📚 AS CIE Sociology: Formula & Theorem Quick Reference Guide | AS CIE 社会学：公式定理速查手册
This quick reference handbook condenses key sociological theories, models and research-method equations into concise “formulas” and “theorems” for AS CIE Sociology (9699). It is designed to help you memorise core mechanisms, from socialisation to sampling error, through clear, paired-language summaries.
本速查手册将 AS CIE 社会学（9699）的核心理论、模型和研究方法方程提炼为简洁的“公式”与“定理”。通过清晰的中英双语对照摘要，帮助你牢记从社会化过程到抽样误差的关键机制。
1. The Core Formula of Socialisation | 社会化的核心公式
Socialisation is the lifelong process through which individuals learn and internalise the norms, values and roles of their society. It can be represented as:
社会化是个体终身学习和内化其社会规范、价值观与角色的过程。它可以用如下公式表示：
Internalisation + Reinforcement → Norms, Values & Roles
Internalisation occurs when we absorb cultural rules so deeply that they feel natural; reinforcement comes from sanctions (rewards and punishments) administered by agents of social control.
内化是指我们如此深刻地吸收文化规则，以至于它们成为天性；强化来自社会控制主体施加的奖惩（制裁）。
Key agents of socialisation include the family, schools, peer groups, mass media and, later, the workplace. Each transmits a partial version of culture, shaping the individual’s social identity.
主要的社会化媒介包括家庭、学校、同辈群体、大众传媒以及后来的工作场所。每一种媒介都传递着文化的部分版本，塑造着个体的社会认同。
2. Cultural Reproduction Equation – Bourdieu | 布迪厄的文化再生产方程
Pierre Bourdieu argued that the education system reproduces class inequalities by privileging the cultural capital of the dominant class. His model can be summarised as:
皮埃尔·布迪厄指出，教育系统通过赋予统治阶级文化资本以特权，从而再生产阶级不平等。他的模型可以概括为：
Cultural Capital (embodied, objectified, institutionalised) + Habitus + Field → Reproduction of Social Class
Cultural capital includes linguistic styles, tastes and qualifications; habitus is a set of deeply ingrained dispositions; and the field is the social arena where struggles over resources occur. Middle-class children enter school already equipped with the dominant cultural capital, giving them an inherent advantage.
文化资本包括语言风格、品味和学历资格；惯习是一套根深蒂固的性情倾向；场域则是资源争夺的社会竞技场。中产阶级子女入学时已具备主流文化资本，因而拥有先天优势。
3. Functional Fit of the Family – Parsons | 帕森斯的家庭功能等式
Talcott Parsons proposed that the nuclear family has a ‘functional fit’ with industrial society. As society evolved, the family lost many of its previous functions and specialised in two irreducible functions:
塔尔科特·帕森斯提出，核心家庭与工业社会存在“功能匹配”。随着社会演变，家庭失去了许多原有功能，专门承担两项不可替代的功能：
Primary Socialisation + Stabilisation of Adult Personalities = Nuclear Family Function
Primary socialisation refers to equipping children with the basic norms of society; stabilisation of adult personalities (the ‘warm bath’ theory) describes the emotional support spouses provide each other after the stresses of work. The extended family becomes less necessary because the nuclear family is geographically and socially mobile.
初级社会化指让孩子掌握社会的基本规范；成年人格的稳定化（“热水澡”理论）描述了配偶在应对工作压力后相互提供的情感支持。由于核心家庭具备地理和社会流动性，扩展家庭的必要性降低。
4. Labelling Theory and the Deviance Amplification Spiral | 标签理论与偏差放大螺旋
Howard Becker and Edwin Lemert demonstrated that deviance is socially constructed through societal reaction. The sequence of amplification can be expressed as:
霍华德·贝克尔与埃德温·莱默特指出，偏差是通过社会反应被建构出来的。放大过程的序列可表达为：
Primary Deviance → Societal Label → Master Status → Secondary Deviance → Deviant Career
Primary deviance is the initial rule-breaking act, which often goes unnoticed. Once the act is labelled and internalised as a ‘master status’, the individual may experience blocked opportunities and respond with further deviance (secondary deviance), eventually joining a deviant subculture.
初级偏差是最初的违规行为，往往未被注意。一旦该行为被贴上标签并内化为“主要身份”，个体可能面临机会受阻，并以进一步的偏差（次级偏差）作为回应，最终加入偏差亚文化，形成偏差生涯。
5. Weber’s Multidimensional Stratification Formula | 韦伯的多维社会分层公式
Max Weber viewed social stratification as more complex than Marx’s single class division. He identified three interlinked dimensions:
马克斯·韦伯认为社会分层比马克思的单一阶级划分更为复杂。他提出了三个相互关联的维度：
Social Stratification = f (Class, Status, Party)
Class is determined by economic position (market situation); Status refers to social prestige and lifestyle; Party denotes the ability to influence political power. These dimensions may overlap but also operate independently, producing a nuanced picture of inequality.
阶级由经济地位（市场处境）决定；地位指社会声望和生活方式；政党指影响政治权力的能力。这些维度既可能重叠，也可以独立运作，从而描绘出一幅精细的不平等图景。
6. Standard Error and Confidence Interval Formulas | 抽样误差与置信区间公式
In sociological research, probability sampling allows researchers to estimate population parameters. The standard error of the sample mean indicates how far the sample mean is likely to be from the true population mean:
在社会学研究中，概率抽样使研究者能够估计总体参数。样本平均值的标准误差反映样本均值与真实总体均值之间可能的偏差：
SE = σ / √n
where σ is the population standard deviation and n is the sample size. When σ is unknown, the sample standard deviation s is used. The 95% confidence interval for the mean is:
其中 σ 是总体标准差，n 为样本大小。当 σ 未知时，用样本标准差 s 替代。均值的 95% 置信区间为：
CI = x̄ ± 1.96 × SE
The z-value increases for higher confidence levels (e.g. 2.58 for 99% CI). Larger sample sizes reduce the standard error, producing narrower, more precise intervals.
置信水平越高，z 值越大（如 99% 置信区间用 2.58）。增大样本量可减小标准误差，得到更窄、更精确的区间。
Common z-values table:
| Confidence Level | z-value |
|---|---|
| 90% | 更多咨询请联系16621398022（同微信）
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