📚 Year 11 CCEA Psychology: Formula & Theorem Quick-Reference Handbook | CCEA 11年级 心理学：公式定理速查手册
Mastering psychology at Year 11 level requires a firm grasp of both statistical techniques and core theoretical models. This quick-reference handbook compiles the essential formulas, theorems, and stage models that appear frequently in CCEA GCSE Psychology assessments, from measures of central tendency to multi-store memory and social learning theory.
掌握 11 年级心理学需要牢固掌握统计技术和核心理论模型。这本速查手册汇集了 CCEA GCSE 心理学评估中频繁出现的基本公式、定理和阶段模型，涵盖集中趋势测量、多存储器记忆模型和社会学习理论等重点内容。
1. Mean, Median, Mode | 均值、中位数与众数
The mean is calculated by summing all scores and dividing by the number of scores. It is the arithmetic average and is sensitive to extreme values.
均值通过将所有分数相加再除以分数个数来计算。它是算术平均数，对极端值敏感。
Mean = (Σx) / n
The median is the middle score when data are arranged in ascending order. If there is an even number of scores, the median is the mean of the two middle values.
中位数是数据按升序排列后位于中间的数值。如果分数个数为偶数，中位数则是中间两个数值的均值。
The mode is the most frequently occurring score in a data set. A set may have one mode, more than one mode (bimodal/multimodal), or no mode at all.
众数是数据集中出现频率最高的数值。一组数据可能有一个众数、多个众数（双峰/多峰）或根本没有众数。
In psychological research, the mean is usually preferred for interval/ratio data, while the median is used when outliers are present, and the mode is most appropriate for nominal data.
在心理学研究中，均值通常适用于等距或比率数据，当存在异常值时使用中位数，而众数最适合称名数据。
2. Range and Standard Deviation | 极差与标准差
The range is the simplest measure of dispersion, found by subtracting the lowest score from the highest score. It shows the spread of data but is affected by outliers.
极差是最简单的离散程度测量指标，用最高分减去最低分即可得到。它显示数据的分布范围，但易受异常值影响。
Range = Highest score – Lowest score
Standard deviation is a more precise measure that tells us how much, on average, each score deviates from the mean. A larger standard deviation means greater variability in the data set.
标准差是一种更精确的测量指标，可以告诉我们每个分数相对于均值的平均偏差程度。标准差越大，表示数据集的变异性越大。
SD = √[ Σ(x – x̄)² / (n – 1) ]
For CCEA exams, it is essential to know that a low standard deviation indicates that data points are clustered closely around the mean, which often suggests higher consistency in participant responses.
对 CCEA 考试而言，必须知道低标准差表明数据点紧密聚集在均值周围，这通常表明参与者反应的一致性较高。
3. Percentages, Ratios and Fractions | 百分比、比率与分数
Psychologists frequently convert raw scores into percentages to compare groups of different sizes. The percentage formula is simply the part divided by the whole, multiplied by 100.
心理学家经常将原始分数转换为百分比，以便比较不同规模的组别。百分比公式很简单，即部分除以总数再乘以 100。
Percentage = (Part / Whole) × 100
A ratio expresses the relationship between two frequencies, for example the number of males to females in a study. Ratios can be simplified like fractions and are useful when reporting observational data.
比率表示两个频数之间的关系，例如研究中男性与女性的人数比。比率可以像分数一样化简，在报告观察数据时非常有用。
Fractions are another way of representing proportions and can be converted into percentages or ratios as required by the research question.
分数是表示比例的另一种方式，根据研究问题的需要，可以转换为百分比或比率。
4. Normal Distribution Curve | 正态分布曲线
The normal distribution is a bell-shaped curve where the mean, median and mode all sit at the centre. It is a key concept in psychological statistics, representing how traits like IQ are distributed in the population.
