📚 AS CCEA Psychology: Formula & Theorem Quick Reference Handbook | AS CCEA 心理学：公式定理速查手册
This quick reference handbook provides a compact summary of essential quantitative formulas and key theoretical models you need to master for the AS CCEA Psychology specification. It covers descriptive statistics, inferential test calculations, and core explanations from cognitive, developmental and social psychology. Use it to check your understanding, support revision and build confidence in applying both numerical and conceptual knowledge.
本速查手册简明扼要地总结了 AS CCEA 心理学课程中必须掌握的核心量化公式与关键理论模型，涵盖描述统计、推断检验计算以及认知、发展和社会心理学的重要解释。可用于检验理解、辅助复习，并增强应用数字与概念知识的信心。
1. Measures of Central Tendency | 集中趋势测量
The mean is the arithmetic average and is most sensitive to extreme scores. It is calculated by summing all the values and dividing by the total number of scores.
平均值是算术平均数，对极端分数最为敏感。计算方法为将所有数值相加，再除以分数的总数。
x̄ = Σx / N
The median is the middle value when data are ordered from smallest to largest; it is unaffected by outliers and is often used for skewed distributions.
中位数是将数据从小到大排列后位于中间的值；它不受异常值影响，常用于偏态分布。
The mode is the most frequently occurring score in a data set. A set may have one mode, more than one (bimodal/multimodal), or no mode at all.
众数是数据集中出现频率最高的分数。一个数据集可能有一个众数、多个众数（双峰/多峰）或根本没有众数。
2. Measures of Dispersion | 离散度测量
The range is the simplest measure of spread, found by subtracting the lowest score from the highest score. It gives a quick sense of variability but can be distorted by a single outlier.
全距是最简单的离散量数，用最高分减最低分得出。它能快速体现变异性，但容易被单个异常值扭曲。
Range = Xmax – Xmin
Standard deviation (s) measures how much scores typically deviate from the mean. A small s indicates scores cluster tightly around the mean; a large s indicates widespread scores. For a sample, the formula uses n-1 in the denominator to give an unbiased estimate.
标准差（s）衡量分数与平均值的典型偏离程度。s 小说明分数紧密围绕平均值；s 大说明分数分布宽散。计算样本标准差时，分母用 n-1 以得到无偏估计。
s = √[ Σ(x – x̄)² / (n – 1) ]
3. Standard Scores & Normal Distribution | 标准分数与正态分布
A z-score expresses a raw score’s distance from the mean in standard deviation units. It allows comparison across different distributions.
z 分数将原始分数表示为距离平均值多少个标准差，便于在不同分布之间进行比较。
z = (x – x̄) / s
In a normal distribution, roughly 68% of scores lie within ±1 standard deviation of the mean, 95% within ±2, and 99.7% within ±3. Psychologists often treat data as normally distributed when justifying parametric tests.
在正态分布中，约 68% 的分数落在平均值 ±1 个标准差之内，95% 落在 ±2 个标准差之内，99.7% 落在 ±3 个标准差之内。心理学家在解释参数检验时常将数据视为近似正态分布。
A z-table can be used to find the proportion of scores above or below a given value. This is essential for interpreting test statistics and setting significance levels.
借助 z 表可以查出某一数值以上或以下的分数比例，这对解释检验统计量和设定显著性水平至关重要。
4. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rho (rₛ) measures the strength and direction of association between two ranked variables. It is a non-parametric test, suitable for ordinal data or when assumptions of normality are violated.
斯皮尔曼等级相关系数（rₛ）测量两个排序变量之间关联的强度与方向。它是一种非参数检验，适用于顺序数据或正态性假设不满足的情形。
rₛ = 1 – [ 6 Σ d² / n ( n² – 1 ) ]
Here, d is the difference between the ranks of each pair, and n is the number of pairs. The resulting value ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation); a value near 0 indicates no relationship.
