📚 Year 13 CCEA Sociology: Quick Reference Handbook of Formulas and Theorems | CCEA Year 13 社会学：公式定理速查手册
This quick reference handbook is designed for Year 13 CCEA Sociology students. It condenses key statistical formulas, methodological concepts, and the core propositions of major sociological theories – the ‘theorems’ that underpin A-level analysis – into one accessible guide. Whether you are revising research methods or consolidating your understanding of structural and interpretivist perspectives, use this resource to boost your confidence and exam efficiency.
本速查手册专为 CCEA Year 13 社会学学生设计。它将关键的统计公式、方法论概念以及主要社会学理论的核心命题——支撑 A-level 分析的“定理”——浓缩为一册便捷指南。无论你是在复习研究方法，还是巩固对结构论和解释论视角的理解，都可以利用此资源提升考试信心与效率。
1. Key Methodological Concepts and Ethical Principles | 关键方法论概念与伦理原则
Validity: The extent to which a research instrument measures what it claims to measure. High internal validity means the findings accurately reflect the social reality being studied; high external validity means results can be generalised beyond the study context.
效度： 研究工具测量其所声称测量的内容的程度。高内部效度意味着研究结果准确反映了所研究的社会现实；高外部效度意味着结果可以推广到研究情境之外。
Reliability: The consistency and repeatability of research findings. If a study is reliable, using the same method on the same sample would produce the same or very similar results. Methods such as structured interviews and questionnaires often yield higher reliability.
信度： 研究结果的一致性和可重复性。如果一项研究是可靠的，那么在相同样本上使用相同方法会产生相同或非常相似的结果。结构化访谈和问卷等方法通常能产生更高的信度。
Representativeness: The degree to which the sample reflects the characteristics of the target population. A large, randomly selected sample improves representativeness and allows researchers to make generalisations.
代表性： 样本反映目标总体特征的程度。大规模随机抽取的样本可以提高代表性，使研究者能够进行概括。
Ethical Principles (BSA guidelines): Informed consent – participants must agree to take part based on full understanding of the research. Anonymity and confidentiality – identities must be protected. Protection from harm – researchers must avoid physical, psychological or social harm. Right to withdraw – participants can leave the study at any time.
伦理原则（英国社会学协会指导方针）： 知情同意——参与者必须在充分了解研究的基础上同意参与。匿名与保密——必须保护参与者的身份。防止伤害——研究者必须避免造成身体、心理或社会伤害。退出权——参与者可以随时退出研究。
2. Sampling Methods and Sampling Error | 抽样方法与抽样误差
Simple Random Sample: Every member of the target population has an equal chance of being selected. It minimises bias but requires a complete sampling frame.
简单随机抽样： 目标总体中的每个成员都有相同被选中的机会。它最大限度地减少了偏差，但需要一个完整的抽样框。
Stratified Sample: The population is divided into relevant strata (e.g., age, gender) and random samples are drawn from each in proportion to their size. This improves representativeness for key subgroups.
分层抽样： 将总体划分为相关层次（如年龄、性别），然后按比例从各层中随机抽取样本。这提高了关键子群体的代表性。
Sampling Error (Standard Error of the Mean): The standard deviation of the sample means distribution. It indicates how much the sample mean is expected to fluctuate from the true population mean.
SE = σ / √n
抽样误差（均值的标准误）： 样本均值分布的标准差。它表明样本均值预期与真实总体均值之间的波动程度。
标准误 = σ / √n
Confidence Interval (95%): x̄ ± 1.96 × (σ / √n). If this range is calculated, we can be 95% confident that it contains the population mean.
置信区间（95%）： 样本均值 ± 1.96 × (σ / √n)。如果计算出该范围，我们可以有 95% 的把握认为它包含了总体均值。
3. Measures of Central Tendency | 集中趋势测度
Mean (x̄): The arithmetic average.
x̄ = Σx / n
平均值 (x̄)： 算术平均数。
x̄ = Σx / n
Median: The middle value when data are arranged in order. It is not influenced by extreme outliers, making it useful for skewed distributions such as income data.
中位数： 将数据按顺序排列后处于中间位置的值。它不受极端异常值的影响，因此适用于收入等偏态分布数据。
Mode: The most frequently occurring value. It can be used with nominal data (e.g., most common ethnic group) but may be less informative with continuous data.
