IGCSE Cambridge Psychology Formula & Theorem Quick Reference | IGCSE 剑桥心理学：公式定理速查手册

📚 IGCSE Cambridge Psychology Formula & Theorem Quick Reference | IGCSE 剑桥心理学：公式定理速查手册

This quick reference organises the most important ‘formulas’, empirical laws, and theoretical relationships tested in IGCSE Cambridge Psychology. It covers research methods, data analysis, memory, learning theory, and social influence so you can revise efficiently before Paper 1 and Paper 2.

本速查手册整理了 IGCSE 剑桥心理学考试中最关键的“公式”、经验法则和理论关系，涵盖研究方法、数据分析、记忆、学习理论与社会影响，帮助你在 Paper 1 和 Paper 2 前高效复习。

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1. Research Methods: IV, DV, Hypothesis | 研究方法：自变量、因变量与假设

The independent variable (IV) is the factor the researcher manipulates or changes. The dependent variable (DV) is the factor that is measured to see the effect of the IV.

自变量（IV）是研究者操纵或改变的因素。因变量（DV）是被测量以观察自变量影响的因素。

Hypothesis: If the IV changes, the DV is expected to change.

假设：若自变量改变，则因变量应随之改变。

A directional (one-tailed) hypothesis states the expected direction of the effect, such as ‘group A will score higher than group B’. A non-directional (two-tailed) hypothesis only predicts a difference, not its direction.

方向性（单尾）假设说明预期的效应方向，例如“A 组分数将高于 B 组”。非方向性（双尾）假设只预测有差异，不预测方向。

The null hypothesis states that there is no difference or relationship between the variables. If data do not support the null, it may be rejected in favour of the experimental hypothesis.

零假设指出变量之间没有差异或关系。如果数据不支持零假设，则可能拒绝零假设并接受实验假设。

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2. Experimental Design Types and Controls | 实验设计类型与控制条件

Independent groups design uses different participants in each condition. Repeated measures design uses the same participants in all conditions. Matched pairs design matches participants on key traits before assignment.

独立组设计在每个条件下使用不同的被试。重复测量设计在所有条件下使用相同被试。配对组设计在分配前按关键特征匹配被试。

Control: keep all variables constant except the IV.

控制：除自变量外，所有变量保持不变。

Random allocation reduces participant variables in independent groups designs. Counterbalancing reduces order effects in repeated measures designs, such as fatigue or practice.

随机分配可减少独立组设计中的被试变量。平衡法可减少重复测量设计中的顺序效应，如疲劳或练习效应。

• Independent groups: no order effects, but more participant variables.
• 独立组：无顺序效应，但被试变量较多。
• Repeated measures: fewer participant variables, but order effects are possible.
• 重复测量：被试变量较少，但可能出现顺序效应。
• Matched pairs: reduces participant variables but time-consuming to match.
• 配对组：减少被试变量，但匹配耗时。

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3. Sampling Methods and Representativeness | 抽样方法与代表性

Sampling is the process of selecting participants from a target population. A sample should be representative so results can be generalised back to the population.

抽样是从目标人群中选取被试的过程。样本应具有代表性，以便将结果推广回总体。

Representativeness ≈ sample characteristics ÷ target population characteristics

代表性 ≈ 样本特征 ÷ 目标总体特征

Random sampling gives every member an equal chance of selection. Opportunity sampling selects people who are available. Stratified sampling divides the population into subgroups and samples proportionally. Volunteer sampling relies on people offering to take part.

随机抽样使每个成员被选中的机会相等。机会抽样选择方便找到的人。分层抽样将总体划分为亚群体并按比例抽样。自愿抽样依赖人们主动参与。

Larger samples tend to be more representative, but size is less important than how well the sample reflects the population structure.

更大的样本通常更具代表性，但样本规模不如样本反映总体结构的程度重要。

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4. Measures of Central Tendency: Mean, Median, Mode | 集中趋势量数：平均数、中位数、众数

The mean is the arithmetic average and uses all data points. The median is the middle score when data are ordered. The mode is the most frequent score.

平均数是算术平均值，使用所有数据点。中位数是数据排序后的中间分数。众数是出现频率最高的分数。

Mean = Σx ÷ n

平均数 = 数据总和 ÷ 数据个数

The mean is the most sensitive measure but can be distorted by extreme outliers. The median is more robust for skewed data. The mode is useful for categorical data.

平均数最灵敏，但易受极端值扭曲。中位数对偏斜数据更稳健。众数适用于分类数据。

In IGCSE Psychology papers, you are often asked to calculate the mean from a table and explain why the median may be more appropriate when there are outliers.

在 IGCSE 心理学考试中，常要求你根据表格计算平均数，并解释当存在离群值时为何中位数可能更合适。

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5. Measures of Spread: Range and Standard Deviation | 离散程度量数：极差与标准差

The range is the simplest measure of spread. It shows the difference between the highest and lowest scores.

极差是最简单的离散程度量数，表示最高分与最低分之间的差异。

Range = maximum score − minimum score

极差 = 最高分 − 最低分

Standard deviation measures the average distance of each score from the mean. A small standard deviation means scores are clustered closely around the mean; a large one means scores are widely spread.

标准差测量每个分数与平均数的平均距离。标准差小意味着分数紧密聚集在平均数附近；标准差大意味着分数分布广泛。

SD = √(Σ(x − mean)² ÷ n)

标准差 = 各离均差平方和的平均数的平方根

When comparing two conditions, the condition with the smaller standard deviation has more consistent results. The condition with the larger standard deviation has more individual differences.

比较两种条件时，标准差较小的条件结果更一致。标准差较大的条件个体差异更大。

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6. Correlation Coefficients: Direction and Strength | 相关系数：方向与强度

A correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, such as stress and exam performance.

相关系数（r）衡量两个变量之间线性关系的强度和方向，例如压力与考试成绩。

r ranges from −1.00 to +1.00

r 的值域为 −1.00 到 +1.00

A positive correlation means both variables increase together, e.g. revision time and marks. A negative correlation means one variable increases while the other decreases, e.g. anxiety and working memory capacity. A zero correlation means no linear relationship.

正相关意味着两个变量同时增加，例如复习时间与分数。负相关意味着一个变量增加而另一个减少，例如焦虑与工作记忆容量。零相关意味着无线性关系。

The closer r is to +1.00 or −1.00, the stronger the relationship. However, correlation does not imply causation because an extraneous variable may explain the link.

r 越接近 +1.00 或 −1.00，关系越强。然而，相关不等于因果，因为可能由额外变量解释这一联系。

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7. Short-Term Memory Capacity: Miller’s 7±2 | 短时记忆容量：米勒的 7±2

Miller’s magic number law states that short-term memory (STM) can hold about 7 items on average, with a range of 5 to 9 items.

米勒的“神奇数字”定律指出，短时记忆平均可容纳约 7 个项目，范围为 5 至 9 个项目。

STM capacity ≈ 7 ± 2 items

短时记忆容量 ≈ 7 ± 2 个项目

Chunking combines smaller units into larger meaningful units, such as remembering a phone number as 0734-892-156 rather than 10 separate digits. Chunking increases the amount of information held in STM.

组块化将较小的单位合并成更大的意义单位，例如将电话号码记为 0734-892-156 而不是 10 个单独数字。组块化可增加短时记忆的信息容量。

Without rehearsal, STM items are lost rapidly. Repeating information in a phonological loop keeps it in short-term storage and supports transfer to long-term memory.

若不进行复述，短时记忆项目会迅速丢失。在语音回路中重复信息可使其保留在短时存储中，并有助于转入长时记忆。

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8. Multi-Store Model and Forgetting Curve | 多存储模型与遗忘曲线

The multi-store model describes memory as three linked stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Information flows through attention, rehearsal, and encoding.

多存储模型将记忆描述为三个相互联系的存储系统：感觉记忆、短时记忆（STM）和长时记忆（LTM）。信息通过注意、复述和编码流动。

Sensory memory → attention → STM → rehearsal → LTM

感觉记忆 → 注意 → 短时记忆 → 复述 → 长时记忆

Store	Capacity	Duration
Sensory memory | 感觉记忆	Very large | 非常大	Less than 0.5 s | 小于 0.5 秒
STM | 短时记忆	7 ± 2 items | 7 ± 2 个项目	18-30 s without rehearsal | 不复述约 18-30 秒
LTM | 长时记忆	Unlimited | 无限	Potentially permanent | 可能永久

Ebbinghaus’s forgetting curve shows that forgetting is rapid immediately after learning, then levels off. Most forgetting occurs within the first hour or day, so spaced revision improves retention.

艾宾浩斯遗忘曲线显示，遗忘在学习后立即迅速发生，然后趋于平稳。多数遗忘发生在最初一小时或一天内，因此间隔复习可提高保持率。

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9. Learning Theory: Classical and Operant Conditioning | 学习理论：经典条件反射与操作性条件反射

Classical conditioning is learning by association. A neutral stimulus (NS) is paired with an unconditioned stimulus (UCS) that naturally produces an unconditioned response (UCR). After repeated pairings, the NS becomes a conditioned stimulus (CS) producing a conditioned response (CR).

经典条件反射是通过联想进行学习。中性刺激（NS）与自然产生无条件反应（UCR）的无条件刺激（UCS）配对。多次配对后，中性刺激变为条件刺激（CS），产生条件反应（CR）。

NS + UCS → UCR; after conditioning, CS → CR

中性刺激 + 无条件刺激 → 无条件反应；条件化后，条件刺激 → 条件反应

Operant conditioning is learning by consequences. Thorndike’s law of effect states that behaviour followed by a satisfying outcome is more likely to be repeated, while behaviour followed by an unpleasant outcome is less likely.

操作性条件反射是通过后果进行学习。桑代克的效果律指出，带来满意结果的行为更可能重复，带来不愉快结果的行为则更少重复。

S → R → Consequence: reinforcement increases behaviour; punishment decreases behaviour.

刺激 → 反应 → 后果：强化增加行为；惩罚减少行为。

Positive reinforcement adds a reward, e.g. praise for homework. Negative reinforcement removes an unpleasant stimulus, e.g. taking painkillers to remove headache. Both increase the behaviour.

正强化增加奖励，例如对作业表扬。负强化移除不愉快刺激，例如服用止痛药消除头痛。两者都增加行为。

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10. Social Influence: Conformity and Obedience Percentages | 社会影响：从众与服从百分比

Asch’s conformity study found that about 75% of participants conformed to the majority at least once, while the average conformity rate across critical trials was around 37%.

阿希的从众研究发现，约 75% 的被试至少从众一次，而在关键试验中的平均从众率约为 37%。

Asch conformity ≈ 37% average on critical trials; 75% conformed at least once

阿希从众率 ≈ 关键试验平均 37%；75% 至少从众一次

Conformity increases with group size up to about three to five confederates, then tends to plateau. Unanimity and task difficulty also increase conformity.

从众随群体规模增大而增加，到约三至五名同谋者后趋于平稳。一致性和任务难度也会增加从众。

Milgram’s obedience study found that 65% of participants continued to the maximum 450-volt shock level. All participants continued up to 300 volts in the original procedure.

米尔格拉姆的服从研究发现，65% 的被试继续到最高 450 伏特电击水平。在原始程序中，所有被试都继续到了 300 伏特。

Milgram obedience = 65% to 450 V

米尔格拉姆服从率 = 65% 到 450 伏特

These empirical rates are often quoted in exam questions to support or challenge situational explanations of behaviour.

这些经验比例常在考题中引用，以支持或挑战行为的情境解释。

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11. Ethics Cost-Benefit Formula | 伦理成本效益公式

Ethical guidelines in psychology protect participants from physical and psychological harm. They include informed consent, right to withdraw, confidentiality, deception rules, debriefing, and protection from harm.

心理学伦理准则保护被试免受身心伤害，包括知情同意、退出权、保密性、欺骗规则、事后说明和免受伤害。

Ethical study: benefits to society > costs to participants, and costs are minimised.

符合伦理的研究：社会收益 > 被试成本，且成本被降至最低。

Deception can be allowed only if the study has clear scientific value and no alternative without deception. Participants must be debriefed afterwards and allowed to withdraw their data.

只有在研究具有明确科学价值且无其他无欺骗方法时才允许欺骗。事后必须向被试说明情况，并允许其撤回数据。

When evaluating a study, you can apply a cost-benefit check: Do the potential benefits to science and society outweigh the potential harm to participants? If not, the study is ethically questionable.

评价研究时，你可以进行成本效益检查：对科学和社会的潜在收益是否大于对被试的潜在伤害？若不是，则该研究在伦理上存疑。

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12. Statistical Significance and p-value | 统计显著性与 p 值

Statistical significance tells us how likely it is that a result occurred by chance. The conventional significance level in psychology is p ≤ 0.05, meaning there is a 5% or lower probability the result is due to chance.

统计显著性告诉我们结果由偶然因素造成的可能性有多大。心理学中惯用的显著水平为 p ≤ 0.05，即结果由偶然造成的概率为 5% 或更低。

Reject the null hypothesis if p ≤ 0.05.

若 p ≤ 0.05，则拒绝零假设。

A Type I error occurs when the null hypothesis is rejected but it is actually true. A Type II error occurs when the null hypothesis is not rejected but it is actually false.

第一类错误发生在零假设为真却被拒绝时。第二类错误发生在零假设为假却未被拒绝时。

Larger sample sizes, strict controls, and robust measures reduce error and increase the validity of conclusions drawn from significance tests.

更大的样本量、严格控制条件和可靠测量可减少误差，提高由显著性检验得出结论的效度。

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