📚 Year 12 AQA Psychology: Formula & Theorem Quick-Reference Guide | AQA 心理学：公式定理速查手册
This handbook compiles the essential statistical formulae, research method concepts and key psychological theorems you need for the Year 12 AQA specification. It is designed as a rapid review tool to support your revision by placing numerical expressions and core theoretical statements side by side.
本手册汇编了 Year 12 AQA 大纲所要求的基本统计公式、研究方法概念和核心心理学定理。它设计为快速复习工具，通过将数值表达式和核心理论陈述并列，帮助你巩固复习。
1. Measures of Central Tendency | 集中趋势的度量
The arithmetic mean is the sum of all scores divided by the number of scores. It is the most sensitive measure of centre but can be distorted by outliers.
算术平均值是所有分数之和除以分数个数。它是对中心最敏感的度量，但可能被异常值扭曲。
Mean (μ or x̄) = ΣX / N
The median is the middle score when data are arranged in order. It is robust against extreme values and often used with ordinal data.
中位数是数据按顺序排列后的中间值。它对极端值鲁棒，常用于定序数据。
The mode is the most frequently occurring value in a data set. It is the only measure of central tendency suitable for nominal (categorical) data.
众数是数据集中出现频率最高的数值。它是唯一适用于名义（类别）数据的集中趋势度量。
For a skewed distribution, the mean is pulled toward the tail, so the median often gives a better sense of 'typical' performance.
对于偏态分布，平均值会被拉向尾部，因此中位数往往更能体现“典型”表现。
2. Measures of Dispersion | 离散度量
The range is the difference between the highest and lowest scores. It gives a quick estimate of spread but ignores the distribution of all intermediate values.
极差是最高分与最低分之差。它能快速估计分散程度，但忽略了所有中间值的分布。
Variance captures the average squared deviation from the mean. A large variance indicates scores are widely scattered.
方差捕捉的是与平均值离差的平方的平均数。方差大表明分数分布很分散。
Variance (σ² or s²) = Σ(X – μ)² / N
The standard deviation is the square root of the variance and returns the measure to the original units. It is the most commonly reported measure of dispersion in psychology.
标准差是方差的平方根，使度量回归原始单位。它是心理学中最常报告的高散度量。
Standard deviation (σ or s) = √[ Σ(X – μ)² / N ]
When working with a sample, the denominator becomes N – 1 to give an unbiased estimate of the population standard deviation.
处理样本时，分母变为 N – 1，以给出总体标准差的无偏估计。
3. Correlational Analysis | 相关分析
Correlation measures the strength and direction of a linear relationship between two co‑variables. The correlation coefficient is symbolised by r.
相关度衡量的是两个共变量之间线性关系的强度和方向。相关系数用符号 r 表示。
Pearson's r = Σxy / √Σx² × Σy²
A positive correlation means that as one variable increases, the other also tends to increase. A negative correlation indicates an inverse relationship.
正相关意味着一个变量增加时，另一个也倾向于增加。负相关表示反向关系。
The closer r is to +1 or –1, the stronger the relationship; an r near 0 suggests a weak or no linear association. Correlation does not imply causation.
r 越接近 +1 或 –1，关系越强；r 接近 0 表明线性关联微弱或不存在。相关不意味着因果关系。
Spearman's rank correlation coefficient (ρ or rₛ) is used when data are ordinal or when the relationship is monotonic but not necessarily linear.
斯皮尔曼等级相关系数 (ρ 或 rₛ) 用于定序数据或关系是单调但不必是线性的情况。
4. Inferential Statistics Essentials | 推断统计基础
Inferential statistics allow psychologists to draw conclusions about a population from a sample. The p‑value is the probability of obtaining a result at least as extreme as the observed one, assuming the null hypothesis is true.
推断统计让心理学家可以从样本对总体做出结论。p 值是假定零假设为真时，得到至少与观察结果一样极端的结果的概率。
tistically significant and the null hypothesis (H₀) is rejected. The typical significance level α is set at 5%.
如果 p ≤ 0.05，结果被宣布为统计显著，拒绝零假设 (H₀)。典型的显著性水平 α 设定为 5%。
A Type I error is a false positive – rejecting a true null hypothesis. A Type II error is a false negative – failing to reject a false null hypothesis.
