IGCSE Edexcel Psychology: Formula & Theorem Quick-Reference Handbook | IGCSE Edexcel 心理学：公式定理速查手册

📚 IGCSE Edexcel Psychology: Formula & Theorem Quick-Reference Handbook | IGCSE Edexcel 心理学：公式定理速查手册

In IGCSE Edexcel Psychology, many key theories and research findings can be expressed as equations, laws or quantitative relationships. This quick-reference handbook collects the essential formulas and theorems you need to recall for the exam, from memory capacity rules to social impact calculations. Each entry is presented with a clear statement, a formula where applicable, and the psychological meaning behind it, helping you use these tools in both short-answer and extended writing questions.

在 IGCSE Edexcel 心理学中，许多关键理论和研究发现都可以用方程、定律或定量关系来表达。这本速查手册汇集了你为考试需要记忆的核心公式和定理，从记忆容量规则到社会影响力计算。每个条目都配有清晰的陈述、适用的公式及其背后的心理学含义，帮助你在简答题和论述题中运用这些工具。

---

1. The Multi-Store Model Memory Capacity Theorem | 多存储模型记忆容量定理

Atkinson and Shiffrin (1968) proposed that memory consists of three separate stores: sensory memory, short-term memory (STM) and long-term memory (LTM). The capacity of each store can be summarised as a simple theorem. Sensory memory has a very large capacity but holds information for only a fraction of a second. STM has a limited capacity of 7 ± 2 items, often called ‘Miller’s magic number’, and without rehearsal, information decays rapidly. LTM is theoretically unlimited in both capacity and duration.

Atkinson 和 Shiffrin（1968）提出，记忆由三个独立的存储系统组成：感觉记忆、短时记忆和长时记忆。每个存储的容量可以概括为一个简单的定理。感觉记忆容量极大，但信息保持时间极短。短时记忆的容量有限，为 7 ± 2 个项目，常被称为“米勒的神奇数字”，如果不进行复述，信息会迅速消退。长时记忆在容量和持续时间上理论上都是无限的。

STM Capacity C = 7 ± 2 chunks

The theorem reminds us that chunking information can expand effective STM capacity, a principle applied in learning and revision strategies.

这一定理提醒我们，通过组块化可以扩大有效的短时记忆容量，这一原则已应用于学习和复习策略中。

---

2. Ebbinghaus Forgetting Curve Retention Formula | 艾宾浩斯遗忘曲线保留公式

Hermann Ebbinghaus (1885) studied his own memory for nonsense syllables and discovered that forgetting follows an exponential decay pattern. The proportion of information retained after a given time can be described by the retention formula R = e⁻ᵗ⁄ˢ, where R is retention, e is Euler’s number, t is time elapsed, and S is the relative stability of the memory trace. In words, memory retention drops sharply at first and then levels off. This curve supports the importance of spaced repetition to strengthen the trace, effectively increasing S.

赫尔曼·艾宾浩斯（1885）以无意义音节为材料研究自己的记忆，发现遗忘遵循指数衰减模式。经过特定时间后信息保持的比例可用保留公式 R = e⁻ᵗ⁄ˢ 来描述，其中 R 为保持量，e 为欧拉常数，t 为经过的时间，S 为记忆痕迹的相对稳定性。通俗地说，记忆保持量起初急剧下降，然后逐渐趋于平缓。这条曲线表明间隔重复对强化痕迹、即提升 S 值至关重要。

R = e⁻ᵗ⁄ˢ

In exam contexts, you can use this formula to explain why cramming leads to rapid forgetting, while distributed revision produces longer-lasting retention.

在考试背景下，你可以用这个公式解释为什么临时抱佛脚会导致快速遗忘，而分散复习能带来更持久的记忆保持。

---

3. The IQ Formula (Stanford-Binet) | 智商公式 (斯坦福-比奈量表)

Intelligence quotient (IQ) was originally conceptualised as a ratio of mental age (MA) to chronological age (CA), multiplied by 100 to eliminate decimals. Even though modern IQ tests use deviation IQ, the historical formula remains a core concept in the IGCSE Edexcel Psychology specification. It captures the idea that intellectual development can be compared across individuals of different ages.

智商（IQ）最初被定义为智力年龄（MA）与实足年龄（CA）的比值，再乘以 100 以消除小数。尽管现代智商测验采用离差智商，但这一历史公式仍然是 IGCSE Edexcel 心理学大纲中的核心概念。它反映了智商可以用于对不同年龄个体进行智力发展比较的思想。

IQ = (MA ÷ CA) × 100

For example, an eight-year-old child who performs at the level of an average ten-year-old would have an IQ of (10/8) × 100 = 125. The formula is a useful tool when discussing how early intelligence tests attempted to quantify mental ability.

