📚 CAIE IGCSE Psychology: Quick Reference to Key Formulas & Principles | CAIE IGCSE 心理学公式定理速查手册
This quick-reference handbook gathers the essential formulas, quantitative relationships and core principles you need to revise for the CAIE IGCSE Psychology (0266) examinations. From the mathematics of memory experiments to the standard measures used in research methods, every key formula is presented with a concise explanation and paired with its Chinese translation to help bilingual learners retain information with confidence.
这本速查手册汇集了CAIE IGCSE心理学（0266）考试中必备的重要公式、数量关系和核心原理。从记忆实验的数学表达，到研究方法的标准化度量，每一项关键公式都配有简洁的说明和中文翻译，帮助双语学习者自信地掌握知识。
1. The Multi-Store Model of Memory | 记忆多存储模型
Atkinson & Shiffrin (1968) proposed that human memory consists of three linked stores: the sensory register, short‑term memory (STM) and long‑term memory (LTM). Information flows from one store to the next through attention and rehearsal.
Atkinson和Shiffrin（1968）提出人类记忆由三个相连的贮存库组成：感觉登记、短时记忆（STM）和长时记忆（LTM）。信息通过注意和复述从一个贮存库流向下一个。
Sensory Register → (Attention) → STM → (Rehearsal) → LTM
感觉登记 →（注意）→ 短时记忆 →（复述）→ 长时记忆
If rehearsal does not take place, information in STM is lost through displacement or decay. Maintenance rehearsal keeps information circulating, while elaborative rehearsal links it to existing knowledge for stronger encoding into LTM.
如果缺乏复述，短时记忆中的信息会因干扰或消退而丧失。维持性复述使信息反复循环，而精细复述则将新信息与已有知识联结，从而更稳固地编码进入长时记忆。
2. Miller’s Magic Number 7±2 | 米勒的魔术数字7±2
George Miller (1956) demonstrated that the capacity of short-term memory is limited. Most people can hold between five and nine meaningful items, or chunks, in STM at any one time.
George Miller（1956）证实短时记忆的容量是有限的。大多数人每次在短时记忆中只能同时保持5至9个有意义的项目，即组块。
STM Capacity ≈ 7 ± 2 chunks
短时记忆容量 ≈ 7 ± 2 个组块
Chunking is the process of grouping individual pieces of information into larger, meaningful units (e.g. remembering 'CAIE IG' as one chunk rather than six letters). This strategy expands the functional capacity of STM without altering its biological limit.
组块化是将零散信息组合成更大、有意义单元的过程（例如把'CAIE IG'当作一个组块来记住，而非六个字母）。这种策略在不变动生物学极限的前提下，扩展了短时记忆的功能容量。
3. Peterson & Peterson’s STM Duration Formula | 皮特森与彼得森的短时记忆持续时间公式
Peterson and Peterson (1959) used trigrams (e.g. CLS, JZQ) and a distractor task to prevent rehearsal. They found that the percentage of correct recall dropped dramatically as the retention interval increased from 3 seconds to 18 seconds.
Peterson和Peterson（1959）使用三字母组（如CLS、JZQ）和干扰任务来阻止复述。他们发现正确回忆的百分比随着保持间隔从3秒增至18秒而急剧下降。
Recall ≈ 80% at 3 s → ≈ 10% at 18 s
3秒时回忆率≈80% → 18秒时≈10%
Without active rehearsal, information in STM fades within approximately 18–30 seconds. This finding supports the idea that STM has a very limited duration and that maintenance rehearsal is crucial for transferring information to LTM.
缺乏主动复述时，短时记忆中的信息在约18–30秒内消退。这一发现支持了短时记忆持续时间极短的观点，并说明维持性复述对于信息转入长时记忆至关重要。
4. Ebbinghaus’s Forgetting Curve and Savings Formula | 艾宾浩斯遗忘曲线与节省公式
Hermann Ebbinghaus (1885) studied his own memory for nonsense syllables and discovered that forgetting is rapid immediately after learning and then levels off. The savings method measures how much time or effort is saved when relearning material.
Hermann Ebbinghaus（1885）用无意义音节研究自身记忆，发现遗忘在学习后最初阶段最快，随后逐渐平缓。节省法衡量重新学习材料时节省了多少时间或努力。
Savings (%) = [(Initial learning time − Relearning time) ÷ Initial learning time] × 100
节省百分比 = [（初始学习时间 − 重新学习时间）÷ 初始学习时间] × 100
If a list originally took 10 repetitions to learn and only 4 repetitions to relearn after a delay, the savings score is 60%. A high savings percentage indicates that some information has been retained in LTM even when it cannot be consciously recalled.
