📚 GCSE CAIE Psychology: Formula & Theorem Quick Reference Handbook | GCSE CAIE 心理学公式定理速查手册
This quick-reference handbook collects every essential formula, statistical rule and psychological law you need for the CAIE GCSE Psychology course. From calculating the mean to applying Weber's Law, each entry is presented in a simple paired bilingual format to support both your understanding and exam revision. Use it alongside your class notes and practice papers.
这本速查手册汇集了CAIE GCSE心理学课程必备的公式、统计规则和心理学定律。从计算平均数到应用韦伯定律，每一项都以简洁的中英对照形式呈现，帮助你理解概念并进行考前复习。建议结合课堂笔记和历年真题一起使用。
1. Measures of Central Tendency – Mean, Median & Mode | 集中趋势测量：平均数、中位数和众数
In psychology, we summarise data sets using measures of central tendency. The mean is the arithmetic average and is calculated by adding all scores together and dividing by the total number of scores.
Mean (x̄) = Σx / n
在心理学中，我们使用集中趋势量数来概括数据。平均数 (x̄) 是算术平均值，将所有分数相加后再除以分数的总个数即可得到。
The median is the middle value when all scores are placed in order. If the number of scores is even, the median is the average of the two middle values.
中位数是将所有分数按大小顺序排列后位于中间的那个值。如果分数的个数是偶数，中位数就是中间两个值的平均数。
The mode is the score that appears most frequently. A data set may have one mode, more than one mode (bimodal/multimodal), or no mode at all.
众数是出现频率最高的那个分数。一组数据可能有一个众数、多个众数（双众数/多众数），或根本没有众数。
2. Measures of Spread – Range & Standard Deviation | 离散程度测量：极差与标准差
The simplest measure of spread is the range, which shows the difference between the highest and lowest scores.
Range = Maximum value − Minimum value
最简单的离散量数是极差，它显示最高分与最低分之间的差距。
For a basic estimate of variability, you may also need to know that standard deviation measures how spread out scores are around the mean, but its formula is not examined in the GCSE core paper. Still, recognising that a larger standard deviation means greater spread is useful when interpreting graphs and summaries.
为了粗略估计变异程度，你还需要知道标准差测量的是分数围绕平均数的分散程度，不过GCSE核心试卷不要求计算具体公式。然而，懂得标准差越大代表分数越分散，对于解释图表和摘要信息非常有用。
3. Percentages, Ratios & Proportions | 百分比、比率与比例
Psychological reports often convert raw frequencies into percentages to make comparisons easier. The formula is straightforward:
Percentage (%) = (Frequency / Total) × 100
心理学报告中常将原始频数转换为百分比，以便于比较。公式很简单：
百分比(%) = (频数 / 总数) × 100
Ratios express the relative size of two categories. For example, a ratio of 3:1 means for every 3 participants who showed behaviour A, 1 showed behaviour B. Proportions are similar but use decimal fractions, such as 0.75 of the sample.
比率表示两个类别之间的相对大小。例如，3:1 的比例意味着每有3名参与者表现出行为A，就有1名表现出行为B。比例与之相似，但使用小数如0.75。
4. Weber’s Law | 韦伯定律
Weber's Law describes the relationship between the physical magnitude of a stimulus and the difference needed to notice a change. The size of the just noticeable difference (JND) is a constant proportion of the original stimulus intensity.
ΔI / I = k
其中 ΔI = 最小可觉差 (JND)，I = 原始刺激强度，k = 韦伯常数。
韦伯定律描述了刺激的物理强度与能察觉到变化所需的差异之间的关系。最小可觉差 (JND) 的大小与原始刺激强度成固定比例。
For example, if the Weber constant for lifted weight is 0.02, you would need to add 2 g to a 100 g weight to notice a difference, but 20 g to a 1000 g weight. This law applies to many sensory judgements, such as brightness and loudness.
以举重为例，如果韦伯常数为0.02，要察觉到差异需要在100克上增加2克，但在1000克上则需要增加20克。此定律适用于亮度、响度等多种感觉判断。
5. Yerkes–Dodson Law | 耶克斯–多德森定律
The Yerkes–Dodson Law explains the link between arousal and performance. It predicts an inverted-U relationship: performance improves as arousal increases, but only up to an optimal point. Beyond that optimal level, further arousal leads to a decline in performance.
耶克斯–多德森定律阐释了唤醒水平与表现之间的关系。它预测呈现倒U形曲线：随着唤醒水平提高，表现会提升，但仅到某个最佳水平为止；超过最佳点后，继续增加唤醒反而导致表现下降。
The optimal arousal level is lower for difficult or cognitively demanding tasks and higher for simple or well-practised tasks. You can apply this law when explaining exam performance or sporting scenarios in psychological terms.
对于困难或认知要求高的任务，最佳唤醒水平较低；对于简单或熟练的任务，最佳唤醒水平较高。在心理学描述中，你可以运用这一定律解释考试表现或运动情境。
6. Miller’s Law – The Magical Number 7±2 | 米勒定律 – 神奇数字7±2
Miller's Law refers to the limited capacity of short-term memory. Research suggests that most people can hold between 5 and 9 items (or chunks) in their short-term memory at one time.
Short-term memory capacity ≈ 7 ± 2 chunks
米勒定律指出短时记忆的容量有限。研究发现，大多数人一次能在短时记忆中保持5到9个信息组块。
短时记忆容量 ≈ 7 ± 2 个组块
Chunking can increase the amount of information remembered because individual letters or digits can be grouped into meaningful wholes. This principle is fundamental to understanding memory improvement techniques.
