📚 OCR GCSE Psychology Formula and Theorem Quick Reference | OCR GCSE 心理学公式定理速查手册
Welcome to your quick reference guide for the key formulas, numerical benchmarks, and psychological theorems you need to ace the OCR GCSE Psychology exam. Whether you are calculating central tendency for research methods or recalling Miller’s magic number for memory, this handbook distils essential quantitative and qualitative principles into easy-to-revise bilingual notes.
欢迎使用这本速查手册，它涵盖了你在 OCR 普通中等教育证书心理学考试中需要掌握的关键公式、数字基准和心理学定理。无论你是在为研究方法计算集中趋势，还是在回忆米勒有关记忆的神奇数字，本手册都将关键的定量与定性原则提炼成易于复习的双语笔记。
1. Miller’s Magic Number (7±2) | 米勒的魔法数字 (7±2)
the capacity of short-term memory (STM) is approximately 7 ± 2 items. This is often called "Miller’s Law" ychology. Chunking can expand this capacity by grouping information into meaningful units.
乔治·米勒（1956年）提出，短时记忆的容量大约是7±2个项目。这常被称为“米勒定律”，是认知心理学中一条重要的数字定理。通过将信息组合成有意义的组块（组块化），可以扩大这个容量。
Formula expression: STM Capacity = 7 ± 2 chunks
公式表达：短时记忆容量 = 7 ± 2 个组块
You must remember this when evaluating studies about memory span, such as Jacob's digit span test (which found an average of 9.3 items for digits and 7.3 for letters).
在评估关于记忆广度的研究（例如雅各布斯的数字广度实验，数字平均9.3项，字母平均7.3项）时，你必须记住这一点。
2. Multi-Store Model Encoding Duration | 多贮存模型编码持续时间
The Multi-Store Model (Atkinson & Shiffrin, 1968) contains specific numerical values for duration: sensory register lasts less than half a second for visual info (iconic store), STM lasts about 18–30 seconds without rehearsal, and long-term memory (LTM) may last a lifetime. These figures function as theoretical benchmarks.
多贮存模型（阿特金森和谢夫林，1968年）包含关于持续时间的具体数值：感觉登记中的视觉信息（图像记忆）持续不到半秒；短时记忆在没有复述的情况下持续约18-30秒；长时记忆可能持续一生。这些数值充当了理论上的基准。
Sensory Store Duration ≤ 0.5 s | STM Duration ≈ 18–30 s | LTM Duration → Unlimited
感觉贮存时间 ≤ 0.5 秒 | 短时记忆时间 ≈ 18–30 秒 | 长时记忆时间 → 无限
3. Ebbinghaus’s Forgetting Curve and Savings Formula | 艾宾浩斯遗忘曲线与节省公式
Hermann Ebbinghaus (1885) quantified memory decay using nonsense syllables. The savings score measures how much faster information is relearned compared to initial learning. The formula is:
赫尔曼·艾宾浩斯（1885年）利用无意义音节量化了记忆的衰减。“节省分数”用来衡量重新学习信息时比初学快了多少。其公式为：
Savings (%) = [(Original Time − Relearning Time) / Original Time] × 100
节省分数 (%) = [(初始学习时间 − 重新学习时间) / 初始学习时间] × 100
The forgetting curve shows rapid forgetting within the first hour and a levelling off after about one day — a key theorem for revision planning.
遗忘曲线显示，在最初的第一个小时内遗忘得非常快，大约一天后趋于平缓——这对制定复习计划来说是一条关键定理。
4. Asch’s Conformity: Baseline Percentage | 阿希从众实验：基线百分比
Solomon Asch (1951) found that about 37% of participants conformed on critical trials (line judgement) when confederates gave wrong answers, while 25% never conformed. These percentages are fundamental quantitative benchmarks in social influence.
所罗门·阿希（1951年）发现，当假被试在关键试验中给出错误答案时，大约37%的参与者发生了从众，而25%的参与者从未从众。这些百分比是社会影响领域的基本定量基准。
Average conformity rate = 37% | Zero conformity = 25%
平均从众率 = 37% | 零从众 = 25%
Unanimity, group size (3+), and task difficulty modify this rate — acting as moderating variables in the conformity formula.
一致性、群体规模（3人及以上）和任务难度会改变这一比率——它们在从众公式中充当了调节变量。
5. Milgram’s Obedience: Voltage and Percentage Theorem | 米尔格拉姆服从实验：电压与百分比定理
Stanley Milgram (1963) reported that 65% of participants administered the maximum 450-volt shock, and 100% reached 300 volts. These numbers are essential when describing destructive obedience.
斯坦利·米尔格拉姆（1963年）报告称，65%的参与者施加了最高450伏的电击，100%的参与者达到了300伏。这些数字是描述破坏性服从的关键内容。
Full Obedience to 450V = 65% | All reached 300V = 100%
完全服从至450伏 = 65% | 所有人都达到了300伏 = 100%
Proximity, location, and uniform act as situational theorems that lower or raise the obedience rate.
