📚 Year 9 CIE Psychology: Formula & Theorem Quick Reference Handbook | Year 9 CIE 心理学：公式定理速查手册
Welcome to your essential quick reference for Year 9 CIE Psychology. This handbook gathers the key statistical formulas, classic psychological theories, and research principles you will encounter throughout the course. Use it to revise with confidence and support your understanding of data analysis and core concepts.
欢迎使用 Year 9 CIE 心理学必备速查手册。本手册汇集了你在课程中会遇到的关键统计公式、经典心理学理论和研究原则。用它来自信地复习，并加深你对数据分析和核心概念的理解。
1. Measures of Central Tendency: Mean, Median, Mode | 集中趋势量数：均值、中位数、众数
Central tendency describes the typical or average value in a data set. The three main measures are the mean, the median, and the mode.
集中趋势描述数据集中典型或平均的值。三个主要量数是均值、中位数和众数。
The mean is calculated by adding all values and dividing by the number of values.
均值通过将所有数值相加再除以数值的个数来计算。
Mean (x̄) = Σx / N
均值 (x̄) = Σx / N
The median is the middle value when the data are arranged in order. If there are two middle numbers, take their mean.
中位数是将数据按顺序排列后位于中间的值。如果有两个中间数，则取它们的均值。
The mode is the most frequently occurring value in the set. A data set can have one mode, more than one mode, or no mode at all.
众数是数据集中出现频率最高的值。一个数据集可能有一个众数、多个众数或没有众数。
2. Range and Spread of Data | 极差与数据离散程度
The range is the simplest measure of dispersion. It tells us how spread out the data are by subtracting the smallest value from the largest.
极差是最简单的离散度量。它通过最大值减去最小值来告诉我们数据的分散程度。
Range = Highest value − Lowest value
极差 = 最大值 − 最小值
A larger range indicates greater variability. While easy to compute, the range is sensitive to extreme values (outliers).
极差越大，表示变异性越大。虽然计算简单，但极差容易受极端值（异常值）的影响。
In Year 9, you are not required to calculate standard deviation, but you should know it measures the average distance of each data point from the mean.
在 Year 9 阶段，你不需要计算标准差，但你应该知道它衡量每个数据点与均值的平均距离。
3. Percentages and Proportional Thinking | 百分比与比例思维
Percentages are frequently used in psychology to describe proportions of participants or to compare conditions.
心理学中经常用百分比来描述参与者的比例或比较不同条件。
Percentage (%) = (Part / Whole) × 100
百分比 (%) = (部分 / 整体) × 100
of 60 participants recalled a word correctly, the percentage correct is (15/60) × 100 = 25%.
例如，如果 60 名参与者中有 15 人正确回忆了一个单词，则正确率为 (15/60) × 100 = 25%。
When comparing the results of an experimental and a control group, converting raw scores into percentages helps make fair comparisons.
在比较实验组和对照组的结果时，将原始分数转换为百分比有助于进行公平的比较。
4. Spearman's Rank Correlation Coefficient (Introduction) | 斯皮尔曼等级相关系数（简介）
Spearman's rho (ρ) is used to measure the strength and direction of a correlation between two sets of ranked data.
斯皮尔曼等级相关系数 ρ 用于衡量两组等级数据之间相关的强度和方向。
ρ = 1 − ( 6 Σd² ) / [ n(n² − 1) ]
ρ = 1 − ( 6 Σd² ) / [ n(n² − 1) ]
Where d is the difference between ranks for each pair, and n is the number of pairs. The result ranges from -1 (perfect negative) to +1 (perfect positive), with 0 meaning no correlation.
其中 d 是每对排名之间的差值，n 是对数。结果范围从 -1（完全负相关）到 +1（完全正相关），0 表示无相关。
In Year 9, you simply need to recognise the formula and understand its purpose; full calculation will be practised in later years.
在 Year 9，你只需要认识这个公式并理解它的用途；完整的计算将在更高的年级中练习。
5. Memory Models: Atkinson & Shiffrin's Multi-store Model | 记忆模型：阿特金森与谢夫林的多储存模型
This model proposes three separate memory stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Information flows through attention and rehearsal.
该模型提出了三个独立的记忆储存：感觉记忆、短时记忆和长时记忆。信息通过注意和复述流动。
Sensory memory holds fleeting impressions (< 1 second) and has a large capacity. Attention moves selected information into STM.
感觉记忆保持短暂的印象（小于1秒），容量很大。注意将选中的信息转入短时记忆。
Short-term memory has a limited capacity of 7±2 items and a duration of about 18– ithout rehearsal. Maintenance rehearsal can keep information in STM or transfer it to LTM.
短时记忆的容量有限，为 7±2 项，持续约 18–30 秒（在没有复述的情况下）。维持性复述可以使信息保留在短时记忆或转入长时记忆。
Long-term memory is considered to have unlimited capacity and can store information for a lifetime. Forgetting from LTM may occur due to interference or retrieval failure.
长时记忆被认为具有无限的容量，并且可以终生储存信息。长时记忆中的遗忘可能是由于干扰或提取失败造成的。
6. Piaget's Stages of Cognitive Development (Summary) | 皮亚杰认知发展阶段（概要）
Jean Piaget theorised that children pass through four invariant stages of intellectual growth. Each stage is defined by qualitatively different ways of thinking.