式中，d 是每对数据的等级之差，n 为数据对的数量。结果取值从 -1（完全负相关）到 +1（完全正相关）；接近 0 的数值表示没有关系。
When n ≤ 30, the observed rₛ must be compared to a critical values table to determine statistical significance. The null hypothesis typically states that there is no correlation in the population.
当 n ≤ 30 时，需要将观察到的 rₛ 值与临界值表进行比较以判断统计显著性。零假设通常认为总体中不存在相关。
5. Chi-Squared Test for Independence | 卡方独立性检验
The chi-squared (χ²) test examines whether two categorical variables are associated or independent. It is often used to analyse frequency data from questionnaires or observational studies.
卡方（χ²）检验考察两个类别变量之间是有关联还是彼此独立，常用于分析问卷或观察研究得出的频数数据。
χ² = Σ ( (O – E)² / E )
O stands for observed frequency and E for expected frequency under the null hypothesis. The larger the χ² value, the less likely the observed pattern is due to chance.
O 代表观察频数，E 代表零假设下的期望频数。χ² 值越大，说明观察到的分布模式是由偶然造成的可能性越小。
Degrees of freedom (df) must be calculated: df = (number of rows – 1) × (number of columns – 1). The computed χ² is then compared with a critical value at the chosen alpha level, usually 0.05.
必须计算自由度：df = (行数 – 1) × (列数 – 1)。随后将计算出的 χ² 与所选 α 水平（通常为 0.05）下的临界值进行比较。
6. Multi-Store Model of Memory (Atkinson & Shiffrin) | 记忆的多重储存模型
The multi-store model proposes three separate memory stores: sensory register, short-term memory (STM), and long-term memory (LTM). Information flows linearly from one store to another through attention and rehearsal.
该模型提出三个彼此分离的记忆储存库：感觉登记器、短时记忆和长时记忆。信息通过注意和复述从一个储存库线性流向下一个。
The sensory register has a large capacity and a very brief duration (less than 0.5 seconds for visual information). Encoding is modality-specific, preserving information in its original sensory form.
感觉登记器的容量很大，持续时间极短（视觉信息不足 0.5 秒）。编码具有模态特异性，信息以其原始感觉形式短暂保留。
STM holds approximately 7±2 chunks of information for about 18-30 seconds without rehearsal. Encoding is mainly acoustic, and maintenance rehearsal can transfer material to LTM.
短时记忆在不进行复述的情况下可容纳约 7±2 个组块，保持大约 18-30 秒。编码以声学为主，维持性复述可将材料转入长时记忆。
LTM has potentially unlimited capacity and duration, and information is encoded largely by meaning (semantic). Evidence from brain-damaged patients, such as HM, supports the distinction between STM and LTM.
长时记忆的容量和持续时间在理论上是无限的，信息主要通过意义（语义）编码。来自脑损伤病人（如 HM）的证据支持短时记忆与长时记忆的区分。
7. Working Memory Model (Baddeley & Hitch) | 工作记忆模型
Baddeley and Hitch replaced the unitary STM with a multi-component working memory system. The model consists of a central executive and two slave systems: the phonological loop and the visuospatial sketchpad, later joined by the episodic buffer.
巴德利与希奇用一个多成分的工作记忆系统取代了单一短时记忆。模型由中央执行系统和两个子系统——语音回路与视空间画板——组成，后来又增加了情节缓冲器。
The central executive allocates attention, switches between tasks, and coordinates the slave systems. It has limited capacity and does not store information itself.
中央执行系统负责分配注意、切换任务并协调子系统。它容量有限，本身不储存信息。
The phonological loop processes speech-based and auditory information; it has a phonological store (inner ear) and an articulatory control process (inner voice). The word-length effect supports its existence.
语音回路处理基于言语和听觉的信息；它包含语音仓库（内在耳朵）和发音控制过程（内在声音）。词长效应为其存在提供了证据。
The visuospatial sketchpad handles visual and spatial information, while the episodic buffer integrates information from different sources into coherent episodes, linking working memory to LTM.