正态分布是一条钟形曲线，均值、中位数和众数都位于中心。它是心理统计学的关键概念，代表了 IQ 等特质在人群中的分布方式。
The curve is symmetrical, with 68% of scores falling within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
曲线是对称的，68% 的分数落在均值的一个标准差范围内，95% 落在两个标准差内，99.7% 落在三个标准差内。
Skewness occurs when a distribution is not symmetrical. A positive skew has a long tail on the right (mean > median), while a negative skew has a long tail on the left (mean < median).
当分布不对称时就会出现偏态。正偏态在右侧有长尾（均值 > 中位数），而负偏态在左侧有长尾（均值 < 中位数）。
5. Multi-store Model of Memory (Atkinson & Shiffrin) | 记忆多存储器模型（阿特金森与希夫林）
The multi-store model proposes that memory consists of three separate stores: sensory register, short-term memory (STM), and long-term memory (LTM). Information moves between them through attention and rehearsal.
多存储器模型提出记忆由三个独立的存储库组成：感觉登记、短时记忆和长时记忆。信息通过注意和复述在它们之间传递。
Sensory register holds information from the senses for a very brief duration (less than a second for visual, a few seconds for auditory). Only attended items pass into STM.
感觉登记以极短的持续时间（视觉信息不到一秒，听觉信息几秒）保存来自感官的信息。只有被注意到的项目才会进入短时记忆。
Short-term memory has a limited capacity of 7±2 items and a duration of around 18–30 seconds without rehearsal. Maintenance rehearsal can keep information in STM and transfer it to LTM.
短时记忆的容量有限，为 7±2 个组块，持续时间在没有复述的情况下约为 18–30 秒。维持性复述可以将信息保留在短时记忆并转移到长时记忆。
Long-term memory is considered to have unlimited capacity and can store information for a lifetime. Forgetting from LTM is mainly due to interference or retrieval failure, not decay.
长时记忆被认为拥有无限容量，可以终身储存信息。长时记忆的遗忘主要是由于干扰或提取失败，而不是消退。
6. Working Memory Model (Baddeley & Hitch) | 工作记忆模型（巴德利与希奇）
The working memory model replaces the idea of a single STM store with a multi-component system. It consists of the central executive, phonological loop, visuo-spatial sketchpad, and the episodic buffer added later.
工作记忆模型用一个多成分系统取代了单一的短时记忆库的观念。它包括中央执行器、语音回路、视空间画板以及后来加入的情景缓冲器。
The central executive acts as a supervisory system, directing attention to incoming information and dividing resources between the slave systems. It has limited capacity and does not store information itself.
中央执行器充当监督系统，将注意力引向传入信息并在从属系统之间分配资源。它的容量有限，本身不储存信息。
The phonological loop deals with speech-based information and has two subcomponents: the phonological store (holding words you hear) and the articulatory control process (allowing subvocal rehearsal).
语音回路处理基于言语的信息，有两个子成分：语音储存库（保存你听到的词语）和发音控制过程（允许无声复述）。
The visuo-spatial sketchpad processes visual and spatial information, helping us navigate environments and manipulate images. The episodic buffer integrates information from the subsystems and links to LTM.
视空间画板处理视觉和空间信息，帮助我们导航环境并操作图像。情景缓冲器整合来自子系统的信息并与长时记忆相连接。
7. Classical Conditioning (Pavlov) | 经典条件作用（巴甫洛夫）
Classical conditioning is learning through association. An unconditioned stimulus (UCS) elicits an unconditioned response (UCR). A neutral stimulus (NS) becomes a conditioned stimulus (CS) after repeated pairings with the UCS, producing a conditioned response (CR).
经典条件作用是通过联想进行的学习。无条件刺激引起无条件反应。中性刺激在与无条件刺激反复配对后变成条件刺激，产生条件反应。
The key formula for conditioning is: UCS → UCR, and after acquisition: NS + UCS → UCR, eventually NS (now CS) → CR. Timing and contingency are crucial to forming strong associations.
