📚 Year 9 OCR Psychology: Formula & Theorem Quick Reference Handbook | Year 9 OCR 心理学：公式定理速查手册
Welcome to your all-in-one quick reference for the essential formulas, numerical theorems, and classic study findings you need to master Year 9 OCR Psychology. This handbook covers the key statistical calculations, memory capacity rules, perceptual laws, and developmental stage benchmarks that appear frequently in assessments. Keep this guide handy for last-minute revision and to boost your confidence in tackling data-based questions and theory recall.
欢迎使用这本全能速查手册，它涵盖了你掌握九年级 OCR 心理学必备的核心公式、数字定理和经典研究结果。本手册整理了常考的平均数、中位数等统计计算法、记忆容量规则、感知定律以及发展心理学各阶段的标准年龄区间。在考前快速复习时查阅它，能帮助你有信心地应对数据分析题和理论回忆题。
1. Mean, Median, Mode & Range | 平均数、中位数、众数与范围
The arithmetic mean is the most common measure of central tendency. It is calculated by summing all the data values and dividing by the total number of values.
算术平均数是最常用的集中趋势量数。计算方法是将所有数据值相加，再除以数据值的总个数。
Mean = (x₁ + x₂ + … + xₙ) / n
平均数 = (x₁ + x₂ + … + xₙ) / n
The median is the middle value when all data are arranged in order from smallest to largest. If there is an even number of values, the median is the mean of the two middle numbers.
中位数是将所有数据从小到大排列后位于中间的值。若数值个数为偶数，中位数就是中间两个数的平均值。
The mode is the most frequently occurring value in a data set. A set can have one mode (unimodal), two modes (bimodal), or no mode at all if all values occur with equal frequency.
众数是数据集中出现频率最高的值。一组数据可以只有一个众数（单峰），可以有两个众数（双峰），如果所有值出现次数相同则没有众数。
The range measures the spread of data and is found by subtracting the smallest value from the largest value.
范围衡量数据的离散程度，等于最大值减去最小值。
Range = Maximum – Minimum
范围 = 最大值 – 最小值
The mean uses all data points but can be distorted by extreme outliers. The median is not affected by outliers and is a better choice for skewed distributions. The range is quick to compute but only considers the two most extreme numbers.
平均数用到每一个数据点，但容易被极端值拉偏。中位数不受极端值影响，更适合偏态分布的数据。范围计算很快，但它只用到最大和最小的两个值。
2. Percentage Change & Proportions | 百分比变化与比例
Percentage change is widely used in psychology to compare scores before and after an intervention or to express the difference between two experimental conditions.
在心理学中，百分比变化广泛用于比较干预前后的分数，或表示两个实验条件之间的差异。
Percentage Change = [(New Value – Old Value) / Old Value] × 100%
百分比变化 = [（新值 – 旧值）/ 旧值] × 100%
decrease. For example, if a memory score rises from 20 to 25, the increase is (5/20) × 100% = 25%.
结果为正表示增长，为负则表示减少。例如，记忆分数从 20 上升到 25，增长幅度为（5/20）× 100% = 25%。
Proportions and fractions also appear in research data. To convert a proportion to a percentage, multiply by 100. Thus, 0.32 of participants showing conformity becomes 32%.
比例和分数在研究数据中也很常见。将比例转换为百分比只需乘以 100。因此，0.32 的参与者表现出从众行为就等于 32%。
Being able to calculate percentages quickly helps you interpret bar charts, pie charts and summary tables used in OCR-style exam questions.
迅速计算百分比的能力有助于你解读 OCR 风格考题中的条形图、饼图和汇总表格。
3. Ethical Guidelines as Principles | 伦理准则作为定理
Although not a mathematical formula, the ethical 'rules' set by the British Psychological Society (BPS) can be thought of as fundamental theorems that must be applied when designing any psychological study.
虽然这不是数学公式，但英国心理学会（BPS）制定的伦理 '规则' 可被视为设计任何心理学研究时必须遵循的基本定理。
Informed consent: participants must be told the aim of the study, what they will be asked to do, and must agree without pressure. They also have the right to withdraw at any time.
知情同意：必须告知参与者研究目的、他们将做什么，并确保他们在没有压力的情况下同意。参与者在任何时候都有权退出。
Deception should be avoided unless scientifically justified. If mild deception is required, researchers must debrief participants as soon as possible, telling them the true purpose and checking their wellbeing.
