📚 CIE IGCSE Year 10 Psychology Formula & Theorem Quick Reference Handbook | CIE IGCSE十年级心理学公式定理速查手册
Psychology is a science built on empirical evidence, yet it also relies on a compact set of formulas and core theoretical propositions that every Cambridge IGCSE learner must master. This quick reference handbook brings together the essential statistical tools you will use in Research Methods and the key theoretical 'theorems' that underpin major topics. Keep these by your side when analysing data, designing investigations, or writing exam answers.
心理学是建立在实证基础上的科学，但它同样依赖一套简练的公式和核心理论命题，每一位剑桥 IGCSE 考生都必须掌握。这份速查手册汇集了你在研究方法中会用到的关键统计工具，以及支撑各大主题的重要理论“定理”。在做数据分析、设计研究或撰写考试答案时，请让这本手册陪伴在你左右。
1. What Is a Formula & Theorem Quick Reference? | 什么是公式定理速查手册？
A formula in psychology is a standardised mathematical expression used to summarise data, measure relationships, or evaluate change. A theorem, in our context, is a well-substantiated explanatory principle that has been repeatedly tested, such as the Multi-Store Model of memory or Bandura’s Social Learning Theory. This handbook unites both, giving you instant access to the quantitative and qualitative tools required by the CIE IGCSE Psychology syllabus.
心理学中的公式是用来总结数据、测量关系或评估变化的标准数学表达式。而定理，在这里指的是经过反复检验、得到充分证实的解释性原则，比如记忆的多储存模型或班杜拉的社会学习理论。本手册将二者结合在一起，让你能即时调取 CIE IGCSE 心理学大纲所要求的定量与定性工具。
2. Mean, Median & Mode: The Central Tendency Trio | 平均数、中位数与众数：集中趋势三大指标
These three measures summarise a data set with a single typical value. The mean is the arithmetic average, the median is the middle score when data are ordered, and the mode is the most frequently occurring value. You must be able to calculate all three and choose the most appropriate one for a given distribution.
这三种量数用一个典型值来概括一组数据。平均数是算术平均值，中位数是将数据排序后位于中间的值，众数则是出现频率最高的数值。你必须能够计算这三者，并为给定的分布选择最合适的一个。
Mean = ∑x / N
平均数 = ∑x / N
s the number of scores. The median is found at the (N+1)/2th position in an ordered list. The mode is simply the category or score that appears most often. For skewed distributions, the median is often more representative than the mean.
其中 ∑x 是所有分数的总和，N 是分数的个数。中位数在有序列表中的位置是 (N+1)/2。众数就是出现次数最多的类别或分数。对于偏态分布，中位数通常比平均数更具代表性。
3. Range: Measuring Spread | 全距：衡量离散程度
The range is the simplest measure of dispersion. It tells you the distance between the highest and the lowest scores in a data set, giving a rough idea of variability. Although it is easy to compute, the range can be heavily influenced by extreme outliers.
全距是最简单的离散程度量数。它告诉你一组数据中最高分与最低分之间的距离，从而大致体现变异性。尽管计算简单，全距很容易受到极端异常值的影响。
Range = Highest score − Lowest score
全距 = 最高分 − 最低分
Always pair the range with a measure of central tendency so that your description of the data is balanced. For example, 'The mean reaction time was 250 ms with a range of 120 ms' gives a fuller picture than the mean alone.
始终将全距与集中趋势量数搭配使用，这样你对数据的描述才会均衡。例如，“平均反应时间是 250 毫秒，全距为 120 毫秒”比仅仅给出平均数更能呈现完整的情形。
4. Percentage Change: Evaluating Differences | 百分比变化：评估差异
In many psychological investigations you need to express how much a score has increased or decreased relative to an original baseline. The percentage change formula lets you compare conditions or assess the effect of an intervention in a standardised way.
在许多心理学研究中，你需要表达一个分数相对于原始基线增加了或减少了多少。百分比变化公式能让你以标准化的方式比较不同的条件或评估干预的效果。
Percentage change = ( (New score − Original score) / Original score ) × 100%
百分比变化 = ( (新分数 − 原始分数) / 原始分数 ) × 100%
Be careful with negative values: a negative percentage change indicates a decrease. This formula is especially useful when analysing repeated measures designs or pre‑test/post‑test data.
注意负值：负的百分比变化表示下降。在分析重复测量设计或前测/后测数据时，这一公式尤其有用。
5. Spearman’s Rank Correlation: A Non-Parametric Tool | 斯皮尔曼等级相关：一种非参数工具
Spearman’s rank correlation coefficient (rₛ) measures the strength and direction of a monotonic relationship between two variables. It works with ordinal data or data that do not meet the assumptions of a parametric test. You will often use it in CIE IGCSE Psychology to analyse questionnaire ratings or observational rankings.