近距离、地点和制服作为情境定理，会降低或提高服从率。
6. Piaget’s Cognitive Development Stages and Age Formulas | 皮亚杰认知发展阶段与年龄公式
Jean Piaget’s stage theorem posits four invariant stages with fixed age ranges. Quick formula: Sensorimotor (0–2 years), Pre-operational (2–7 years), Concrete operational (7–11 years), Formal operational (11+ years). These age thresholds are often tested in OCR 13-mark essays.
让·皮亚杰的阶段定理提出了四个不变的发展阶段及其固定年龄段。速记公式：感知运动阶段（0-2岁）、前运算阶段（2-7岁）、具体运算阶段（7-11岁）、形式运算阶段（11岁以上）。这些年龄界限在OCR的13分论文题中经常被考查。
| Stage / 阶段 | Age Range / 年龄范围 | Key Milestone / 关键里程碑 |
|---|---|---|
| Sensorimotor / 感知运动 | 0–2 years / 岁 | Object permanence / 客体永久性 |
| Pre-operational / 前运算 | 2–7 years / 岁 | Egocentrism, conservation failure / 自我中心，不能守恒 |
| Concrete operational / 具体运算 | 7–11 years / 岁 | Conservation, class inclusion / 守恒，类包含 |
| Formal operational / 形式运算 | 11+ years / 岁 | Abstract reasoning, hypothetical thinking / 抽象推理，假设性思维 |
7. Mean, Median, Mode, and Range: Research Methods Formulas | 平均数、中位数、众数和极差：研究方法公式
In OCR GCSE research methods, you must calculate the mean, median, mode, and range for a data set. These are your core statistical formulas.
在OCR普通中等教育证书心理学的研究方法中，你必须计算一组数据的平均数、中位数、众数和极差。这些是你核心的统计公式。
- Mean (x̄): Sum of all scores ÷ number of scores. 平均数 (x̄)： 所有分数之和 ÷ 分数的个数。
- Median: Middle value when data are ordered. 中位数： 将数据排序后位于中间的值。
- Mode: Most frequently occurring value. 众数： 出现次数最多的值。
- Range: Highest value − Lowest value. 极差： 最大值 − 最小值。
For data set [5, 7, 7, 8, 12], Mean = 39÷5 = 7.8; Median = 7; Mode = 7; Range = 12−5 = 7.
示例：对于数据集 [5, 7, 7, 8, 12]，平均数 = 39÷5 = 7.8；中位数 = 7；众数 = 7；极差 = 12−5 = 7。
8. Percentage Change Formula for Psychological Studies | 心理学研究中的百分比变化公式
Many psychological investigations require you to compute the percentage change in a variable (e.g. recall scores before and after an intervention). The formula is:
许多心理学调查要求你计算某个变量的百分比变化（例如干预前后的回忆分数）。公式为：
Percentage Change = [(New Value − Old Value) / Old Value] × 100
百分比变化 = [(新值 − 旧值) / 旧值] × 100
If the result is negative, it indicates a decrease. A positive percentage signals an increase. This is a vital component of the AO2 calculation questions.
如果结果为负，则表明下降。正百分比则表示上升。这是AO2计算题的重要组成部分。
9. Standard Deviation (Conceptual Formula) for Compulsory Understanding | 标准差（概念公式）必修理解
Although OCR GCSE does not require you to perform full standard deviation calculations from raw data in the exam, you are expected to understand that a larger SD means greater variation in a data set. The formula is introduced here for reference:
尽管OCR普通中等教育证书考试并不要求你根据原始数据进行完整的标准差计算，但你需要理解较大的标准差意味着数据集的变异更大。此处引入公式以供参考：
Standard Deviation σ = √[ Σ(x − μ)² / N ]
标准差 σ = √[ Σ(x − μ)² / N ]
e mean, x is each score, and N is the number of scores. In a normal distribution, about 68% of values fall within ±1 SD from the mean.
其中 μ 代表平均数，x 代表每一个分数，N 代表分数的个数。在正态分布中，大约68%的数据落在平均数的 ±1 个标准差之内。
10. The Ratio Formula for Social Impact Theory | 社会影响理论的比率公式
Bibb Latané s (N): Impact = f(S × I × N). This is a mathematical theorem for conformity and obedience.
比布·拉塔内的社会影响理论（1981年）指出，社会影响是影响源强度(S)、直接性(I)和数量(N)的乘积函数：影响 = f(S × I × N)。这是关于从众与服从的一条数学定理。
al Impact = S × I × N; diffusion of responsibility reduces impact per person in a group (Ī = 1/√N for Psychosocial Law).
在OCR的论文中，要记住公式：社会影响 = S × I × N；责任分散会减少团体中每个人受到的影响（心理社会定律中 Ī = 1/√N）。
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