视空间画板处理视觉和空间信息，而情节缓冲器将来自不同来源的信息整合成连贯的情节，把工作记忆与长时记忆连接起来。
8. Ainsworth’s Strange Situation & Attachment Types | 安斯沃斯陌生情境与依恋类型
Ainsworth designed the Strange Situation to assess the quality of infant–caregiver attachment. The procedure involves a series of separations and reunions with the caregiver and a stranger, observing the infant’s exploratory and security-seeking behaviours.
安斯沃斯设计了陌生情境以评估婴儿与照料者之间依恋的质量。程序包括一系列与照料者和陌生人的分离与重聚，观察婴儿的探索与安全寻求行为。
Three main attachment types were identified: secure (Type B), insecure-avoidant (Type A), and insecure-resistant/ambivalent (Type C). Securely attached infants show distress on separation, seek comfort at reunion, and use the caregiver as a safe base for exploration.
确认了三种主要依恋类型：安全型（B 型）、不安全回避型（A 型）和不安全反抗/矛盾型（C 型）。安全型婴儿在分离时表现出不安，重聚时寻求安慰，并将照料者作为探索的安全基地。
Insecure-avoidant infants appear indifferent to the caregiver’s presence or departure and avoid closeness at reunion. Insecure-resistant infants cling to the caregiver, are extremely distressed by separation, and resist comfort when reunited.
不安全回避型婴儿对照料者的在场或离开显得无所谓，重聚时回避亲近。不安全反抗型婴儿紧紧黏住照料者，分离时极度不安，重聚时又抗拒安抚。
Attachment type is strongly influenced by the caregiver’s sensitivity. Ainsworth’s work has been foundational for developmental psychology and later research into the internal working model.
依恋类型在很大程度上受照料者敏感性的影响。安斯沃斯的研究为发展心理学以及后来有关内部工作模型的研究奠定了基础。
9. Bowlby’s Theory of Attachment | 鲍尔比的依恋理论
Bowlby proposed that attachment is an innate biological drive that enhances survival. He argued that infants have an inbuilt readiness to become attached to a primary caregiver, usually the mother, through social releasers such as crying and smiling.
鲍尔比提出，依恋是一种有助于生存的先天生物内驱力。他认为婴儿天生具有通过哭、笑等社会释放器与主要照料者（通常为母亲）建立依恋的倾向。
The concept of monotropy suggests that the infant forms one special, primary attachment that is qualitatively different from all others. This bond serves as the prototype for later relationships through the internal working model.
单一依恋概念指出，婴儿会形成一种与其他关系有本质区别的特殊主要依恋。这一联结通过内部工作模型成为日后人际关系的原型。
Bowlby also emphasised a critical period (roughly the first two years) during which the attachment system is most sensitive. Failure to form a secure attachment within this window could lead to long-term social and emotional difficulties, a view supported by his maternal deprivation hypothesis.
鲍尔比还强调依恋系统在发展上的关键期（大约出生后两年内），在此窗口期内若未能形成安全依恋，可能导致长期的社会与情感困难，其母爱剥夺假说亦支持这一观点。
The theory is supported by evidence of continuity between early attachment security and later social competence, though critics point to overemphasis on the mother and underestimation of multiple attachments.
该理论得到了早期依恋安全性与日后社会能力之间存在连续性的证据支持，但批评者指出它过度强调母亲并低估了多重依恋的作用。
10. Milgram’s Agency Theory & Obedience | 米尔格拉姆的代理理论及服从
Milgram’s famous obedience experiments revealed that 65% of ordinary participants were willing to administer what they believed were severe electric shocks to a learner, simply because an authority figure instructed them to do so.
米尔格拉姆著名的服从实验显示，65% 的普通参与者愿意仅仅因为权威人物的指令而对学习者施加他们认为极其痛苦的电击。
To explain these findings, Milgram proposed the agency theory. When people enter an agentic state, they see themselves as carrying out the wishes of another and feel no personal responsibility for their actions. The opposite is the autonomous state, where they act according to their own conscience.
