📚 Year 8 Edexcel Psychology: Quick Reference Handbook of Formulas & Theorems | Year 8 Edexcel 心理学：公式定理速查手册
This handbook brings together the essential models, laws, and core principles from the Year 8 Edexcel Psychology curriculum, transforming key concepts into formula-like summaries. Use it as a quick reference to reinforce your understanding of memory, perception, learning, social influence, and cognitive development. Each entry captures the fundamental relationship or theorem at the heart of the topic, helping you to recall and apply psychological knowledge with confidence.
本手册汇集了 Year 8 Edexcel 心理学课程中的核心模型、定律与基本原理，将关键概念提炼为类似于公式的速查形式。你可以把它当作快速参考，用于巩固对记忆、知觉、学习、社会影响和认知发展等主题的理解。每个条目都抓住了该主题背后的基本关系或定理，帮助你自信地回忆和应用心理学知识。
1. The Multi-Store Model of Memory | 记忆的多储存模型
The multi-store model (Atkinson & Shiffrin, 1968) describes memory as a flow of information through three stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Attention filters input into STM, and maintenance rehearsal transfers information into LTM. The key formula is that LTM encoding strength is a function of rehearsal depth.
多储存模型（Atkinson & Shiffrin, 1968）将记忆描述为信息流经三个储存库：感觉记忆、短时记忆（STM）和长时记忆（LTM）。注意力将输入过滤进短时记忆，而保持性复述将信息转入长时记忆。核心公式是长时记忆的编码强度是复述深度的函数。
Encoding → STM (Capacity: 7 ± 2 chunks, Duration: 18–30 s) → Rehearsal → LTM
r Sensory memory holds an exact copy for less than a second; STM can hold approximately 7 ± 2 chunks of information for around 18–30 seconds without rehearsal; LTM has potentially unlimited capacity and duration.
感觉记忆在不到一秒内保持精确副本；没有复述的情况下，短时记忆可容纳约 7 ± 2 个组块并持续 18–30 秒；长时记忆的容量和持续时间理论上没有限制。
2. Ebbinghaus' Forgetting Curve | 艾宾浩斯遗忘曲线
Hermann Ebbinghaus discovered that memory fades rapidly at first and then levels off. His forgetting curve can be approximated by an exponential decay function, showing that the proportion of retained material drops steeply within the first hour unless information is rehearsed.
赫尔曼·艾宾浩斯发现记忆会先快速消退，然后趋于平缓。他的遗忘曲线可以用指数衰减函数来近似，显示出除非进行复述，否则所学材料的保留比例在第一个小时内急剧下降。
Retention (%) ≈ 100 × e-t/τ
Where t is time since learning and τ is the time constant (roughly 20–30 minutes for nonsense syllables). After 20 minutes, retention is about 58%; after one hour, about 44%.
其中 t 为学习后经过的时间，τ 为时间常数（对无意义音节而言约 20–30 分钟）。20 分钟后记忆保留率约为 58%，一小时后约为 44%。
3. Weber's Law | 韦伯定律
Weber's Law states that the just noticeable difference (JND) between two stimuli is a constant proportion of the original stimulus intensity. This law applies to various senses and helps explain how we perceive changes in brightness, weight, sound, and taste.
韦伯定律指出，两个刺激之间的最小可觉差（JND）与原始刺激强度成固定比例。这一定律适用于多种感觉，有助于解释我们如何感知亮度、重量、声音和味道的变化。
ΔI / I = k
The table below lists Weber fractions (k) for different senses.
下表列出了不同感觉的韦伯分数（k）。
| Sense | 感觉 | Weber fraction (k) | 韦伯分数 |
|---|---|
| Brightness (视觉亮度) | ~0.08 |
| Weight (重量) | ~0.02 |
| Pitch (音高, 1000 Hz) | ~0.003 |
| Salt taste (咸味) | ~0.20 |
A lower k means greater sensitivity; for example, we are more sensitive to changes in pitch than to changes in saltiness.
k 值越小，表示灵敏度越高；例如，我们对音高变化的敏感度高于对咸味变化的敏感度。
4. Operant Conditioning: Law of Effect | 操作条件作用：效果律
Thorndike's Law of Effect states that behaviours followed by satisfying consequences are more likely to be repeated, while those followed by discomfort are less likely. Skinner developed this into a formula of reinforcement and punishment.
桑代克的效果律指出，带来满意后果的行为更有可能被重复，而带来不适后果的行为则较不易重复。斯金纳将此发展为强化与惩罚的公式。
Behaviour frequency ∝ (Reinforcement – Punishment)
Positive reinforcement adds a pleasant stimulus to increase behaviour; negative reinforcement removes an unpleasant stimulus to increase behaviour. Positive punishment adds an unpleasant stimulus to decrease behaviour; negative punishment removes a pleasant stimulus to decrease behaviour.
正强化通过增加愉悦刺激来提高行为频率；负强化通过移除厌恶刺激来提高行为频率。正惩罚通过增加厌恶刺激来降低行为频率；负惩罚通过移除愉悦刺激来降低行为频率。
5. Asch's Conformity Formula | 阿希从众公式
Solomon Asch's experiments showed that the pressure to conform increases with group size (up to about 4–5 people), is stronger when the group is unanimous, and weaker when the task is easy or there is a dissenter.
所罗门·阿希的实验表明，从众压力随着群体人数增加（约至 4–5 人）而增大；群体意见一致时压力更强；当任务简单或有异议者时，压力减弱。
Conformity = f(Group Size, Unanimity, Task Difficulty)
In an unambiguous line-judgement task, about 75% of participants conformed at least once. The conformity rate drastically reduces with just one ally.