应避免欺骗，除非有科学上的充分理由。如果必须进行轻微欺骗，研究者必须尽快进行事后解释，告知真实目的并确认参与者状态良好。
Confidentiality: personal data must be kept anonymous, using codes or pseudonyms, and stored securely. Protection from physical and psychological harm is also a non-negotiable rule.
保密性：个人数据必须匿名处理，使用代码或化名，并安全保存。同时，保护参与者免受身体和心理伤害也是一项不可妥协的铁则。
When evaluating any study in Year 9, ask yourself: was consent obtained? Could participants withdraw? Did the researchers respect these ethical theorems?
在九年级评价任何研究时，问问自己：是否获得了同意？参与者能否退出？研究者是否遵守了这些伦理定理？
4. Miller's Magic Number 7±2 | 米勒的神奇数字 7±2
George Miller (1956) published a landmark paper arguing that the capacity of short-term memory (STM) is limited to about seven items, plus or minus two.
乔治·米勒（1956）发表了一篇里程碑式论文，指出短时记忆的容量限于大约 7 项，上下浮动 2 项。
STM Capacity Theorem: 7 ± 2 items
短时记忆容量定理：7 ± 2 项
This 'chunk' limit means that when we try to hold a list of digits, letters or words, we can typically recall 5–9 meaningful chunks. Chunking information can expand the amount of data stored, but the number of chunks stays the same.
这个 '组块' 界限意味着当我们试图记住一串数字、字母或单词时，通常能回忆 5–9 个有意义的组块。对信息进行组块化可以扩充存储的数据量，但组块数量保持不变。
Miller's theorem is tested directly in OCR research method questions. You might be asked to explain why a phone number of 11 digits is hard to hold without rehearsal, or why chunking helps recall.
OCR 研究方法题目中会直接考查米勒定理。你可能需要解释为什么 11 位的电话号码在没有复述的情况下很难记住，或者为什么组块化有助于回忆。
rule applies to the capacity, not the duration, of STM. Duration was found to be around 18–30 seconds without rehearsal, according to Peterson and Peterson's study with trigrams.
重要的是，7±2 规律适用于短时记忆的容量，而非持续时间。根据 Peterson 和 Peterson 的三字母组实验，没有复述时短时记忆的持续时间大约为 18–30 秒。
5. Ebbinghaus' Forgetting Curve | 艾宾浩斯的遗忘曲线
Hermann Ebbinghaus studied his own memory using nonsense syllables to avoid prior knowledge interfering. He discovered that forgetting follows a predictable curve – rapid loss at first, then slowing down.
赫尔曼·艾宾浩斯使用无意义音节研究自己的记忆，以避免已有知识干扰。他发现遗忘遵循一条可预测的曲线——起初急剧下降，然后逐渐减缓。
The classic data from Ebbinghaus’ work provides a numerical theorem on memory decay. After just 20 minutes, about 42% of the material is lost; after 1 hour, 56% is lost; after 1 day, 66% is lost; and after 6 days, roughly 75% is forgotten.
艾宾浩斯研作的经典数据提供了记忆衰退的数字定理。仅仅 20 分钟后，约 42% 的材料被遗忘；1 小时后遗忘 56%；1 天后遗忘 66%；6 天后大约 75% 被遗忘。
This theorem can be summarised as: the rate of forgetting decreases over time. The steepest part of the curve is within the first hour of learning, which explains why last-minute cramming is so ineffective.
这个定理可以概括为：遗忘速率随着时间推移而降低。曲线最陡峭的部分落在学习后的第一个小时，这也解释了为什么临时抱佛脚如此低效。
For revision, the forgetting curve theorem teaches us that spaced practice and regular review produce stronger long-term retention, countering the rapid initial decay.
对于复习而言，遗忘曲线定理告诉我们，间隔练习和定期回顾能形成更牢固的长期记忆，从而对抗初期的快速遗忘。
6. Atkinson & Shiffrin Multi-Store Model | 阿特金森与谢弗林的多存储模型
The multi-store model proposes three separate memory stores, each with its own coding, capacity and duration. These can be thought of as fixed parameters – almost like constants in physics.
