📚 Year 13 OCR Sociology: Formula & Theorem Quick Reference Handbook | OCR A2社会学公式定理速查手册
Welcome to the OCR Year 13 Sociology Quick Reference for formulas and theorems. Sociology may not be as equation-heavy as physics, but quantitative research methods demand a solid understanding of statistical formulas, and theoretical frameworks articulate key ‘theorems’ of social life. This guide consolidates the essential formulas for data analysis and the core theoretical propositions you need for the exam. Use it to revise measures of central tendency, dispersion, correlation, and inferential tests such as chi-square, alongside classic sociological theorems from functionalism, Marxism, and interactionism.
欢迎使用OCR A2社会学公式定理速查手册。社会学虽不像物理那样充斥着公式，但定量研究方法要求你扎实掌握统计公式，而理论框架则阐明了社会生活的关键“定理”。本指南汇总了数据分析必备公式和你考试所需的核心理论命题。利用它来复习集中趋势、离散程度、相关性和卡方等推论性检验，以及来自功能主义、马克思主义和互动论的经典社会学定理。
1. Measures of Central Tendency | 集中趋势度量
The three main measures of central tendency are the mean, median, and mode. They summarise the centre of a data set.
集中趋势的三个主要度量为平均数、中位数和众数，它们概括了数据集的中心。
Mean (arithmetic average): Sum of all values divided by the number of values. For a sample, it is often denoted by x̄.
平均数（算术平均）：所有数值之和除以数值个数。在样本中通常用 x̄ 表示。
Mean = Σx / n
Median: The middle value when data are ordered. If n is even, median = (value at position n/2 + value at position n/2 + 1) / 2.
中位数：数据排序后的中间值。若 n 为偶数，中位数 = (第 n/2 个值 + 第 n/2+1 个值) / 2。
Mode: The value that appears most frequently. A data set may have no mode, one mode (unimodal), or several modes (bimodal/multimodal).
众数：出现次数最多的数值。数据集可能无众数、有一个众数（单峰）或有多个众数（双峰/多峰）。
2. Measures of Dispersion | 离散程度度量
Dispersion tells us how spread out the data are. Key measures include range, interquartile range, variance, and standard deviation.
离散程度告诉我们数据的分散程度。关键度量包括极差、四分位距、方差和标准差。
Range: Maximum value minus minimum value.
极差：最大值 – 最小值。
Interquartile Range (IQR): Q3 – Q1, where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile).
四分位距 (IQR)：Q3 – Q1，其中 Q1 为第一四分位数（第25百分位数），Q3 为第三四分位数（第75百分位数）。
Sample variance (s²): Average of squared deviations from the mean. Formula:
样本方差 (s²)：距离均值的偏差平方的平均值。公式：
s² = Σ(x – x̄)² / (n – 1)
Sample standard deviation (s): Square root of variance.
样本标准差 (s)：方差的平方根。
s = √[ Σ(x – x̄)² / (n – 1) ]
Population standard deviation (σ): Uses N instead of n-1, and population mean μ.
总体标准差 (σ)：用 N 代替 n-1，使用总体均值 μ。
σ = √[ Σ(x – μ)² / N ]
3. The Pearson Correlation Coefficient (r) | 皮尔逊相关系数 (r)
Pearson’s r measures the strength and direction of a linear relationship between two continuous variables (e.g., income and health). It ranges from -1 to +1.
皮尔逊 r 衡量两个连续变量（如收入和健康）之间线性关系的强度和方向，取值范围从 -1 到 +1。
r = Σ[(x – x̄)(y – ȳ)] / √[Σ(x – x̄)² Σ(y – ȳ)²]
Interpretation: r = +1 perfect positive correlation; r = 0 no linear correlation; r = -1 perfect negative correlation. Typically, 0.1-0.3 weak, 0.4-0.6 moderate, 0.7-0.9 strong.
解读：r = +1 完全正相关；r = 0 无线性相关；r = -1 完全负相关。通常 0.1-0.3 弱相关，0.4-0.6 中等相关，0.7-0.9 强相关。
Coefficient of determination (r²): The proportion of variance in y explained by x.
决定系数 (r²)：由 x 解释的 y 的方差比例。
4. Chi-Square Test (χ²) | 卡方检验 (χ²)
The chi-square test of association is used with categorical (nominal) data to see if two variables are related or independent. It compares observed frequencies with expected frequencies.
卡方关联检验用于分类（名义）数据，判断两个变量是否相关或独立。它比较观测频数和期望频数。
χ² = Σ [ (O – E)² / E ]
where O = observed frequency, E = expected frequency. Expected frequency = (row total x column total) / grand total.
其中 O = 观测频数，E = 期望频数。期望频数 = (行合计 x 列合计) / 总计。
Degrees of freedom (df): For a contingency table, df = (number of rows – 1) x (number of columns – 1). Compare calculated χ² with critical value at chosen significance level (usually 0.05). If χ² calculated > critical, reject the null hypothesis of independence.
自由度 (df)：对于列联表，df = (行数 – 1) x (列数 – 1)。将计算所得 χ² 与所选显著性水平（通常 0.05）的临界值比较。若计算 χ² > 临界值，拒绝独立的零假设。
5. Choosing the Right Statistical Test | 选择正确统计检验
Choosing an appropriate test is crucial for validity. Consider the level of measurement (nominal, ordinal, interval/ratio) and the research purpose (difference, correlation, association).