斯皮尔曼等级相关系数（rₛ）测量两个变量之间单调关系的强度与方向。它适用于顺序数据或不符合参数检验假设的数据。在 CIE IGCSE 心理学中，你常会用它来分析问卷评分或观察排序。
rₛ = 1 − ( 6∑d² ) / ( n(n² − 1) )
rₛ = 1 − ( 6∑d² ) / ( n(n² − 1) )
Here, d is the difference between the ranks of each pair, and n is the number of paired observations. The coefficient ranges from −1 (perfect negative correlation) to +1 (perfect positive correlation). A value close to 0 suggests no meaningful relationship.
此处，d 是每对数据的等级差，n 是成对观测的数目。该系数的范围从 −1（完全负相关）到 +1（完全正相关）。接近 0 的值表示没有有意义的关系。
6. Operationalising Variables: Making Concepts Measurable | 变量操作化：让概念可测量
Before any formula can be applied, you must turn abstract psychological constructs into something measurable. Operationalisation means defining the independent variable (IV) and the dependent variable (DV) in precise, replicable terms. For example, 'aggression' could be operationalised as the number of loud bangs on a desk per minute.
在应用任何公式之前，你必须把抽象的心理学构念转化为可测量的东西。操作化意味着用精确、可重复的术语来定义自变量（IV）和因变量（DV）。例如，“攻击性”可以被操作化为每分钟敲打桌子的响亮次数。
IV (manipulated) → Operational definition → DV (measured)
自变量（操纵） → 操作定义 → 因变量（测量）
This sequence is a theorem in itself: a study is only as valid as its operational definitions. Without them, you cannot collect reliable data, and no statistical formula will rescue a poorly defined variable.
这一序列本身就是一个定理：一项研究的效度仅如其操作定义。没有它们，你就无法收集到可靠的数据，任何统计公式也挽救不了定义模糊的变量。
7. Experimental Design Essentials: IV, DV & Controls | 实验设计要素：自变量、因变量与控制变量
The core causal theorem of experimental psychology states that any systematic change in the DV is attributable to the manipulation of the IV, provided all extraneous variables are controlled. You can use the expression below as a mental checklist for every experiment you evaluate.
实验心理学核心的因果定理指出，只要所有额外变量都被控制住，因变量的任何系统性变化都可归因于对自变量的操纵。你可以把下面的表达式当作每项实验评估时的思维清单。
Change in IV → Change in DV (if CVs are constant)
自变量的改变 → 因变量的改变（前提是控制变量保持恒定）
Control variables (CVs) must be held constant or eliminated. Common CVs include time of day, noise level, and participant characteristics. This logic underpins the experimental method and explains why we randomise participants and counterbalance conditions.
控制变量必须保持恒定或被消除。常见的控制变量包括一天中的时段、噪音水平和被试特征。这一逻辑是实验方法的基石，也解释了为什么我们要随机分配被试并对条件进行平衡。
8. Sampling Formulas: Representative Groups | 抽样公式：代表性样本
Sampling directly affects the generalisability of findings—a key theorem in research methodology. While CIE IGCSE does not require complex probability equations, you should grasp the proportional principles that govern stratified or quota sampling. A simple proportional formula helps determine how many participants to draw from each subgroup.
抽样直接影响研究结论的可推广性，这是研究方法论中的一条关键定理。虽然 CIE IGCSE 并不要求复杂的概率方程，但你应该掌握支配分层抽样或配额抽样的比例原则。一个简单的比例公式有助于确定每个子群应抽取多少名被试。
Subgroup sample size = (Subgroup % in population / 100) × Total desired sample size
子群样本容量 = (该子群在总体中的百分比 / 100) × 计划总样本容量
For instance, if 40% of a school population is Year 10 and you need a sample of 50, you would aim for 20 Year‑10 participants. This proportional theorem ensures your sample mirrors the important strata of the target population.
例如，某校 40% 的学生是十年级，你需要的样本容量为 50，那么你应当选取 20 名十年级被试。这一比例定理能确保你的样本反映目标总体中的重要层次。
9. Ethical Principles as Fundamental Theorems | 伦理原则作为基本定理
The BPS and APA ethical guidelines function as non‑negotiable theorems for all psychological research. They can be summarised in a decision‑making sequence that protects participants' wellbeing and the integrity of the discipline. You must remember the acronym CONSENT: Competence, No harm, Confidentiality, Observers’ role, Social responsibility, Ethics committee, Naturalistic observation constraints, and Thorough debriefing.