假如某列项目起初需要10次复述才能学会，而延迟后只需4次复述重新掌握，则节省分为60%。较高的节省百分比表示即使不能有意识地回忆，长时记忆中也保留了一部分信息。
5. Percentage, Ratio and Proportion Calculations | 百分比、比率与比例计算
In psychological research, percentages and ratios are frequently used to summarise observations, compare conditions or evaluate the reliability of scores. The basic formula is straightforward but must be applied precisely.
在心理学研究中，百分比和比率常被用于汇总观察结果、比较实验条件或评估评分的可靠性。基本公式虽简单，但必须准确应用。
Percentage = (Number of target outcomes ÷ Total number of outcomes) × 100
百分比 = （目标结果数量 ÷ 结果总数）× 100
nts conformed to a group’s incorrect answer, the conformity rate is (15 ÷ 40) × 100 = 37.5%. Ratios are expressed as a:b, where a and b are the two compared quantities.
例如，如果40名参与者中有15人从众做出了错误回答，那么从众率为（15 ÷ 40）× 100 = 37.5%。比率表示为a:b，其中a和b是比较的两个数量。
6. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：平均数、中位数、众数
Three core measures summarise the ‘centre’ of a data set. Choosing the most appropriate measure depends on the level of measurement and the shape of the distribution.
三种核心度量用于概括数据集的'中心'。选择最恰当的度量取决于测量尺度级别和数据分布的形状。
Mean = Σx ÷ n
平均数 = 所有数值之和 ÷ 数值个数
Median = middle value when data are ordered
中位数 = 数据排序后位于中间的值
Mode = most frequently occurring value
众数 = 出现频率最高的值
The mean is sensitive to extreme scores, whereas the median is resistant. In skewed distributions, the median usually gives a more realistic picture of the typical score. The mode is the only measure that can be used with nominal (categorical) data.
平均数易受极值影响，而中位数更具抗性。在偏态分布中，中位数通常更能反映典型值。众数是唯一可用于名义（类别）数据的集中趋势度量。
7. Measures of Spread: Range | 离散度量：极差
While a measure of central tendency tells you where the middle of the data is, a measure of spread describes how much the scores vary. The simplest measure of spread is the range.
集中趋势度量告诉您数据的中心在哪里，而离散度量则描述分数变动的程度。最简单的离散度量是极差。
Range = Highest score − Lowest score
极差 = 最高分 − 最低分
A small range suggests the data are tightly clustered, while a large range implies high variability. However, the range only considers two values and can be distorted by a single outlier. Researchers often also report the standard deviation when more precise dispersion information is needed.
极差小表明数据紧密聚集，极差大则意味着变异性高。然而，极差只考虑两个数值，易受单一异常值影响。当需要更精确的分散度信息时，研究者通常还会报告标准差。
8. Correlation Coefficients | 相关系数
A correlation coefficient (r) measures the strength and direction of the linear relationship between two co‑variables, such as hours of sleep and alertness scores. The value of r ranges from –1 to +1.
相关系数（r）衡量两个协变量（如睡眠时长与警觉度分数）之间线性关系的强度和方向。r的取值介于–1到+1之间。
−1 ≤ r ≤ +1
−1 ≤ 相关系数 ≤ +1
| r = +1 | Perfect positive correlation | 完全正相关 |
| r = 0 | No linear correlation | 无线性相关 |
| r = −1 | Perfect negative correlation | 完全负相关 |
Causation cannot be inferred from correlation alone. A strong correlation could be explained by a third variable or simply be coincidental. CAIE questions often ask you to outline the difference between correlation and cause‑and‑effect.
不能仅凭相关性推断因果关系。强相关可能由第三个变量解释，也可能纯属巧合。CAIE考题常要求简述相关与因果的区别。
9. Independent, Dependent and Extraneous Variables | 自变量、因变量与额外变量
In any experiment, researchers manipulate one factor and measure its effect on another. The independent variable (IV) is the one deliberately changed; the dependent variable (DV) is the outcome that is recorded.