让·皮亚杰认为，儿童会经历四个固定的智力发展阶段。每个阶段都有质上不同的思维方式。
| Stage | 阶段 | Age Range | 年龄范围 | Key Feature | 关键特征 |
| Sensorimotor | 感觉运动 | 0–2 years | Object permanence develops. Learning through senses and actions. |
| Pre-operational | 前运算 | 2–7 years | Symbolic thinking, egocentrism, lack of conservation. |
| Concrete operational | 具体运算 | 7–11 years | Logical thought about concrete events, conservation mastered. |
| Formal operational | 形式运算 | 11+ years | Abstract reasoning, hypothetical thinking. |
These stages are often examined alongside practical tasks like Piaget's conservation experiments. Understanding them helps explain children's cognitive abilities.
这些阶段常常与皮亚杰的守恒实验等实践任务一同考查。理解它们有助于解释儿童的认知能力。
7. Maslow's Hierarchy of Needs | 马斯洛需求层次理论
Abraham Maslow proposed a five‑tier model of human needs, often shown as a pyramid. Basic needs must be satisfied before higher-order needs become motivating.
亚伯拉罕·马斯洛提出了人类需求的五层模型，常以金字塔形式呈现。基本需求必须得到满足后，更高层次的需求才会成为驱动力。
From bottom to top: Physiological (food, water, warmth), Safety (security, stability), Love/belonging (friendship, intimacy), Esteem (achievement, respect), and Self-actualisation (realising one's full potential).
从下到上依次为：生理需求（食物、水、温暖），安全需求（安全感、稳定），爱与归属需求（友谊、亲密关系），尊重需求（成就、尊重），以及自我实现需求（发挥全部潜能）。
This theory is used in humanistic psychology to explain motivation and well-being. Limitations include cultural differences and difficulties in defining self‑actualisation empirically.
这一理论在人本主义心理学中用于解释动机和幸福感。其局限性包括文化差异，以及难以从实证角度定义自我实现。
8. Key Ethical Principles (BPS Guidelines) | 关键伦理原则（英国心理学会指南）
All psychological research must follow strict ethical standards to protect participants. The British Psychological Society (BPS) issues a code of conduct researchers must adhere to.
所有心理学研究都必须遵循严格的伦理标准，以保护参与者。英国心理学会（BPS）发布了研究者必须遵守的行为准则。
The key principles include: Informed consent – participants should know the aims and procedures; Deception should be avoided unless necessary and must be justified; Right to withdraw at any time; Confidentiality of data; Protection from harm, both physical and psychological; and Debriefing after the study to explain the true purpose and offer support.
关键原则包括：知情同意——参与者应了解研究的目的和程序；欺骗应尽量避免，除非必要且需证明其合理性；随时退出研究的权利；数据的保密性；避免身心伤害；以及研究结束后的事后解说，以解释真实目的并提供支持。
For Year 9, you should be able to identify ethical issues in a piece of research and suggest how they might be resolved.
对 Year 9 的学生来说，你应该能识别研究中的伦理问题，并提出可能的解决方案。
9. Research Methods: Key Terms and Symbols | 研究方法：关键术语与符号
Familiarise yourself with the standard notation used in hypothesis testing and experimental design.
熟悉假设检验和实验设计中使用的标准符号。
Null hypothesis (H₀): predicts no difference or no relationship between variables. Alternative hypothesis (H₁ or Hₐ): predicts a difference or relationship.
虚无假设 (H₀)：预测变量之间没有差异或没有关系。备择假设 (H₁ 或 Hₐ)：预测存在差异或关系。
Independent variable (IV): the variable the researcher manipulates. Dependent variable (DV): the variable that is measured. Extraneous variables: any other variables that might affect the DV and should be controlled.
自变量 (IV)：研究者操纵的变量。因变量 (DV)：被测量的变量。额外变量：可能影响因变量的任何其他变量，应加以控制。
Design types include independent groups, repeated measures, and matched pairs. Each has its strengths and limitations regarding order effects and participant variables.
实验设计类型包括独立组设计、重复测量设计和匹配对设计。每种设计在顺序效应和参与者变量方面都有其优缺点。
10. Formula and Theorem Summary Table | 公式与定理汇总表
Keep this table handy for quick revision before assessments.
将此表放在手边，便于评估前快速复习。
| Concept | 概念 | Formula / Key Point | 公式 / 要点 |
| Mean | 均值 | x̄ = Σx / N |
| Median | 中位数 | Middle value (ordered data) |
| Mode | 众数 | Most frequent value |
| Range | 极差 | Highest − Lowest |
| Percentage | 百分比 | (Part / Whole) × 100 |
| Spearman's ρ | 斯皮尔曼ρ | 1 − (6 Σd²) / [ n(n² − 1) ] |
| Null hypothesis | 虚无假设 | H₀: no difference/relationship |
| STM capacity | 短时记忆容量 | 7 ± 2 items (Miller, 1956) |
| Piaget's stages | 皮亚杰阶段 | Sensorimotor, pre-operational, concrete operational, formal operational |
| Maslow's hierarchy | 马斯洛需求层次 | Physiological → Safety → Love → Esteem → Self-actualisation |
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