英国心理学会和美国心理学会的伦理准则是一切心理学研究中不可违背的定理。它们可以用一个保护被试福祉和学科诚信的决策序列来概括。你必须记住缩略词 CONSENT：胜任力、无伤害、保密、观察者角色、社会责任、伦理委员会、自然观察的限制以及彻底的后续解释。
ical research = Informed consent + Avoidance of deception + Debriefing + Right to withdraw
伦理研究 = 知情同意 + 避免欺骗 + 事后解释 + 退出权
Whenever you evaluate a study, apply this theorem: if any of these elements is missing, the study’s ethical standing is compromised, and its findings may be questioned regardless of statistical significance.
每当你评价一项研究时，请运用这条定理：如果缺失其中任何一个要素，该研究的伦理地位就会受损，其结论无论统计上如何显著都可能受到质疑。
10. Multi-Store Model of Memory: The Atkinson–Shiffrin Theorem | 记忆的多储存模型：阿特金森–谢夫林定理
The Multi-Store Model proposes that memory consists of three structurally distinct stores: sensory register, short‑term memory (STM), and long‑term memory (LTM). Information flows linearly, provided it receives attention and is rehearsed. This can be expressed as a processing theorem.
多储存模型提出，记忆由三个结构上截然不同的储存库组成：感觉登记、短时记忆和长时记忆。信息在获得注意并被复述的前提下线性流动。这可以表达为一条加工定理。
Sensory input → (Attention) → STM ⇌ (Rehearsal) → LTM
感官输入 → (注意) → 短时记忆 ⇌ (复述) → 长时记忆
STM has a limited capacity of 7±2 chunks and a duration of around 18– rs primarily through displacement, while LTM forgetting is often due to retrieval failure.
短时记忆的容量有限，为 7±2 个组块，持续时间约为 18–30 秒。长时记忆被认为拥有无限的容量和持续时间。短时记忆的遗忘主要通过干扰替代发生，而长时记忆的遗忘常源于提取失败。
11. Bandura’s Social Learning Theory: The Observational Theorem | 班杜拉的社会学习理论：观察学习定理
Bandura’s core proposition—often treated as a theorem in developmental psychology—states that behaviour can be acquired by observing and imitating role models. The process involves four mediational processes: attention, retention, reproduction, and motivation (ARRM). These form a logical chain.
班杜拉的核心命题——在发展心理学中常被当作定理——指出，行为可以通过观察和模仿榜样而习得。这一过程包含四个中介过程：注意、保持、复制和动机（ARRM）。它们构成了一条逻辑链。
Model performs behaviour → Attention → Retention → Reproduction → Motivation → Imitation
榜样表现出行为 → 注意 → 保持 → 复制 → 动机 → 模仿
The Bobo doll study provided empirical support: children who observed an aggressive model were significantly more likely to imitate the aggressive acts. This theorem highlights that learning does not require direct reinforcement; cognitive mediation is sufficient.
波波玩偶研究提供了实证支持：观察到攻击榜样的儿童显著更可能模仿攻击行为。这一定理强调，学习不需要直接强化；认知中介就已经足够。
12. Quick Reference Summary Table | 速查总结表
The table below consolidates every formula and theorem covered in this handbook. Use it for last‑minute revision or as a checklist when you design and evaluate studies.
下表汇总了本手册涵盖的每一个公式和定理。可在最后冲刺复习时使用，或作为你设计和评价研究时的检查清单。
| Category 类别 | Formula / Theorem 公式/定理 | Key Expression 核心表述 |
|---|---|---|
| Central Tendency 集中趋势 | Mean / Median / Mode | ∑x / N ; (N+1)/2th ; most frequent |
| Dispersion 离散程度 | Range | Highest − Lowest |
| Change 变化 | Percentage change | ((New−Original)/Original)×100% |
| Correlation 相关 | Spearman's rₛ | 1 − (6∑d²)/(n(n²−1)) |
| Variables 变量 | Operationalisation | IV → definition → DV |
| Causality 因果关系 | Experimental logic | Δ IV → Δ DV (CV constant) |
| Sampling 抽样 | Stratified proportion | (%/100)×Total n |
| Ethics 伦理 | Ethical research theorem | Consent + no harm + debrief + withdraw |
| Memory 记忆 | Multi-Store Model | Input→STM⇌LTM |
| Learning 学习 | Social Learning Theory | Attention→Retention→Reproduction→Motivation |
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