在任何实验中，研究者操控一个因素并测量其对另一个因素的影响。自变量（IV）是被有意改变的因素；因变量（DV）是记录到的结果。
IV = variable that is manipulated
自变量 = 被操控的变量
DV = variable that is measured
因变量 = 被测量的变量
Extraneous variables (EV) are any other factors that could influence the DV. If an EV systematically varies with the IV, it becomes a confounding variable and can ruin the internal validity of the experiment. Standardisation, random allocation and counterbalancing are used to control EVs.
额外变量（EV）是可能影响因变量的任何其他因素。如果额外变量随自变量系统性地变化，它就成为混淆变量，可能破坏实验的内部效度。标准化、随机分配和平衡技术可用于控制额外变量。
10. Experimental Designs and Counterbalancing | 实验设计与平衡法
Three main experimental designs are used to allocate participants to conditions: independent groups, repeated measures and matched pairs. Each design has its own strengths and weaknesses regarding participant variables and order effects.
有三种主要的实验设计用于分配参与者到不同条件：独立组设计、重复测量设计和配对组设计。每种设计在处理参与者变量和顺序效应方面各有优缺点。
| Independent groups | Different participants in each condition. | 每条件使用不同参与者。 |
| Repeated measures | Same participants do all conditions; order effects are a risk. | 同批参与者完成所有条件；存在顺序效应风险。 |
| Matched pairs | Participants are paired on a relevant trait, then split between conditions. | 参与者按相关特质配对，再将每对成员分到不同条件。 |
Counterbalancing is used especially in repeated measures designs to control order effects. The simplest form, ABBA counterbalancing, follows a fixed pattern where half the participants experience condition A then B, and the other half B then A.
平衡法尤其用于重复测量设计以控制顺序效应。最简单的ABBA平衡法按照固定模式：一半参与者先接受条件A再接受B，另一半则先B后A。
Participant 1 order: A → B
参与者1顺序：A → B
Participant 2 order: B → A
参与者2顺序：B → A
11. Bartlett’s Schema Theory and Recall Reconstruction | 巴特利特的图式理论与回忆重构
Bartlett (1932) argued that memory is not a passive replay but an active reconstruction influenced by schemas – mental frameworks built from past experience. His 'War of the Ghosts' study showed that recall became shorter, more coherent and culturally familiar over successive reproductions.
Bartlett（1932）认为记忆不是被动的回放，而是由过去经验建构的心理框架——图式所影响的主动重建。他的'幽灵之战'研究表明，随着时间的推移，回忆会变得更简短、更连贯且更符合文化熟悉度。
Recall = verbatim trace + schema‑based reconstruction
回忆 = 字面痕迹 + 图式性重建
Distortions such as omission (leaving out unfamiliar details), transformation (changing details to fit existing schemas) and rationalisation (adding reasons to make the story logical) are common. These findings demonstrate that memory is reconstructive rather than reproductive.
常见的扭曲包括省略（剔除不熟悉的细节）、转化（改变细节以符合已有图式）和合理化（添加理由使故事更有逻辑）。这些发现表明记忆是重建性的，而非复制的。
12. Classical Conditioning: UCS-UCR-CS-CR Sequence | 经典条件作用：无条件刺激-无条件反应-条件刺激-条件反应
Pavlov's work (1927) on classical conditioning shows how a neutral stimulus can come to elicit a learned response through repeated pairing with an unconditioned stimulus. The standard terms form a clear sequence that can be expressed as a formula.
Pavlov（1927）对经典条件作用的研究显示，中性刺激通过反复与无条件刺激配对，可以引发习得反应。标准术语构成一个清晰的顺序，可以表示为公式。
Before conditioning: NS (bell) → No response; UCS (food) → UCR (salivation)
条件作用前：中性刺激（铃声）→ 无反应；无条件刺激（食物）→ 无条件反应（分泌唾液）
During conditioning: NS + UCS → UCR (repeated pairings)
条件作用中：中性刺激 + 无条件刺激 → 无条件反应（反复配对）
After conditioning: CS (bell) → CR (salivation)
条件作用后：条件刺激（铃声）→ 条件反应（分泌唾液）
Extinction occurs when the CS is repeatedly presented without the UCS, causing the CR to weaken. Spontaneous recovery may follow a rest period. Generalisation and discrimination further explain how conditioned responses spread or narrow.
当条件刺激反复单独呈现而无无条件刺激时，消退发生，条件反应减弱。休息后可能出现自发恢复。泛化和分化则进一步说明条件反应如何扩展或变得专一。
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