I 类错误是假阳性——拒绝了真的零假设。II 类错误是假阴性——未能拒绝错误的零假设。
The observed value of a test statistic (e.g. U, S, χ²) must be compared with a critical value from a table. The critical value depends on N, the chosen significance level, and whether the test is one‑tailed or two‑tailed.
检验统计量的观察值（例如 U, S, χ²）必须与表中的临界值进行比较。临界值取决于 N、所选显著性水平以及检验是单尾还是双尾。
5. The Multi-Store Model of Memory | 记忆的多存储模型
Information flows through three separate stores: the sensory register, short‑term memory (STM) and long‑term memory (LTM), as proposed by Atkinson and Shiffrin.
信息流经三个独立的存储：感觉登记、短时记忆（STM）和长时记忆（LTM），由 Atkinson 和 Shiffrin 提出。
The sensory register holds modality‑specific information for a very brief duration (around 0.25–2 seconds) but has a virtually unlimited capacity. Attention transfers selected items to STM.
感觉登记以特定感觉形态保持信息，持续时间极短（约 0.25–2 秒），但容量几乎无限。注意将选中的项目转入 STM。
STM has a limited capacity of approximately 7 ± 2 items and a duration of around 18– rsal. Maintenance rehearsal can keep information in STM and eventually encode it into LTM.
STM 的容量有限，约为 7 ± 2 个项目，不经复述的持续时间约为 18–30 秒。维持性复述可把信息保持在 STM 中并最终编码进入 LTM。
LTM is a permanent store with unlimited capacity. Forgetting occurs mostly through interference or retrieval failure rather than decay.
LTM 是一个永久的存储，容量无限。遗忘主要源于干扰或提取失败，而非痕迹消退。
6. Attachment Theories and Laws | 依恋理论与定律
Bowlby's monotropic theory states that infants have an innate drive to become attached to one primary caregiver. This attachment provides a secure base and acts as an internal working model for later relationships.
Bowlby 的单一依恋理论指出，婴儿具有与一个主要照顾者建立依恋的内驱力。这种依恋提供了一个安全基地，并成为日后关系的内部工作模型。
The law of continuity proposes that the more constant and predictable the caregiving, the stronger the attachment. The law of accumulated separation warns that repeated separations can damage the bond.
连续性定律提出，照料行为越稳定和可预测，依恋就越牢固。累积分离定律告诫，反复的分离会损害依恋纽带。
Lorenz's principle of imprinting showed that in certain species, attachment forms rapidly during a critical period based on the first moving object seen. Harlow's contact‑comfort theorem demonstrated that tactile comfort is more important than food in forming attachment.
洛伦兹的印刻原理表明，某些物种的依恋在关键期内快速形成，基于看到的第一个移动物体。哈洛的接触安慰定理证明，触觉安慰比食物对形成依恋更重要。
Ainsworth's Strange Situation identified three main attachment styles, showing that sensitive responsiveness consistently leads to secure attachment – a key predictive principle.
安斯沃思的陌生情境识别出三种主要依恋风格，表明敏感的回应始终导致安全依恋——这是一个关键的预测原则。
7. Social Influence Principles | 社会影响原理
Normative social influence describes conformity driven by the desire to be liked and accepted. This often leads to public compliance without private acceptance.
规范社会影响描述了因渴望被喜欢和接纳而产生的从众。这常导致公开顺从而私下并不接受。
Informational social influence occurs when individuals accept information from others as evidence about reality, particularly in ambiguous situations. It can lead to genuine internalisation.
信息社会影响发生在个体接受他人信息作为现实证据时，尤其是在模糊情境下。它能导致真正的内化。
Obedience to authority is shaped by situational factors, including proximity of the authority figure, perceived legitimacy of the context, and the presence of disobedient role models – a set of situational axioms derived from Milgram's research.
对权威的服从由情境因素塑造，包括权威人物的接近度、情境的感知合法性以及不服从榜样的存在——这组情境公理源于米尔格拉姆的研究。
Minority influence is most effective when the minority is consistent, shows commitment, and demonstrates flexibility. The conversion theorem states that a consistent minority can trigger private attitude change through deeper processing.
