际学习技巧。
11. Piaget’s Stages of Cognitive Development | 皮亚杰的认知发展阶段
Jean Piaget proposed that children’s thinking progresses through four invariant and universal stages, each characterised by distinct cognitive abilities. Although not a ‘law’ in the statistical sense, the stage sequence is a foundational model that organises much of developmental psychology and is essential learning for Cambridge GCSE.
让·皮亚杰提出，儿童的思维发展会经历四个不变且普遍的阶段，每个阶段具有独特的认知能力。尽管这并非统计学意义上的“定律”，但阶段序列是组织发展心理学内容的基础模型，也是剑桥 GCSE 必须掌握的知识。
Sensorimotor (0–2 years) → Pre‑operational (2–7 years) → Concrete operational (7–11 years) → Formal operational (11+ years)
- Sensorimotor: The infant explores the world through senses and actions, developing object permanence – knowing objects exist even when out of sight.
- 感觉运动阶段：婴儿通过感官和动作探索世界，发展物体永久性——知道物体即使看不见也依然存在。
- Pre‑operational: Children use symbols (words, images) but are egocentric, struggle with conservation and lack logical reasoning.
- 前运算阶段：儿童使用符号（词语、图像），但以自我为中心，难以理解守恒概念，缺乏逻辑推理。
- Concrete operational: Logical thought about concrete events emerges; children master conservation, classification and reversibility.
- 具体运算阶段：对具体事件产生了逻辑思维；儿童掌握守恒、分类和可逆性。
- Formal operational: Adolescents can think abstractly, reason hypothetically and use deductive logic. Piaget tested this with the pendulum problem.
- 形式运算阶段：青少年能够抽象思维、假设推理并运用演绎逻辑。皮亚杰用钟摆问题对此进行了检验。
Criticisms highlight cultural variation and the fact that not all adults reach formal operations, but the sequence remains a powerful framework for understanding child development.
批评意见指出存在文化差异，且并非所有成人都能达到形式运算阶段，但该序列仍是理解儿童发展的有力框架。
12. Key Ethical Guidelines in Psychological Research | 心理学研究的关键伦理准则
Every study you evaluate in your GCSE exam must be judged against a set of ethical standards. While not algebraic formulas, these principles function as ‘rules’ that protect participants from harm and ensure research is conducted with integrity. The British Psychological Society (BPS) code of ethics provides the benchmark used in Cambridge questions.
在 GCSE 考试中评价每一项研究时，都必须依据一套伦理标准进行评判。这些原则虽非代数公式，却起着保护参与者免受伤害、确保研究诚信进行之“法则”的作用。英国心理学会的伦理准则正是剑桥考题中使用的基准。
on (or justified & debriefed) → Right to withdraw → Confidentiality → Protection from harm Published by TutorHao | GCSE Psychology Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图