众数： 出现频率最高的值。可用于名义数据（如最常见的族裔群体），但对于连续数据可能信息量较少。
4. Measures of Dispersion | 离散程度测度
Range: The difference between the highest and lowest values. It is simple to calculate but highly sensitive to outliers.
全距： 最大值与最小值之差。计算简单，但对异常值高度敏感。
Interquartile Range (IQR): The range of the middle 50% of data (Q3 – Q1). It is resistant to outliers and often used alongside the median.
四分位距 (IQR)： 中间 50% 数据的范围（第三四分位数 – 第一四分位数）。不易受异常值影响，常与中位数一起使用。
Variance (σ² for population, s² for sample): The average squared deviation from the mean.
σ² = Σ(x − μ)² / N s² = Σ(x − x̄)² / (n−1)
方差（总体 σ²，样本 s²）： 离差平方的平均值。
σ² = Σ(x − μ)² / N s² = Σ(x − x̄)² / (n−1)
Standard Deviation (σ or s): The square root of the variance. It is the most widely used measure of dispersion and is expressed in the original units of measurement.
σ = √[Σ(x − μ)² / N] s = √[Σ(x − x̄)² / (n−1)]
标准差 (σ 或 s)： 方差的平方根。它是使用最广泛的离散程度测度，与原始数据单位相同。
σ = √[Σ(x − μ)² / N] s = √[Σ(x − x̄)² / (n−1)]
5. Correlation and Tests of Association | 相关性与关联性检验
Spearman’s Rank Correlation Coefficient (rₛ): Used to test the strength and direction of association between two ranked (ordinal) variables. The value ranges from −1 (perfect negative) to +1 (perfect positive).
rₛ = 1 − (6 Σ d²) / [n (n² − 1)]
斯皮尔曼等级相关系数 (rₛ)： 用于检验两个定序变量之间关联的强度和方向。值域从 −1（完全负相关）到 +1（完全正相关）。
rₛ = 1 − (6 Σ d²) / [n (n² − 1)]
Chi-Square Test (χ²): Tests for association or independence between two categorical variables. It compares observed frequencies with expected frequencies under the null hypothesis of no association.
卡方检验 (χ²)： 检验两个类别变量之间的关联性或独立性。它在无关联的零假设下比较观察频数和期望频数。
Interpreting Correlation: Correlation does not imply causation. Sociologists must consider intervening variables and the direction of influence before drawing causal conclusions.
解释相关性： 相关关系不等于因果关系。社会学研究者在下因果结论前必须考虑中介变量和影响方向。
6. Core Propositions of Functionalism | 功能主义的核心命题
Organic Analogy Theorem: Society is like a biological organism. Each institution (family, education, religion) functions as an organ, contributing to the survival and stability of the whole social body.
有机类比定理： 社会像一个生物有机体。每一个制度（家庭、教育、宗教）如同一个器官，共同维持整个社会机体的生存与稳定。
Functional Prerequisites (AGIL): Parsons argued that for society to survive, it must meet four needs: Adaptation to the environment, Goal attainment, Integration of its members, and Latency (pattern maintenance). Any institution that fails to perform its function generates strain.
功能先决条件 (AGIL)： 帕森斯认为，社会要存续就必须满足四个需要：适应环境、目标达成、成员整合以及潜在模式维持。任何机构若不能履行其功能，就会产生紧张状态。
Manifest vs. Latent Functions (Merton): Manifest functions are intended and recognised consequences; latent functions are unintended and often hidden. For example, education’s manifest function is teaching skills, while its latent function may be occupying young people and reducing unemployment.
显性功能与隐性功能（默顿）： 显性功能是有意且被认识到的后果；隐性功能是无意且常隐藏的后果。例如，教育的显性功能是传授技能，隐性功能则可能是安置年轻人、降低失业率。
7. Core Propositions of Marxism | 马克思主义的核心命题
Base and Superstructure Theorem: The economic base – the relations and means of production – fundamentally shapes the superstructure, which includes the state, law, education, media and ideologies. However, the superstructure also helps reproduce the economic base.