少数派影响在小团体保持一致、投入承诺且展现灵活性时最为有效。转换定理指出，一致的少数派可以通过深层加工引发私下态度转变。
8. Psychopathology: Key Diagnostic Formulae | 心理病理学：关键诊断准则
Statistical infrequency defines abnormality as any behaviour that is statistically rare, typically falling more than two standard deviations from the population mean.
统计稀有性将异常定义为任何在统计上罕见的行为，通常落在总体平均值两个标准差之外。
Deviation from social norms sees abnormality as behaviour that violates implicit or explicit rules of society. Such judgements are culturally and historically relative.
社会规范偏离将异常视为违反社会隐性或显性规则的行为。这种判断具有文化和历史相对性。
Failure to function adequately is operationalised by Rosenhan and Seligman's seven criteria, including personal distress, unpredictability and observer discomfort. The distress‑dysfunction index requires at least two criteria to be met.
功能失调由 Rosenhan 和 Seligman 的七条标准进行操作，包括个人痛苦、不可预测性和观察者不适。痛苦‑功能障碍指数要求至少满足两条标准。
Deviation from ideal mental health, derived from Jahoda, catalogs six characteristics of optimal living. The failure to display a sufficient number of these characteristics is taken as a sign of disorder.
偏离理想心理健康源自 Jahoda，列举了最佳生活的六项特征。未能展现足够数量的这些特征被视作障碍的迹象。
9. Research Design and Ethics | 研究设计与伦理
The independent variable (IV) is the factor manipulated by the researcher; the dependent variable (DV) is the outcome measured. All other potential influences are called extraneous variables.
自变量 (IV) 是研究者操纵的因素；因变量 (DV) 是测量到的结果。所有其他潜在影响称为额外变量。
Counterbalancing is a technique used in repeated‑measures designs to control for order effects. It ensures that each condition appears equally often in each ordinal position.
平衡法是一项用于重复测量设计的技术，用以控制顺序效应。它确保每种条件在各个顺序位置上出现频率相同。
Ethical guidelines are summarised by the acronym COPCAR: Consent, Deception protection, Right to withdraw, Protection from harm, Confidentiality, and Debriefing.
伦理指南可以用 COPCAR 来概括：知情同意、免受欺骗保护、退出权利、免受伤害保护、保密以及事后解说。
A pilot study is a small‑scale trial conducted before the main investigation to check procedures, instructions, and the measurement of variables. It can prevent costly design flaws.
先导研究是在主要调查之前进行的小规模试验，以检查程序、指导语和变量测量。它可以避免代价高昂的设计缺陷。
10. Quick Revision of Key Formulae | 关键公式速查
Percentage change = [(new value – . This is useful for interpreting longitudinal data or the size of an experimental effect.
百分比变化 = [(新值 – 旧值) / 旧值] × 100。这对解释纵向数据或实验效应大小很有用。
Chi‑square (χ²) = Σ [ (O – E)² / E ]
xpected frequency. The degrees of freedom (df) for a contingency table are (number of rows – 1) × (number of columns – 1).
其中 O 为观察频数，E 为期望频数。列联表的自由度（df）为 (行数 – 1) × (列数 – 1)。
Sign test: S = the smaller of the two totals (plus or minus signs)
The sign test compares the number of positive and negative differences in a repeated‑measures design. The observed S is compared with a critical value of S to judge significance.
符号检验比较重复测量设计中正差异和负差异的个数。观察到的 S 值与临界 S 值进行比较以判断显著性。
When calculating effect size with Cohen's d, a value of 0.2 is considered small, 0.5 medium, and 0.8 large. Effect size adds meaning to statistical significance.
使用科恩 d 计算效应量大小时，0.2 被认为小，0.5 中等，0.8 大。效应量能为统计显著性增添意义。
Remember that all formulae used in Year 12 AQA Psychology rely on simple arithmetic and clearly labelled symbols. Keep this sheet close during exam practice to build automatic recall.
请记住，Year 12 AQA 心理学中使用的所有公式都依赖于简单算术和清晰标记的符号。在考试练习期间将本页放在手边，以建立自动回忆。
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