在明确的线段判断任务中，约 75% 的参与者至少从众一次。只要有一个盟友，从众率就显著降低。
6. Piaget's Conservation Law | 皮亚杰守恒定律
Piaget's conservation tasks test whether a child understands that quantity remains the same despite changes in appearance. The formula represents the logical rule that the amount is invariant under perceptual transformation.
皮亚杰的守恒任务测试儿童是否理解外观变化时数量保持不变。该公式表示数量在知觉转换下不变的逻辑规则。
QuantityA = QuantityB before and after transformation
Concrete operational stage (7–11 years) children grasp conservation of number, mass, and liquid volume, realising that changes in shape do not alter the underlying quantity.
具体运算阶段（7–11 岁）的儿童掌握数量、质量和液体容积的守恒，认识到形状的改变不会改变潜在的数量。
7. Signal Detection Theory (Simplified) | 信号检测论（简化）
Signal detection theory distinguishes between sensitivity to a stimulus and response bias. It measures the ability to detect a weak signal against background noise. A basic sensitivity index can be written as the difference between hit rate and false alarm rate.
信号检测论区分了对刺激的敏感性和反应偏向，衡量在背景噪音中检测微弱信号的能力。一个基本的敏感度指标可以用击中率减去虚报率来表示。
d' ≈ Z(Hit Rate) – Z(False Alarm Rate)
For a simplified qualitative view: Sensitivity = Hit Rate – False Alarm Rate. A higher value means better ability to tell signal from noise.
简化的定性视角为：敏感度 = 击中率 – 虚报率。数值越高，区分信号与噪音的能力越强。
8. Serial Position Effect (Primacy and Recency) | 序列位置效应（首因与近因）
When recalling a list of items, people tend to remember the first items (primacy effect) and the last items (recency effect) best, while middle items are often forgotten. This creates a U-shaped serial position curve.
在回忆一系列项目时，人们往往对开头的项目（首因效应）和结尾的项目（近因效应）记忆最佳，而中间的项目则容易遗忘。这形成了 U 形的序列位置曲线。
P(Recall) = f(Primacy from LTM, Recency from STM)
The primacy effect is attributed to more rehearsal and transfer to LTM, while the recency effect reflects items still available in STM at the time of immediate recall.
首因效应归因于更多的复述以及向长时记忆的转移；近因效应反映了在立即回忆时，短时记忆中仍然可用的项目。
9. Classical Conditioning: Association Formula | 经典条件作用：联结公式
Classical conditioning (Pavlov) involves forming an association between a neutral stimulus and an unconditioned stimulus so that the neutral stimulus alone eventually elicits a conditioned response. The strength of conditioning depends on the number and timing of pairings.
经典条件作用（巴甫洛夫）涉及中性刺激与无条件刺激之间形成联结，使得中性刺激最终单独引发条件反应。条件作用的强度取决于配对次数与时机。
CR = f(CS–US pairings, Contiguity, Contingency)
Generalisation occurs when stimuli similar to the conditioned stimulus (CS) also produce the conditioned response (CR); discrimination occurs when the organism learns to respond only to the specific CS.
当与条件刺激（CS）相似的刺激也能引发条件反应（CR）时，就发生了泛化；当有机体学会只对特定的条件刺激作出反应时，便发生了分化。
10. Bandura's Social Learning Formula | 班杜拉社会学习公式
Bandura's social learning theory states that people learn by observing models. The likelihood of imitating a behaviour depends on four mediational processes: attention, retention, reproduction, and motivation. Learning can occur without a change in behaviour unless all four factors are present.
班杜拉的社会学习理论指出，人们通过观察榜样来学习。模仿行为的可能性取决于四个中介过程：注意、保持、再现和动机。除非这四个因素全部具备，否则学习可能并不伴随行为改变。
Imitation = Attention × Retention × Reproduction × Motivation
Vicarious reinforcement – seeing the model rewarded – increases motivation, while vicarious punishment decreases it.
替代强化——看到榜样受到奖励——会提高动机，而替代惩罚则会降低动机。
11. Müller-Lyer Illusion: Perceptual Length Formula | 缪勒-莱耶错觉：知觉长度公式
The Müller-Lyer illusion causes two lines of equal physical length to appear unequal because of the orientation of arrowheads at their ends. This misperception can be expressed as a function of the angle and length of the fins.
缪勒-莱耶错觉使得两条物理长度相等的线段因为两端箭头方向不同而显得不等长。这种错觉可表达为线段末端翼角与翼长的函数。
Perceived Length = Physical Length ± δ (fin orientation, fin length)
Inward-pointing fins (→←) make the line appear shorter, while outward-pointing fins (←→) make it appear longer, likely due to size-constancy scaling and depth cues.
箭头向内（→←）使线条显得更短，箭头向外（←→）使线条显得更长，这可能是由于大小恒常性定标与深度线索引起的。
12. Brain Localisation of Function | 大脑功能定位原理
Different regions of the cerebral cortex are specialised for different functions. The two most well-known language areas are Broca's area (speech production) and Wernicke's area (language comprehension). The general formula is that specific mental processes are mapped to specific cortical zones.
大脑皮层的不同区域各司其职。两个最著名的语言区是布罗卡区（言语产生）和韦尼克区（语言理解）。基本原理是特定的心理过程映射到特定的皮层区域。
Function (e.g., language) → Localised cortical area (e.g., Broca's, Wernicke's)
Damage to Broca's area typically results in non-fluent aphasia with preserved comprehension, whereas damage to Wernicke's area leads to fluent but meaningless speech and poor comprehension.
布罗卡区受损通常导致非流畅性失语症但理解力保留，而韦尼克区受损则导致流畅但毫无意义的言语以及糟糕的理解能力。
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