例如，一个八岁儿童的智力表现达到普通十岁儿童的水平，其智商即为 (10/8) × 100 = 125。在讨论早期智力测验如何试图量化心智能力时，该公式是一个有用的工具。

---

4. Latané’s Social Impact Formula | 拉塔内社会影响公式

Latané (1981) proposed Social Impact Theory, claiming that the amount of social influence a person experiences is a multiplicative function of three forces: Strength (S) – the importance of the influencing group, Immediacy (I) – the closeness in time and space, and Number (N) – how many people are present. While the mathematical formula is represented as I = f(SIN), the theory clarifies that the impact of adding more people follows a decelerating power curve. The first few additions have a much greater effect than later ones.

拉塔内（1981）提出了社会影响理论，认为个体所受到的社会影响量是三种力量的乘积函数：强度（S）——施加影响群体的重要性，接近性（I）——在时间和空间上的邻近程度，数量（N）——在场的人数。虽然数学上表示为 I = f(SIN)，但该理论阐明，增加人数所带来的影响遵循一条减速的幂函数曲线，最初增加的人数比后期增加的人数影响大得多。

Social Impact I = f(S, I, N)

The multiplicative rule means that if any one factor is zero, the total impact is zero. This principle explains phenomena such as why a highly important but distant source can still exert considerable influence, and why the pressure to conform increases most sharply when the group size moves from one to three or four.

乘法规则意味着，如果任何一个因素为零，总影响力即为零。这一原理可以解释为何一个非常重要但距离较远的来源仍能产生相当大的影响，以及为何从众压力在群体人数从一增加到三或四人时上升得最为显著。

---

5. Size–Distance Invariance Hypothesis Equation | 大小-距离不变假设方程

The size–distance invariance hypothesis (also known as Emmert’s law in its afterimage form) states that perceived size (S) is jointly determined by the size of the retinal image (R) and the perceived distance (D) of the object. The equation S = R × D illustrates that the visual system takes distance information into account when computing object size, which underlies size constancy – our tendency to see objects as maintaining the same size even when retinal image size changes.

大小-距离不变假设（以其后像形式称为埃默特定律）指出，知觉大小（S）由视网膜成像大小（R）和物体的知觉距离（D）共同决定。公式 S = R × D 表明，视觉系统在计算物体大小时会利用距离信息，这正是大小恒常性的基础——尽管视网膜成像大小改变，我们仍然倾向于将物体知觉为保持同一尺寸。

Perceived Size S = R × D

In the IGCSE syllabus, this equation helps explain visual illusions such as the Ponzo illusion, where distance cues trick the brain into scaling up the perceived size of an object that appears farther away.

在 IGCSE 课程大纲中，这个方程有助于解释视错觉，比如庞佐错觉，其中距离线索让大脑误判，将看似更远的物体知觉为更大。

---

6. Yerkes–Dodson Law of Arousal and Performance | 耶克斯–多德森唤醒与绩效定律

The Yerkes–Dodson law (1908) posits an inverted-U relationship between arousal level and task performance: performance improves as arousal increases up to an optimal point, after which further arousal leads to a decline in performance. The law can be phrased as a qualitative theorem: Optimal performance occurs at moderate arousal, with the exact optimum shifting leftwards for complex tasks and rightwards for simple tasks.

耶克斯-多德森定律（1908）假设唤醒水平与任务绩效之间存在倒 U 型关系：绩效随唤醒水平提高而上升，直至达到最佳点，之后唤醒继续增强则导致绩效下降。该定律可表述为一个定性定理：最佳绩效出现在中等唤醒水平，且复杂任务的最佳点向左偏移，简单任务的最佳点向右偏移。

Performance ∝ Arousal (Inverted-U function)

For a complex cognitive task like solving an unfamiliar exam problem, a lower level of arousal is ideal; for a simple, well-rehearsed task like running a race, higher arousal yields better results. This theorem is used to evaluate the effectiveness of stress management and revision environments.

对于解答陌生考题这样的复杂认知任务，较低的唤醒水平最为理想；对于赛跑这类简单且熟练的任务，较高的唤醒水平效果更好。这一理论可用于评估压力管理和复习环境的有效性。

---

7. Weber’s Law of Just Noticeable Difference | 韦伯最小可觉差定律

Weber’s law states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus. This relationship is expressed as ΔI / I = k, where ΔI is the smallest detectable change in intensity, I is the initial stimulus intensity, and k is the Weber fraction, which is constant for a given sensory modality. For example, in judging weight, k is approximately 0.02–0.03; you would notice a 2–3 g difference on a 100 g weight, but to notice a change on a 1 kg weight, you would need about 20–30 g.