经济基础与上层建筑定理： 经济基础——生产关系和生产资料——从根本上决定着上层建筑，包括国家、法律、教育、媒体和意识形态。然而上层建筑也有助于再生产经济基础。
Class Struggle as Engine of History: All history is the history of class struggles. In capitalist society, the conflict between the bourgeoisie (owners) and proletariat (workers) will eventually lead to revolution and the establishment of a classless, communist society.
阶级斗争是历史动力： 一切历史都是阶级斗争的历史。在资本主义社会中，资产阶级（所有者）和无产阶级（工人）之间的冲突最终将导致革命，并建立起无阶级的共产主义社会。
Ideological Hegemony (Gramsci): The ruling class maintains dominance not only through coercion but through hegemony – winning consent by shaping ideas, values and norms via civil society institutions. This makes inequality appear natural.
意识形态霸权（葛兰西）： 统治阶级不仅通过强制手段，更通过霸权——借助市民社会机构塑造观念、价值观和规范、赢得同意——来维持统治。这使得不平等显得理所当然。
8. Core Propositions of Feminism | 女性主义的核心命题
Patriarchy Theorem: Society is structured by male dominance and female subordination. Patriarchy operates in all major institutions – the family, the workplace, the state and cultural representation – and is a source of systematic inequality.
父权制定理： 社会由男性支配和女性从属的结构构成。父权制贯穿所有主要制度——家庭、工作场所、国家和文化表征——是系统性不平等的根源。
Intersectionality Theorem: Gender inequality cannot be understood in isolation. It intersects with race, class, sexuality and disability to create distinct experiences of oppression. A black working-class woman’s experience of patriarchy differs from that of a white middle-class woman.
交叉性定理： 性别不平等不能被孤立理解。它与种族、阶级、性取向和残疾相互交织，形成独特的压迫体验。一位黑人工人阶级女性所经历的父权制与一位白人中产阶级女性截然不同。
Liberal, Radical and Marxist Feminist Propositions: Liberal feminism seeks legal reforms and equal opportunities; radical feminism sees patriarchy as the primary and most universal form of oppression, often rooted in biological reproduction; Marxist feminism links women’s subordination to capitalism’s need for unpaid domestic labour.
自由、激进和马克思主义女性主义命题： 自由女性主义追求法律改革和机会平等；激进女性主义认为父权制是最主要、最普遍的压迫形式，常根植于生物性再生产；马克思主义女性主义将妇女的从属地位与资本主义对无酬家务劳动的需求联系起来。
9. Understanding Social Stratification: Key Indices and Mobility | 理解社会分层：关键指标与流动
Gini Coefficient Measure: A statistical measure of inequality where 0 represents perfect equality and 1 represents maximum inequality. It is derived from the Lorenz curve and is used to compare income or wealth distributions across societies.
基尼系数测度： 衡量不平等的统计指标，0 代表完全平等，1 代表最大不平等。它基于洛伦兹曲线，用于比较不同社会的收入或财富分配状况。
Absolute Social Mobility Rate: The proportion of individuals who end up in a different social class from that of their parents. Formula:
Absolute Mobility = (Number in a different class) / (Total sample size)
绝对社会流动率： 最终与父母处于不同社会阶层的个体比例。公式：
绝对流动率 = （处于不同阶层的数量）/（样本总量）
Relative Mobility and Odds Ratios: Relative mobility measures the chances of individuals from different class origins reaching a particular destination class. For example, an odds ratio compares the chance of a service-class child staying in the service class with the chance of a working-class child entering it. If the ratio is far from 1.0, inequality of opportunity exists.
相对流动与几率比： 相对流动衡量来自不同阶层出身的个体进入某一特定目标阶层的机会。例如，一个几率比会比较高服务阶层子女留在服务阶层的机会与工薪阶层子女进入服务阶层的机会。若该比值远离 1.0，即表明存在机会不平等。
10. Strain Theory and Subcultural Theories: Adaptation Equations | 紧张理论与亚文化理论：适应等式
Merton’s Strain Theory Equation: Deviance results from a disjunction between culturally approved goals and the legitimate means to achieve them. Individuals can adapt in five ways according to their acceptance (+) or rejection (−) of goals and means:
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply