Pre-U CIE Psychology: Formula and Theorem Quick Reference Handbook | Pre-U CIE 心理学：公式定理速查手册

📚 Pre-U CIE Psychology: Formula and Theorem Quick Reference Handbook | Pre-U CIE 心理学：公式定理速查手册

This concise handbook gathers essential statistical formulas and core psychological theorems required for the Cambridge Pre-U Psychology syllabus. It is designed as a last-minute revision tool to help you quickly recall the calculations and key principles that underpin research methods, biological processes, cognitive functions, learning behaviours, and social interactions.

这本简明手册汇集了剑桥 Pre-U 心理学课程所必需的核心统计公式与重要心理学定理。它被设计为一款考前快速复习工具，帮助你在最后关头迅速回顾那些支撑研究方法、生物过程、认知功能、学习行为和社会互动的计算与关键原则。

1. Measures of Central Tendency | 集中趋势量数

Mean (x̄): Sum of all scores divided by the number of scores. It is the most sensitive measure but can be distorted by outliers.

平均数（x̄）： 所有分数之和除以分数个数。它是最敏感的量数，但可能被异常值扭曲。

x̄ = Σx / n

Median: The middle value when data are ordered. It is robust against outliers and is used for ordinal data.

中位数： 将数据排序后居于中间位置的值。它对异常值有抗扰性，适用于顺序数据。

Mode: The most frequently occurring score. It is the only measure suitable for nominal data.

众数： 出现频次最高的分数。它是唯一适用于名义数据的集中量数。

2. Measures of Dispersion | 离散量数

Range: The difference between the highest and lowest scores. It gives a quick but crude indication of spread.

全距： 最高分与最低分之差。它能快速但粗略地反映数据的离散程度。

Range = Xₘₐₓ − Xₘᵢₙ

Variance (s²): The average of the squared deviations from the mean. It reflects how far scores are spread out around the mean.

方差（s²）： 各数据与平均数离差平方的平均数。它反映了分数围绕平均数的散布宽度。

s² = Σ(x − x̄)² / (n − 1)

Standard Deviation (s): The square root of the variance. It is expressed in the original units and is fundamental for inferential statistics.

标准差（s）： 方差的平方根。它以原始单位表示，是推断统计的基础。

s = √[ Σ(x − x̄)² / (n − 1) ]

3. Inferential Statistics: The t-Test | 推断统计：t 检验

Independent samples t-test: Compares the means of two unrelated groups. The formula calculates the t-statistic based on the difference in means relative to the combined standard error.

独立样本 t 检验： 比较两个无关组的平均数。该公式根据平均数之差与合并标准误的比值计算 t 统计量。

t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)

Repeated measures (paired) t-test: Compares two conditions within the same participants. It focuses on the mean of the difference scores.

重复测量（配对）t 检验： 比较同一批参与者在两种条件下的得分。它聚焦于差值分数的平均数。

t = d̄ / (s_d / √n) where d̄ is the mean difference and s_d is the standard deviation of differences.

t = d̄ / (s_d / √n) 其中 d̄ 为差值平均数，s_d 为差值的标准差。

4. Chi-Square Test (χ²) | 卡方检验（χ²）

Chi-square test of association: Tests whether there is a significant association between two categorical variables. It compares observed frequencies with expected frequencies.

卡方独立性检验： 检验两个类别变量之间是否存在显著关联。它比较观察频数与期望频数。

χ² = Σ (O − E)² / E

O = observed frequency, E = expected frequency (row total × column total / grand total). Degrees of freedom: df = (r − 1)(c − 1).

O 为观察频数，E 为期望频数（行合计 × 列合计 / 总计）。自由度：df = (r − 1)(c − 1)。

5. Correlation Coefficients | 相关系数

Spearman’s rho (ρ): A non-parametric test for correlation between two sets of ranked data. It is used when the relationship is monotonic but not necessarily linear.

斯皮尔曼等级相关系数（ρ）： 一种用于两组等级数据之间相关性的非参数检验。适用于单调但不一定是线性的关系。

ρ = 1 − [ 6 Σd² / n(n² − 1) ] where d is the difference between ranks.

ρ = 1 − [ 6 Σd² / n(n² − 1) ] 其中 d 为等级之差。

Pearson’s r: A parametric test for linear correlation between two continuous variables. It requires data at interval or ratio level and assumes normal distribution.

皮尔逊积差相关系数 r： 一种用于两个连续变量线性相关的参数检验。要求数据为间距或比率水平，并假设正态分布。

r = Σ(x − x̄)(y − ȳ) / √[ Σ(x − x̄)² Σ(y − ȳ)² ]

6. Weber’s Law | 韦伯定律

Weber’s Law: The just noticeable difference (JND) between two stimuli is proportional to the magnitude of the original stimulus. This is a fundamental theorem in psychophysics linking physical intensity to perceptual discrimination.

