📚 Year 8 AQA Psychology: Formula and Theorem Quick Reference Handbook | AQA 八年级心理学：公式定理速查手册
This handbook brings together the key formulas, laws and theoretical models that appear in the Year 8 AQA Psychology course. Whether you are calculating memory span, plotting a forgetting curve, or understanding the Yerkes-Dodson law of arousal and performance, having these concepts at your fingertips will strengthen your written answers and help you interpret data in research methods questions. Each entry is presented with a concise explanation and a ready-to-use formula or rule statement so you can revise efficiently.
本手册汇集了 AQA 八年级心理学课程中出现的核心公式、定律和理论模型。无论是计算记忆广度、绘制遗忘曲线，还是理解耶克斯–多德森的唤醒与表现定律，熟记这些概念都能帮助你写出更完整的答案，更好地分析研究方法题目中的数据。每个条目都配有简明扼要的解释和可以直接使用的公式或规则表述，让你的复习更加高效。
1. Miller's Law – Capacity of Short-Term Memory | 米勒定律 – 短时记忆的容量
George Miller (1956) proposed that the average number of items a person can hold in short‑term memory (STM) is 7, plus or minus 2. The items can be individual digits, letters, or words, but the capacity can be increased if we group small pieces into larger chunks. This 'magic number' explains why telephone numbers are often broken into smaller groups – each group becomes one chunk.
乔治·米勒（1956）提出，一个人短时记忆中平均能保持的项目数量是 7 加减 2。这些项目可以是单个数字、字母或单词，但如果我们将小信息组合成较大的组块，容量就可以增加。这个“神奇数字”解释了为什么电话号码经常被分成几个小组——每个小组成为一个组块。
STM capacity ≈ 7 ± 2 chunks
短时记忆容量 ≈ 7 ± 2 个组块
When you see a question about digit‑span tests or the number of words recalled immediately after a list is presented, think of Miller's Law and the idea of chunking. Remember that the range can be slightly lower in younger children and that rehearsal keeps information in STM for a few seconds.
当你遇到关于数字广度测试或呈现列表后立即回忆单词数量的问题时，就要想到米勒定律和组块的概念。要记得，在年幼儿童中，容量范围可能略低一些，而复述能让信息在短时记忆中保持几秒钟。
2. The Multi‑Store Model of Memory (Atkinson & Shiffrin, 1968) | 记忆的多重存储模型（阿特金森和谢夫林，1968）
The multi‑ es memory as a flow of information through three separate stores: sensory register → short‑term memory → long‑ a series of processes rather than a mathematical formula, but it helps to think of it as a 'memory equation' of encoding, storage and retrieval.
多重存储模型把记忆描述为信息流经三个独立存储库的过程：感觉登记 → 短时记忆 → 长时记忆。如果我们对信息加以注意并进行复述，信息就会从一个存储库转移到下一个。这个模型可以概括为一系列加工过程，而不是数学公式，但我们可以把它看作由编码、存储和提取组成的“记忆方程”。
Attention → STM Rehearsal loop ↔ LTM
注意 → 短时记忆 复述回路 ↔ 长时记忆
When you are asked to label a diagram of the three stores or to explain why rehearsal matters, use this simplified 'formula' to structure your answer. It also helps you understand the serial position effect: items at the beginning of a list (rehearsed into LTM) become the primacy effect, and items at the end (still in STM) become the recency effect.
如果题目要求你给三个存储库的示意图添加标签，或者解释为什么复述很重要，就可以用这个简化的“公式”来组织答案。这也有助于理解系列位置效应：列表开头的项目（经复述进入长时记忆）形成首因效应，末尾的项目（仍留在短时记忆中）形成近因效应。
3. The Primacy and Recency Effects – Serial Position Curve | 首因效应与近因效应 – 系列位置曲线
When people are given a long list of words to remember and then asked to recall them in any order (free recall), they tend to remember the first few and the last few words best. The U‑shaped serial position curve is the visual 'formula' that shows recall probability as a function of an item's position in the list.
当人们拿到一长串需要记忆的单词，然后以任意顺序进行自由回忆时，他们往往对开头几个和末尾几个单词的记忆效果最好。呈 U 形的系列位置曲线就是一种可视化的“公式”，它表现了回忆概率随项目在列表中位置变化而变化的规律。
Recall probability = f(list position) with peaks at the beginning and end
回忆概率 = f(列表位置) 在开头和末尾处出现峰值
The primacy effect occurs because the first items have been rehearsed and transferred into LTM. The recency effect occurs because the last items are still available in STM. If you insert a distractor task before recall, the recency effect disappears but the primacy effect remains – a powerful demonstration of the separate stores.
首因效应的产生是因为开头的项目经过复述已经转入长时记忆。近因效应的产生则是因为末尾的项目仍然留在短时记忆中。如果在回忆前插入一项干扰任务，近因效应就会消失，而首因效应依然存在——这有力地证明了两个存储库是彼此独立的。
4. Ebbinghaus Forgetting Curve – Rate of Forgetting | 艾宾浩斯遗忘曲线 – 遗忘的速率
Hermann Ebbinghaus (1885) studied his own memory for nonsense syllables and discovered that forgetting happens very rapidly at first and then levels off. The forgetting curve can be described by a power‑law or exponential decay, but for Year 8 psychology you can use a simple percentage description: roughly 50% of newly learned information is forgotten within the first hour unless it is rehearsed.
赫尔曼·艾宾浩斯（1885）以自己为被试，研究对无意义音节的记忆，发现遗忘一开始非常迅速，随后逐渐趋于平缓。遗忘曲线可以用幂律或指数衰减来描述，但对八年级心理学来说，你只需要掌握一个简单的百分比描述：大约 50% 的新学信息在第一个小时内就会被遗忘，除非进行了复述。
Retention (%) ≈ initially steep decay, then gradual plateau
保持量(%) ≈ 起初急剧下降，然后逐渐趋于平稳
Ebbinghaus's work highlights the importance of regular review and rehearsal. When you draw the curve on an exam paper, label the axes: 'Time since learning' on the x‑axis and 'Percentage recalled' on the y‑axis, then show the sharp drop followed by the flattening out.
艾宾浩斯的研究凸显了定期复习和复述的重要性。在试卷上绘制曲线时，要标注坐标轴：x 轴为“学习后的时间”，y 轴为“回忆百分比”，然后画出先急剧下降、再逐渐趋平的形状。
5. Classical Conditioning Formula – Pavlov's Dogs | 经典条件作用公式 – 巴甫洛夫的狗
Ivan Pavlov's experiments showed how a neutral stimulus can come to trigger a natural reflex through association. The entire process can be written as a series of paired associations, almost like a chemical equation. Mastering this 'formula' will help you identify the unconditioned stimulus (UCS), unconditioned response (UCR), neutral stimulus (NS), conditioned stimulus (CS) and conditioned response (CR) in any example.
伊万·巴甫洛夫的实验表明，一个中性刺激可以通过联结引发一种天然反射。整个过程可以用一系列配对联结来表示，就像化学方程式一样。掌握这个“公式”后，你就能在任何例子中准确找出无条件刺激（UCS）、无条件反应（UCR）、中性刺激（NS）、条件刺激（CS）和条件反应（CR）。
Before conditioning: UCS (food) → UCR (salivation)
During conditioning: NS (bell) + UCS (food) → UCR (salivation)
After conditioning: CS (bell) → CR (salivation)
条件作用前： UCS（食物）→ UCR（唾液分泌）
条件作用中： NS（铃声）+ UCS（食物）→ UCR（唾液分泌）
条件作用后： CS（铃声）→ CR（唾液分泌）
Remember that timing and repetition matter: the NS must be presented just before the UCS, and repeated pairings are needed to establish the conditioned link. Extinction occurs when the CS is repeatedly presented without the UCS, and spontaneous recovery shows that the link is not completely erased.
要记住，时间间隔和重复次数至关重要：NS 必须在 UCS 之前刚刚呈现，并且需要多次配对才能建立起条件联结。消退发生在 CS 反复单独呈现而不伴随 UCS 之时，而自发恢复则表明这种联结并没有被完全消除。
6. Operant Conditioning – Thorndike's Law of Effect & Skinner's Reinforcement | 操作性条件作用 – 桑代克效果律与斯金纳强化
Edward Thorndike proposed the Law of Effect: behaviours followed by pleasant consequences are more likely to be repeated, while behaviours followed by unpleasant consequences are less likely. B.F. Skinner later developed this into operant conditioning, using the concepts of positive reinforcement, negative reinforcement and punishment. These can be recorded in a simple table of consequences that function like a decision‑making formula for behaviour.
爱德华·桑代克提出了效果律：伴随着愉快结果的行为更有可能被重复，而伴随着不愉快结果的行为则不太可能被重复。B.F. 斯金纳后来将其发展为操作性条件作用，引入了正强化、负强化和惩罚等概念。这些概念可以汇总成一张简单的后果表，就像是行为的决策公式。
| Consequence / 后果 | Effect on behaviour / 对行为的影响 |
|---|---|
| Positive reinforcement (add pleasant stimulus) / 正强化（增加愉快刺激） | Behaviour increases / 行为增加 |
| Negative reinforcement (remove unpleasant stimulus) / 负强化（移除不愉快刺激） | Behaviour increases / 行为增加 |
| Punishment (add unpleasant stimulus or remove pleasant one) / 惩罚（增加不愉快刺激或移除愉快刺激） | Behaviour decreases / 行为减少 |
In an exam, always check whether a scenario involves adding or removing a stimulus, and whether the desired behaviour becomes more or less frequent. This logical approach turns Thorndike's Law of Effect into a practical formula for analysing real‑world situations like training a pet or using a reward chart.
在考试中，务必先判断某个情境涉及的是增加还是移除刺激，以及目标行为的频率是增加还是减少。这种逻辑思路将桑代克的效果律转变成一个分析现实情境（如训练宠物或使用奖励表）的实用公式。
7. The Yerkes-Dodson Law – Arousal and Performance | 耶克斯–多德森定律 – 唤醒与表现
The Yerkes-Dodson Law states that performance on a task improves with increased arousal – but only up to an optimal point. Beyond that point, further increases in arousal cause performance to decline. The relationship on a graph is an inverted U‑shape. In addition, the optimal arousal level is lower for difficult tasks and higher for simple or well‑learned tasks.
耶克斯–多德森定律指出，随着唤醒水平的提高，任务表现会先上升——但只到某个最佳点为止。超过这个点之后，唤醒水平的继续提高反而会导致表现下降。这一关系在图形上呈现为倒 U 形。此外，困难任务的最佳唤醒水平较低，简单或熟练任务的最佳唤醒水平较高。
Performance = f(arousal) inverted‑U function with task‑dependent optimum
表现 = f(唤醒) 倒 U 形函数，最佳点因任务而异
When you see a question about exam nerves or sports performance, link it to the Yerkes-Dodson curve. A moderate level of nervousness can boost focus (uphill side), but too much anxiety impairs memory and thinking (downhill side). This is why relaxation techniques are useful before exams – they help keep arousal near the optimum.
当你看到关于考试紧张或运动表现的问题时，要将其与耶克斯–多德森曲线联系起来。适度的紧张能提高专注力（曲线上升段），但过多的焦虑则损害记忆和思维（曲线下降段）。这就是为什么考前放松技巧很有用——它们有助于把唤醒水平保持在最佳点附近。
8. Social Facilitation – The Effect of an Audience | 社会助长 – 观众效应
Social facilitation theory says that the mere presence of other people increases our arousal level, making us perform better on simple or well‑practised tasks (the dominant response) but worse on complex or new tasks. This can be expressed as an 'if‑then' rule that depends on task difficulty and audience presence.
社会助长理论认为，仅仅是他人在场就会提高我们的唤醒水平，从而使我们在简单或熟练的任务（主导反应）上表现得更好，但在复杂或新任务上表现得更差。这可以用一条依托于任务难度和观众存在的“如果–那么”规则来表述。
If task is easy/well‑learned + audience present → performance ↑
If task is difficult/new + audience present → performance ↓
如果任务是简单/熟练的 + 有观众在场 → 表现提升 ↑
如果任务是困难/新异的 + 有观众在场 → 表现下降 ↓
Robert Zajonc's (1965) explanation was that increased arousal enhances the emission of dominant responses. For simple tasks, the dominant response is usually the correct one; for hard tasks, it may be an incorrect one. Use this theorem when discussing why a basketball player scores more free throws in front of a crowd but a novice pianist makes more mistakes during a recital.
罗伯特·扎荣茨（1965）的解释是，提升的唤醒水平增强了主导反应的释放。对于简单任务，主导反应通常是正确的；而对于困难任务，主导反应可能是错误的。在讨论为什么篮球运动员在观众面前罚球命中率更高，而钢琴新手在独奏会上却会犯更多错误时，就可以用上这条定理。
9. Asch's Conformity Formula – Majority Influence | 阿希的从众公式 – 多数派影响
Solomon Asch's (1951) line‑judgement experiment showed that about 32% of participants conformed to the wrong answer given by confederates on critical trials, and 75% of participants conformed at least once. This group pressure effect behaves almost like a percentage‑driven rule: as majority size increases, conformity rises – but only up to a group size of about three. Beyond that, adding more people does not produce more conformity.
所罗门·阿希（1951）的线段判断实验表明，在关键次尝试中，约 32% 的参与者会屈从于同伙给出的错误答案，而 75% 的参与者至少屈从过一次。这种群体压力效应几乎就像一条以百分比驱动的规则：随着多数派规模增大，从众程度会上升——但只到大约 3 人的群体规模为止。超过了这个人数，再增加同伴并不能带来更多的从众。
Conformity rate = f(majority size, task difficulty, unanimity)
从众比例 = f(多数派规模, 任务难度, 一致性)
The key variables to remember are: size of the majority (optimum at 3), task difficulty (harder tasks lead to more informational conformity), and whether the majority is unanimous (a single dissenter sharply reduces conformity). When writing a 4‑mark describe question, quote the famous 32% figure and the conditions that change it.
需要记住的关键变量是：多数派的人数（以 3 人为佳）、任务难度（越难的任务导致越多的信息性从众），以及多数派是否一致（只需一名异议者就可以大幅降低从众）。在完成 4 分的描述题时，要引用著名的 32% 数据，并说明有哪些条件会改变它。
10. Milgram's Obedience Rate – The 'Agentic State' Formula | 米尔格拉姆的服从比率 – “代理人状态”公式
Stanley Milgram (1963) found that 65% of participants were willing to deliver the maximum 450‑volt shock when ordered by an authority figure. This obedience level was influenced by several situational variables, each acting like a term in an equation. In Psychology, we summarise this with a set of factors: proximity, location, and uniform. The 'agentic state' – feeling you are just an agent carrying out someone else's orders – provides the theoretical mechanism.
斯坦利·米尔格拉姆（1963）发现，65% 的参与者在权威人物的命令下愿意施加最高 450 伏的电击。这一服从水平受到多种情境变量的影响，每一个变量都像方程式中的一个项。在心理学中，我们用一组因素来总结：接近性、地点、制服。“代理人状态”——感觉自己只是执行他人命令的代理人——提供了理论上的解释机制。
nce level = f(proximity of authority, proximity of victim, legitimacy of context, uniform)
服从水平 = f(权威的接近性, 受害者的接近性, 情境的合法性, 制服)
In your revision, create a mini‑table showing how obedience changed when each variable was altered: teacher and learner in the same room (obedience dropped to 40%); experimenter gave orders by telephone (dropped to 20.5%); study moved to a run‑down office (dropped to 47.5%). These numbers let you turn Milgram's findings into a predictive 'theorem' about social influence.
复习时可以做一张小表格，展示当每个变量发生变化时，服从水平是如何改变的：教师和学习者在同一房间时（服从降至 40%），实验者通过电话下达命令（降至 20.5%），研究地点转移到简陋办公室（降至 47.5%）。这些数字能让你把米尔格拉姆的发现转化为一条关于社会影响的预测性“定理”。
11. Research Methods – Descriptive Statistics Formulas | 研究方法 – 描述统计公式
The Year 8 course also requires you to calculate and interpret basic descriptive statistics: mean, median, mode and range. These are the 'mathematical formulas' of psychology, and you will be expected to use them when analysing data from experiments, questionnaires or observations. The mean is the arithmetic average, the median is the middle value when data are ordered, the mode is the most frequent value, and the range is the difference between the highest and lowest scores.
八年级课程还要求你计算并解释基础描述统计：平均数、中位数、众数和全距。这些是心理学的“数学公式”，在分析实验、问卷或观察数据时，你需要用到它们。平均数是算术平均值，中位数是数据排序后位于中间的值，众数是出现频率最高的值，全距则是最高分与最低分之间的差。
Mean = Σx ÷ n Median = middle value Mode = most frequent Range = max – min
平均数 = Σx ÷ n 中位数 = 中间值 众数 = 频率最高值 全距 = 最大值 – 最小值
You should also know the strengths and limitations of each measure. The mean uses all scores but can be distorted by outliers. The median is unaffected by extreme values but ignores most of the data. The mode is easy to find but may not exist or may not be representative. The range is simple but only uses two data points. Being able to decide which statistic to report is just as important as calculating it.
你还需要了解每种量度的优点与局限。平均数使用了所有分数，但可能被异常值扭曲。中位数不受极端值的影响，但忽略了大部分数据。众数很容易找到，但可能不存在或不具代表性。全距计算简单，但只用了两个数据点。能决定报告哪个统计量，与能计算出它同样重要。
12. Percentage Calculations – A Quick Tool for Data Interpretation | 百分比计算 – 数据解读的快捷工具
Many psychological studies report findings as percentages: the 65% obedience in Milgram, the 32% conformity in Asch, or the proportion of information recalled from a list. Knowing how to convert raw frequencies into percentages allows you to compare results across different sample sizes and to present data clearly in a bar chart or pie chart.
许多心理学研究都以百分比报告结果：米尔格拉姆实验中 65% 的服从比率，阿希实验中 32% 的从众比率，或是从列表中回忆出的信息比例。知道如何将原始频数换算成百分比，能让你在不同样本量之间比较结果，并通过条形图或饼图清晰地展示数据。
Percentage (%) = (Number of target observations ÷ Total number of observations) × 100
百分比(%) = (目标观察数量 ÷ 观察总数) × 100
ed at least 5 words from a list. The percentage recalling 5+ words is (18 ÷ 30) × 100 = 60%. Expressing this as 60% rather than just '18 people' This is a simple but powerful formula that runs through the entire AQA psychology course.
你可以用一组假想的数据进行练习，例如 30 名参与者中有 18 人从列表中回忆出至少 5 个单词。那么回忆出 5 个及以上单词的百分比就是 (18 ÷ 30) × 100 = 60%。用 60% 而不是“18 人”来表述，能够更容易地与另一项使用了 50 名参与者的研究进行比较。这个简单但强大的公式贯穿了整个 AQA 心理学的学习。
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