条件作用的关键公式是：UCS → UCR，经过习得后：NS + UCS → UCR，最终 NS（现已变成 CS）→ CR。时机和依存关系对形成强联结至关重要。
Extinction occurs when the CS is repeatedly presented without the UCS, causing the CR to weaken. Spontaneous recovery can happen when the CR reappears after a rest period.
消退发生在条件刺激反复呈现而不伴随无条件刺激时，导致条件反应减弱。自然恢复可能发生在休息一段时间后条件反应重新出现时。
Generalisation means that stimuli similar to the CS also produce the CR, while discrimination is the ability to distinguish between the CS and other stimuli and not respond to them.
泛化意味着与条件刺激相似的刺激也会引起条件反应，而分化是指能够区分条件刺激和其他刺激并不对它们做出反应的能力。
8. Operant Conditioning (Skinner) | 操作条件作用（斯金纳）
Operant conditioning is learning through consequences. Behaviour is shaped and maintained by reinforcement (increases behaviour) and punishment (decreases behaviour). Both can be positive (adding something) or negative (removing something).
操作条件作用是通过后果进行的学习。行为通过强化（增加行为）和惩罚（减少行为）来塑造和维持。两者都可以是正向的（添加某物）或负向的（移除某物）。
Positive reinforcement involves adding a desirable stimulus to strengthen behaviour, e.g. praise. Negative reinforcement strengthens behaviour by removing an unpleasant stimulus, e.g. stopping an annoying noise.
正强化涉及添加令人满意的刺激以加强行为，例如表扬。负强化通过移除令人不快的刺激来加强行为，例如停止烦人的噪音。
Positive punishment adds an aversive consequence to weaken behaviour, e.g. a fine. Negative punishment removes a pleasant stimulus, e.g. taking away a privilege.
正惩罚添加令人厌恶的后果以削弱行为，例如罚款。负惩罚移除令人愉快的刺激，例如取消一项特权。
Schedules of reinforcement affect the rate and pattern of responding. Continuous reinforcement leads to fast acquisition but quick extinction, while partial schedules (fixed/variable, interval/ratio) produce more persistent behaviour.
强化程序影响着反应的速率和模式。连续强化导致快速习得但消退也快，而部分强化程序（固定/变动的时距/比率）产生更持久的行为。
9. Social Learning Theory (Bandura) | 社会学习理论（班杜拉）
Bandura proposed that we learn not only through direct experience but also by observing others. The key processes are attention, retention, motor reproduction, and motivation (sometimes called ARRM).
班杜拉提出我们不仅通过直接经验学习，还通过观察他人学习。关键过程是注意、保持、动作再现和动机（有时简称为 ARRM）。
Attention: the observer must focus on the model’s behaviour. Retention: they must remember what they observed. Motor reproduction: the observer must be physically capable of imitating the behaviour. Motivation: they must have a reason to imitate, such as vicarious reinforcement.
注意：观察者必须专注于榜样的行为。保持：他们必须记住观察到的东西。动作再现：观察者必须有能力模仿该行为。动机：他们必须有模仿的理由，例如替代性强化。
Vicarious reinforcement occurs when the observer sees the model being rewarded, increasing the likelihood of imitation. Vicarious punishment reduces the chance of imitation.
替代性强化发生在观察者看到榜样受到奖励时，这增加了模仿的可能性。替代性惩罚则会降低模仿的可能性。
The Bobo doll experiments demonstrated that children imitated aggressive behaviour after observing an adult model, especially when the model was rewarded or not punished.
波波玩偶实验表明，儿童在观察到成年榜样后会模仿攻击行为，尤其是当榜样受到奖励或没有受到惩罚时。
10. Piaget’s Stages of Cognitive Development | 皮亚杰认知发展阶段
Piaget’s theory states that children move through four universal stages in a fixed order. Each stage is characterised by distinct schemas and logical abilities.
皮亚杰的理论认为儿童按固定顺序经历四个普遍阶段。每个阶段以不同的图式和逻辑能力为特征。
Sensorimotor stage (0–2 years): infants learn through senses and actions. They develop object permanence — understanding that objects continue to exist even when out of sight.