韦伯定律： 两个刺激之间的最小可觉差（JND）与原始刺激的强度成正比。这是心理物理学中将物理强度与知觉辨别力联系起来的根本定理。

ΔI / I = k where I is intensity, ΔI is the increment threshold, and k is the Weber fraction.

ΔI / I = k 其中 I 为强度，ΔI 为增量阈值，k 为韦伯分数。

Example: For lifted weights, k ≈ 0.02; a 100 g weight requires an increment of roughly 2 g to be noticed.

示例：对于举重，k ≈ 0.02；一个 100 克的重量大约需要增加 2 克才能被察觉。

7. Fechner’s Law | 费希纳定律

Fechner’s Law: Sensation magnitude (S) is proportional to the logarithm of the stimulus intensity (I). This theorem extends Weber’s Law to account for the decreasing sensitivity as intensity increases.

费希纳定律： 感觉大小（S）与刺激强度（I）的对数成正比。该定理拓展了韦伯定律，用以解释随强度增加而递减的敏感性。

S = k log I

It predicts that equal ratios of stimulus intensity produce equal increments in sensation, which is central to understanding brightness and loudness perception.

它预测，刺激强度的等比变化会产生感觉的等量增加，这对理解明度与响度知觉至关重要。

8. Ebbinghaus Forgetting Curve | 艾宾浩斯遗忘曲线

Ebbinghaus’s theorem of memory decay: Memory retention decreases rapidly in the first hours after learning and then levels off. This demonstrates the exponential nature of forgetting.

艾宾浩斯记忆衰减定理： 记忆保持量在学习后最初几小时内迅速下降，随后趋于平缓。这体现了遗忘的指数型本质。

R = e^(−t/S) where R is retention, t is time, and S is the relative strength of memory.

R = e^(−t/S) 其中 R 为保持量，t 为时间，S 为记忆的相对强度。

Key implication: Spaced repetition and active recall can combat this decay, forming the basis of the testing effect.

关键启示：分散复习与主动回忆可以对抗这种衰退，构成了测试效应的基础。

9. Yerkes-Dodson Law | 耶克斯-多德森定律

Yerkes-Dodson Law: Performance increases with physiological or mental arousal, but only up to an optimal point, after which performance declines. This relationship describes an inverted-U curve.

耶克斯-多德森定律： 表现随生理或心理唤醒水平的提高而提升，但仅到某一最佳点，随后表现下降。这一关系描绘为倒 U 型曲线。

The optimal level of arousal is lower for difficult tasks and higher for simple tasks. This theorem is crucial in studies of stress, motivation, and eyewitness testimony.

困难任务的最佳唤醒水平较低，而简单任务较高。这一定理在压力、动机和目击证词研究中至关重要。

10. Signal Detection Theory | 信号检测论

Signal Detection Theory (SDT): A psychophysical theorem that separates sensitivity (d’) from response bias (criterion). It explains how decisions are made under uncertainty.

信号检测论（SDT）： 一个将感觉敏感性（d’）与反应偏向（判断标准）分离开来的心理物理学定理。它解释了在不确定条件下如何做出决策。

d’ = z(Hit) − z(False Alarm)

A high d’ indicates good discrimination between signal and noise. SDT is applied to memory recognition, medical diagnosis, and perceptual experiments.

高 d’ 值表示对信号与噪声的良好辨别力。信号检测论被应用于记忆再认、医学诊断和知觉实验。

11. Cognitive Dissonance Theory | 认知失调理论

Cognitive Dissonance Theorem (Festinger): When a person holds two or more inconsistent cognitions, they experience psychological discomfort (dissonance), which motivates them to reduce the inconsistency, often by changing attitudes or beliefs.

认知失调定理（费斯廷格）： 当一个人持有两个或多个不一致的认知时，会体验到心理不适（失调感），这促使他们减少不一致，通常是通过改变态度或信念。

This is a foundational theorem in social psychology explaining phenomena such as effort justification and induced compliance.

这是社会心理学中解释努力正当化与诱导服从等现象的基础性定理。

12. Social Identity Theory | 社会认同理论

Social Identity Theorem (Tajfel & Turner): An individual’s self-concept is partly derived from perceived membership in a social group. The theory posits three processes: social categorisation, social identification, and social comparison, which lead to in-group favouritism and out-group discrimination.

社会认同定理（塔杰菲尔 & 特纳）： 个体的自我概念部分来源于其感知到的社会群体成员身份。该理论提出三个过程：社会分类、社会认同和社会比较，导致内群体偏好和外群体歧视。

This theorem underpins much of the research on prejudice, stereotyping, and intergroup conflict within the Pre-U syllabus.

这一定理是 Pre-U 课程中大量关于偏见、刻板印象和群际冲突研究的基础。

---

Published by TutorHao | Psychology Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）