多存储模型提出了三个独立的记忆储存库，各自有不同的编码、容量和持续时间。这些可被视为固定参数——几乎就像物理学中的常数。
| Store | Coding | Capacity | Duration |
|---|---|---|---|
| Sensory Register | Sense-specific (iconic/echoic) | Very large | ½ second (iconic) 2-3 seconds (echoic) |
| Short-Term Memory (STM) | Mainly acoustic | 7±2 chunks | 18-30 seconds |
| Long-Term Memory (LTM) | Mainly semantic | Unlimited | Potentially forever |
感觉登记：编码为感觉形式（图像或声像），容量非常大，持续时间极短，图像记忆约 0.5 秒，声像记忆 2–3 秒。短时记忆：编码以听觉为主，容量 7±2 组块，持续时间 18–30 秒。长时记忆：编码以语义为主，容量无限，持续时间可能是永久。
To remember this store theorem, think 'CCD': Coding, Capacity, Duration. Every OCR question on the multi-store model asks you to identify or compare these three parameters.
要记住这个存储定理，可以想着 'CCD'：编码、容量、持续时间。OCR 关于多存储模型的每个问题都会要求你识别或比较这三个参数。
7. Weber's Law in Perception | 感知中的韦伯定律
Ernst Weber discovered that the smallest detectable change in a stimulus – the just noticeable difference (JND) – depends on the intensity of the original stimulus. This relationship is constant and can be written as a simple theorem.
恩斯特·韦伯发现，可觉察到的最小刺激变化——最小可觉差（JND）——依赖于原始刺激的强度。这种关系是恒定的，可写为一个简单定理。
ΔI / I = k
ΔI / I = k
Where ΔI is the change in intensity needed to notice a difference, I is the original intensity, and k is the Weber fraction, a constant unique to each sense.
其中 ΔI 是察觉差异所需的强度变化，I 是原始强度，k 是韦伯分数，是一个对每种感官都唯一的常数。
For lifted weights, k ≈ 0.02 (2% extra 2 g to notice it is heavier. For a 500 g weight, you would need an additional 10 g.
对于举重，k ≈ 0.02（2%）。这意味着如果你拿着 100 克的物体，需要增加 2 克才能觉察它变重了。对于 500 克的物体，则需要增加 10 克。
Weber's law helps explain why you can hear a whisper in a quiet room but need a much louder sound in a noisy classroom – the background intensity (I) is higher, so the JND is larger.
韦伯定律有助于解释为什么你在安静的房间能听见低语，而在嘈杂教室却需要大得多的声音——背景强度（I）更高，所以最小可觉差更大。
8. Piaget's Stage Theorem | 皮亚杰的阶段定理
Jean Piaget proposed that cognitive development occurs in four invariant stages through which all children pass in the same order. These stages act as a stair-step model of mental growth.
让·皮亚杰提出，认知发展经历四个不变的阶段，所有儿童都按照相同顺序通过这些阶段。这些阶段构成了心理成长的阶梯模型。
| Stage | Approx. Age | Key Milestone Theorem |
|---|---|---|
| Sensorimotor | 0-2 years | Object permanence (objects exist when out of sight) |
| Pre-operational | 2-7 years | Egocentrism, symbolic play, focused on one aspect at a time |
| Concrete operational | 7-11 years | Conservation, classification, logical thought about concrete events |
| Formal operational | 11+ years | Abstract reasoning, hypothetical thinking, systematic problem solving |
感觉运动阶段（0–2 岁）：客体永久性定理。前运算阶段（2–7 岁）：自我中心、符号游戏、一次只聚焦一个特征。具体运算阶段（7–11 岁）：守恒、分类、对具体事件进行逻辑思考。形式运算阶段（11 岁以上）：抽象推理、假设性思维、系统性地解决问题。
When applying Piaget's stage theorem, you can use these age bands to predict what type of thinking a child should be capable of, and to explain why certain tasks are too difficult at a particular age.
应用皮亚杰的阶段定理时，你可以用这些年龄区间来预测儿童应具备的思维类型，并解释为什么某些任务对特定年龄的儿童过难。
9. Classic Social Influence Findings | 经典社会影响研究的关键发现
Landmark experiments in social psychology have produced benchmark numbers that serve as 'social theorems' for explaining how people behave under situational pressure. These numerical results help you support arguments in exam essays.
社会心理学的标志性实验产生了一些基准数字，可作为解释人们在情境压力下如何行事的 '社会定理'。这些数字结果有助于你在考试论述中证明论点。
Asch's Conformity Line Experiment: on average, around 32% of response trials resulted in conformity to an obviously wrong group judgment. Furthermore, about 75% of participants conformed at least once during the procedure.
阿希从众线段实验：平均而言，约 32% 的反应试次出现了遵从明显错误群体判断的从众行为。此外，约 75% 的参与者在实验过程中至少从众过一次。
Milgram's Obedience Study: 65% of participants obeyed the experimenter up to
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