组块化可以增加记忆的信息量，因为单个字母或数字能被组合成有意义的整体。这一原理是理解记忆提升技巧的基础。
7. Thorndike’s Law of Effect | 桑代克的效果律
Thorndike's Law of Effect states that behaviours which produce a satisfying outcome are likely to be repeated, while behaviours followed by an unsatisfying outcome become less likely. This law forms the basis of operant conditioning.
桑代克的效果律指出：产生满意结果的行为会得到加强，更可能被重复；而带来不满意结果的行为则会减弱，发生的可能性降低。这一定律是操作性条件反射的基础。
In puzzle-box experiments, cats learnt to press a lever to escape and obtain food. Satisfying consequences stamped in the connection between stimulus and response, whereas annoying consequences weakened it.
在谜箱实验中，猫学会按压杠杆以逃脱并获得食物。满意的后果强化了刺激与反应之间的联结，而厌烦的后果则削弱了这一联结。
8. The Serial Position Effect | 序列位置效应
The serial position effect refers to the pattern whereby recall accuracy varies with the position of an item in a list. Two sub-effects are commonly observed:
- Primacy effect – better recall of items from the beginning of the list, thought to reflect long-term memory rehearsal.
- Recency effect – better recall of items from the end of the list, thought to reflect short-term memory.
序列位置效应指的是回忆准确率随项目在列表中的位置而变化的现象。一般可观察到两种子效应：
- 首因效应 – 列表开头项目的回忆效果更好，被认为是长时记忆复述所致。
- 近因效应 – 列表末尾项目的回忆效果更好，被认为是短时记忆的作用。
This effect is a standard finding in memory research and is often explained using the multi-store model. When a distractor task is added after the list, the recency effect disappears, whereas the primacy effect remains.
这一效应是记忆研究中的经典发现，通常可用多储存模型来解释。如果在列出项目后加入干扰任务，近因效应会消失，而首因效应依然存在。
9. Gestalt Principles of Perceptual Organisation | 格式塔知觉组织原则
Gestalt psychologists proposed that we perceive whole patterns rather than merely collections of parts. Several key principles describe how sensory information is organised:
- Proximity – elements close together are grouped together.
- Similarity – similar items are seen as a group.
- Closure – we fill in gaps to see complete figures.
- Continuity – we perceive smooth, continuous lines rather than abrupt changes.
格式塔心理学家认为，我们感知的是整体模式而非个别部分的简单集合。以下几个关键原则描述了感觉信息如何被组织：
- 接近性 – 彼此靠近的元素会被视为一组。
- 相似性 – 相似的项目会被看作一个整体。
- 闭合性 – 我们会填补空缺以看到完整的图形。
- 连续性 – 我们倾向于感知平滑、连续的线条，而非突兀的变化。
These principles explain visual illusions and everyday perception. They are not formulaic but act as perceptual 'theorems' that predict how the brain organises sensory input.
这些原则能解释视错觉和日常感知现象。它们虽不是方程式，但可作为感知上的“定理”，用来预测大脑如何组织感觉输入。
10. Piaget’s Stages of Cognitive Development | 皮亚杰的认知发展阶段
Piaget's theory describes four invariant stages through which children progress as their thinking becomes more logical and abstract. Although not a mathematical formula, the stages provide a theorem-like framework for understanding cognitive growth.
皮亚杰的理论描述了思维逐渐逻辑化和抽象化的四个恒定阶段。虽然这并非数学公式，但这些阶段为理解认知发展提供了一个类似定理的框架。
Sensorimotor (0–2 years) → Preoperational (2–7 years) → Concrete operational (7–11 years) → Formal operational (11+ years)
认知发展的顺序不变，但不同儿童达到各阶段的年龄可能存在个体差异。熟悉每个阶段的关键特征，如客体永恒性、自我中心、守恒和抽象推理，对考试至关重要。
11. Attachment Theories and Key Laws | 依恋理论及其关键规律
Several ethological and learning-theory principles act as 'laws' in the study of attachment. Lorenz demonstrated imprinting in geese: the tendency of young animals to follow the first moving object they encounter during a critical period. Imprinting is rapid and apparently irreversible.
在依恋研究中，若干习性学和学习理论的原理充当着“定律”。洛伦茨证明了鹅的印刻现象：幼鹅在关键期内倾向于跟随它们遇到的第一个移动物体。印刻发生迅速且似乎不可逆。
Bowlby's law of continuity states that the more constant and predictable a child's care, the more secure the attachment. A related law of 'accumulated separation' suggests that the negative effects of each separation add up, potentially harming psychological development.
鲍尔比的连续性定律指出，对儿童的照料越是持续且可预测，依恋就越安全。与之相关的“累积分离”规律表明，每一次分离的负面效应会累积，可能损害心理发展。
12. Key Statistical Symbols & Notation | 关键统计符号与标记
In psychological studies, consistent notation is used to report data. Being fluent in these symbols will help you read research tables and answer exam questions accurately.
在心理学研究中，报告数据时使用一致的符号。熟悉这些符号有助于你准确阅读研究表格并回答问题。
- Σ (upper-case sigma) – 'sum of'
- x̄ – sample mean
- n – number of scores or participants
- s or SD – standard deviation
- p – probability; p < 0.05 often indicates significance
- Σ – 求和
- x̄ – 样本平均数
- n – 分数或参与者个数
- s 或 SD – 标准差
- p – 概率；p < 0.05 通常表示结果显著
A common exam requirement is to read a table and comment on mean differences or variability. Recognising these symbols quickly saves time and improves accuracy in data-response questions.
考试中常见的要求是阅读表格并评论平均数差异或变异程度。快速辨认这些符号能节省时间，并提高数据题的回答准确性。
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