为解释这一发现，米尔格拉姆提出代理理论。当人进入代理状态时，会认为自己只是执行他人意愿，从而不对自身行为感到个人责任。与之相对的是自主状态，此时行为发自个人良心。
Binding factors, such as the desire to appear polite, the fear of disrupting the experiment, or the gradual escalation of demands, keep individuals in the agentic state. The presence of a legitimate authority in a prestigious setting further increases obedience.
希望显得礼貌、担心干扰实验进程、要求逐步升级等约束因素使个体停留在代理状态。在具有声望的环境中出现的合法权威会进一步增加服从。
The theory is supported by variations in Milgram’s study: obedience dropped sharply when the experimenter was not physically present or when orders were given by phone, showing that proximity of authority matters.
该理论得到米尔格拉姆实验变式的支持：当主试不在场或通过电话下达命令时，服从率大幅下降，证明权威的接近程度至关重要。
11. Piaget’s Stages of Cognitive Development | 皮亚杰认知发展阶段
Piaget viewed cognitive development as a process of building schemas through assimilation and accommodation. He identified four invariant, universal stages through which children progress.
皮亚杰将认知发展视为通过同化与顺应构建图式的过程，并识别出四个不可变的普遍发展阶段。
The sensorimotor stage (birth to 2 years) is characterised by learning through senses and actions. A key achievement is object permanence, the understanding that objects continue to exist when out of sight.
感觉运动阶段（0-2 岁）的特征是通过感官和动作学习。关键成就是客体永久性，即理解物体在看不见时仍然存在。
During the pre-operational stage (2-7 years), children use symbols and language but lack logical reasoning. They demonstrate egocentrism and fail at conservation tasks because they cannot mentally manipulate concepts like volume and number.
前运算阶段（2-7 岁）的儿童运用符号和语言，但缺乏逻辑推理。他们表现出自我中心，且在守恒任务中失败，因为无法在心理上操作体积、数量等概念。
In the concrete operational stage (7-11 years), logical thinking emerges for concrete events. Children master conservation, classification and reversibility, though they struggle with abstract ideas.
具体运算阶段（7-11 岁）发展出对具体事件的逻辑思维。儿童掌握守恒、分类和可逆性，但仍在抽象观念上遇困。
The formal operational stage (11 years onward) brings abstract reasoning, hypothetical thinking and systematic problem-solving. Not all individuals reach this stage or use formal operations consistently.
形式运算阶段（11 岁以后）带来了抽象推理、假设性思维和系统性解决问题的能力。并非所有人都能达到这一阶段或持续使用形式运算。
12. Asch’s Conformity Paradigm | 阿希从众范式
Solomon Asch demonstrated the power of majority influence through a line-judgement task. Naive participants, seated among confederates who deliberately gave wrong answers, conformed on about 37% of critical trials, and 75% conformed at least once.
所罗门·阿希通过线段判断任务展示了多数人影响的力量。天真的参与者坐在故意给出错误答案的假被试中间，在约 37% 的关键试验中发生从众，75% 的人至少从众一次。
Asch identified three main reasons for conformity: normative social influence (wanting to be liked and accepted), informational social influence (believing others have better knowledge), and the desire to avoid social rejection.
阿希确定了从众的三个主要原因：规范性社会影响（希望被喜欢和接纳）、信息性社会影响（相信他人掌握更准确的信息）以及避免社会排斥的愿望。
Conformity increased with group size up to about three confederates, after which additional members added little effect. The presence of a single dissenter drastically reduced conformity, showing that unanimity is a powerful variable.
当假被试人数增至约 3 人时从众率上升，超出此人数之后再增加成员效果很小。只要存在一个异议者，从众率就大幅下降，表明一致性是一个强有力的变量。
Task difficulty also affected conformity: when line lengths were made more ambiguous, conformity increased, as participants became more uncertain and relied more on others’ judgements.
任务难度同样影响从众：当线段长度变得更模糊时，从众率升高，因为参与者更加不确定，转而更多地依赖他人判断。
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