感知运动阶段（0–2 岁）：婴儿通过感官和动作学习。他们发展客体永久性——理解即使物体不在视野中也仍然存在。
Pre-operational stage (2–7 years): children use symbols and language but are egocentric (cannot see others’ viewpoints) and lack conservation (understanding that quantity stays the same despite changes in appearance).
前运算阶段（2–7 岁）：儿童使用符号和语言，但以自我为中心（无法看到他人的观点），并且缺乏守恒（不理解尽管外观改变，数量保持不变）。
Concrete operational stage (7–11 years): logical thinking develops for concrete events. Children master conservation and classification but struggle with abstract ideas.
具体运算阶段（7–11 岁）：对具体事件的逻辑思维得以发展。儿童掌握守恒和分类，但难以处理抽象概念。
Formal operational stage (11+ years): abstract and hypothetical thinking emerges. Adolescents can solve problems systematically and consider multiple possibilities.
形式运算阶段（11 岁以上）：抽象和假设性思维出现。青少年能够系统地解决问题并考虑多种可能性。
11. ABC Model in Cognitive Behavioural Therapy (Ellis & Beck) | 认知行为疗法中的 ABC 模型（埃利斯与贝克）
The ABC model explains how our beliefs about an activating event (A) lead to emotional and behavioural consequences (C), mediated by beliefs (B). This is central to CBT interventions for psychological problems.
ABC 模型解释了我们对激发事件（A）的信念（B）如何导致情绪和行为后果（C）。它是针对心理问题的 CBT 干预的核心。
A = Activating event (something that happens). B = Beliefs (rational or irrational thoughts about the event). C = Consequences (how we feel and behave).
A = 激发事件（发生的事情）。B = 信念（关于事件的理性或非理性想法）。C = 后果（我们的感受和行为）。
Therapy focuses on challenging irrational beliefs and replacing them with rational ones. The extended form, ABCDEF, adds Disputing, Effect of disputing, and new Feelings.
治疗的重点是挑战非理性信念并用理性信念取而代之。扩展形式 ABCDEF 增加了辩论、辩论效果和新的感受。
This model has been effectively applied to depression, anxiety, and phobias, aligning closely with the cognitive approach in CCEA Psychology.
该模型已有效应用于抑郁症、焦虑症和恐惧症，与 CCEA 心理学中的认知取向密切吻合。
12. Social Influence: Conformity and Obedience Theorems | 社会影响：从众与服从定理
Asch’s conformity theorem states that individuals will often conform to a unanimous group judgement even when the group is clearly wrong. Conformity can be normative (wanting to fit in) or informational (believing the group is correct).
阿希的从众定理指出，个体常常会顺从一致的群体判断，即使该群体明显错误。从众可以是规范的（想要融入群体）或信息的（相信群体是正确的）。
Key factors affecting conformity include group size (conformity increases up to about 4–5 confederates), unanimity (a dissenter sharply reduces conformity), and task difficulty (harder tasks increase informational influence).
影响从众的关键因素包括群体规模（从众随人数增加而增加，约 4-5 人后趋于平稳）、一致性（一个异议者会显著降低从众）和任务难度（更难的任务会增加信息影响）。
Milgram’s obedience to authority theorem demonstrated that ordinary people are surprisingly willing to follow orders to harm another person, especially when the authority figure is perceived as legitimate and physically close.
米尔格拉姆的服从权威定理表明，普通人极其愿意服从命令去伤害他人，尤其是当权威人物被认为是合法且在场时。
Situational factors affecting obedience include proximity of the victim and authority, location prestige, and social support. Agentic state theory explains that people shift responsibility to the authority, entering an ‘agentic state’.
影响服从的情境因素包括受害者和权威的接近程度、地点声望以及社会支持。代理状态理论解释说，人们将责任转移给权威，从而进入“代理状态”。
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