韦伯定律指出，两个刺激之间的最小可觉差（JND）与初始刺激的大小成正比。这一关系表述为 ΔI / I = k，其中 ΔI 为可察觉的最小强度变化，I 为初始刺激强度，k 为韦伯分数，对特定感觉通道为常数。例如，在重量判断中，k 约等于 0.02–0.03；你在一个 100 克的重量上能觉察到 2–3 克的变化，但在 1 千克的重量上则需要大约 20–30 克的变化才能觉察。

ΔI / I = k

Though not a core standalone topic in IGCSE, Weber’s law is referenced in discussions of sensory thresholds and perception experiments. It demonstrates that the perceptual system works on relative rather than absolute changes, explaining why we struggle to detect a small weight difference in a heavy suitcase.

尽管不是 IGCSE 中的独立核心主题，但韦伯定律在感觉阈限和知觉实验的讨论中会被提及。它表明知觉系统依据相对变化而非绝对变化运作，这可以解释为什么我们难以察觉一个沉重行李箱中微小的重量差异。

---

8. Correlation Coefficient r Quick Reference | 相关系数 r 速查

In the Research Methods section of IGCSE Edexcel Psychology, the correlation coefficient r is a statistical measure of the strength and direction of a linear relationship between two co-variables. The formula for r is derived from the sum of the cross-products of deviation scores, divided by the product of the standard deviations and (n-1). Although the specification does not require you to compute r by hand, you should understand its meaning and the range from –1 to +1.

在 IGCSE Edexcel 心理学的研究方法部分，相关系数 r 是衡量两个协变量之间线性关系强度和方向的统计指标。r 的公式来源于偏差分数乘积之和，除以标准差乘积和 (n–1) 的乘积。虽然大纲不要求手算 r，但你需要理解其含义以及 –1 到 +1 的取值范围。

r = [ Σ (xᵢ – x̄) (yᵢ – ȳ) ] / [ (n–1) sₓ sᵧ ]

A coefficient of +1 indicates a perfect positive correlation, –1 a perfect negative correlation, and 0 no linear correlation. You can use this knowledge to evaluate the conclusions of correlational studies, always remembering that correlation does not imply causation.

系数 +1 表示完全正相关，–1 表示完全负相关，0 表示无线性相关。你可以运用这一知识来评价相关研究的结论，并时刻牢记相关关系并不意味因果关系。

---

9. Percentage Change Formula in Research | 研究中的百分比变化公式

When comparing before-and-after measurements in experimental and observational studies, students of IGCSE Psychology often need to compute and interpret percentage change. The percentage change formula expresses the relative increase or decrease from an original value to a new value, making it easier to judge the meaningfulness of a difference.

在进行实验或观察研究的前后测量对比时，IGCSE 心理学学生常常需要计算和解释百分比变化。百分比变化公式表达了从原始值到新值的相对增减，以便判断差异的实际意义。

% Change = (New Value – Old Value) ÷ Old Value × 100

For instance, if the mean score of an experimental group increased from 40 to 54, the percentage change is (54–40)/40 × 100 = 35%. A positive value indicates an increase; a negative value indicates a decrease. This formula is a staple in evaluation of results and in describing the effectiveness of an intervention.

例如，若实验组的平均分从 40 分上升到 54 分，百分比变化为 (54–40)/40 × 100 = 35%。正值表示增加，负值表示减少。这个公式是评估实验结果以及描述干预效果时的常用工具。

---

10. Measures of Central Tendency Quick Reference | 集中趋势测量速查

Central tendency gives a single value that represents the centre of a data set. The three main measures are mean, median and mode, each with its own situational advantages. The mean is calculated by summing all values and dividing by the number of values; the median is the middle value when data are ordered; the mode is the most frequently occurring value. Expressed as operational theorems, they help you decide which measure to use when analysing IGCSE research data.

集中趋势可以给出一个代表数据集中心的单一数值。三种主要的集中趋势量数是平均数、中位数和众数，每种都有其适用的情境。平均数的计算是将所有数值相加再除以数值的个数；中位数是数据排序后居中的数值；众数是出现频率最高的数值。将它们表述为操作性定理，有助于你在分析 IGCSE 研究数据时决定选用哪种量数。

Mean = (Σx) ÷ n   |   Median = middle ordered value   |   Mode = most frequent

The mean is sensitive to outliers, so in skewed distributions the median often gives a better picture of the typical score. The mode is the only measure suitable for nominal data. Memorising these rules will strengthen your evaluation of descriptive statistics in the IGCSE exam.

平均数对极端值敏感，因此在偏态分布中中位数往往能更准确地反映典型分数。众数是唯一适用于称名数据集中趋势的量数。记住这些规则将加强你在 IGCSE 考试中对描述性统计的评鉴。

---

Published by TutorHao | Psychology Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）