选择恰当的检验对效度至关重要。需考虑测量水平（名义、定序、定距/定比）和研究目的（差异、相关、关联）。
For a test of difference between two unrelated groups on interval data, an independent t-test is used. (中文：对于两个独立组在定距数据上的差异检验，使用独立样本 t 检验。)
For comparing the same group before and after (paired data), use a paired t-test. (中文：比较同一组前后数据（配对数据），使用配对 t 检验。)
For difference among three or more groups on interval data, one-way ANOVA is appropriate. (中文：对三个或以上组在定距数据上的差异，适用单因素方差分析。)
For ordinal data from two unrelated groups, the Mann-Whitney U test is used; for paired ordinal data, use Wilcoxon signed-rank. (中文：对于两个独立组的定序数据，使用曼-惠特尼 U 检验；对于配对的定序数据，使用威尔科克森符号秩检验。)
For correlation between two interval variables, use Pearson’s r; for ordinal or non-normal interval data, use Spearman’s rho. (中文：对于两个定距变量的相关，使用皮尔逊 r；对于定序或非正态定距数据，使用斯皮尔曼 rho。)
For association between two nominal variables, use chi-square test of association. (中文：对于两个名义变量的关联，使用卡方关联检验。)
6. Key Demographic Rate Formulas | 重要人口率公式
Sociologists frequently use rates to study population processes. The following formulas are standard in demography.
社会学家常用率来研究人口过程。以下是人口学中的标准公式。
Crude Birth Rate (CBR): Number of live births per 1,000 population in a given year.
粗出生率 (CBR)：某年每千人口活产数。
CBR = (Live births / Total population) × 1000
Crude Death Rate (CDR): Number of deaths per 1,000 population in a year.
粗死亡率 (CDR)：某年每千人口死亡数。
CDR = (Deaths / Total population) × 1000
General Fertility Rate (GFR): Number of live births per 1,000 women aged 15-44 (or 15-49) in a year.
一般生育率 (GFR)：某年每千名15-44（或15-49）岁妇女的活产数。
GFR = (Live births / Women aged 15-44) × 1000
Crime Rate: Number of recorded crimes per 1,000 or 100,000 population.
犯罪率：每千人或十万人中记录在案的犯罪数量。
Crime Rate = (Recorded offences / Total population) × 1000 (or 100,000)
7. Anomie-Strain Theorem (Merton) | 失范—紧张定理 (默顿)
Merton’s strain theorem states: When a society places strong emphasis on culturally approved goals (e.g., wealth) but provides unequal access to legitimate means, a state of anomie arises, leading to deviant adaptations.
默顿的紧张定理指出：当一个社会过分强调文化上认可的目标（如财富），但通往合法手段的机会分配不均时，就会产生失范状态，从而导致越轨适应模式。
The five adaptations form a typological theorem: conformity, innovation, ritualism, retreatism, and rebellion. Innovation (accepting goals, rejecting or lacking means) is the most common source of working-class crime.
五种适应模式构成一种类型学定理：遵从、创新、仪式主义、退却主义和反叛。创新（接受目标，拒绝或缺乏手段）是工人阶级犯罪最常见的来源。
8. False Consciousness Theorem (Marx) | 虚假意识定理 (马克思)
Marx’s theorem of class consciousness: The proletariat’s transition from a ‘class in itself’ to a ‘class for itself’ is impeded by false consciousness—ideological distortion perpetuated by the ruling class that masks the true exploitative nature of capitalism.
马克思的阶级意识定理：无产阶级从“自在阶级”向“自为阶级”的转变受到虚假意识的阻碍——一种由统治阶级维持的意识形态扭曲，掩盖了资本主义真实的剥削本质。
When false consciousness prevails, workers misidentify their real interests and accept the existing order. Revolution becomes possible only when class consciousness and revolutionary consciousness develop.
当虚假意识盛行时，工人会错认自己的真实利益并接受现有秩序。只有当阶级意识和革命意识发展起来，革命才成为可能。
9. Labelling Theorem (Becker) | 标签定理 (贝克尔)
Becker’s labelling theorem: Deviance is not an inherent quality of an act but the result of the application by others of rules and sanctions to an ‘offender’. The deviant is one to whom the label has been successfully applied.
贝克尔的标签定理：越轨并非行为固有的性质，而是他人对“违规者”运用规则和制裁的结果。越轨者就是那个被成功贴上标签的人。
This leads to a self-fulfilling prophecy: labelling can create a master status, reinforce deviant identity, and push individuals into secondary deviance and deviant careers.
这导致自证预言：贴标签会制造一种主导身份，强化越轨认同，并将个体推向继发越轨和越轨生涯。
10. Hidden Curriculum Reproduction Theorem | 隐性课程再生产定理
Bowles and Gintis’s correspondence theorem states that the hidden curriculum of schooling reproduces the social relations of production. Schools mirror the workplace by rewarding obedience, punctuality, and acceptance of hierarchy.
鲍尔斯和金蒂斯的对应定理指出，学校教育的隐性课程再生产了生产中的社会关系。学校通过奖励服从、守时和接受等级制度，映射了职场。
This theorem explains how class inequality is reproduced across generations: working-class pupils are socialised to accept subordinate roles, while middle-class pupils internalise values of autonomy and leadership.
该定理解释了阶级不平等如何跨代再生产：工人阶级学生被社会化以接受从属角色，而中产阶级学生则内化自主和领导的价值观。
11. Cultural Capital Conversion Theorem (Bourdieu) | 文化资本转换定理 (布迪厄)
Bourdieu’s theorem: Cultural capital (knowledge, tastes, credentials) can be converted into economic capital and social capital. The education system legitimates this conversion by treating cultural capital as innate ability.
布迪厄的定理：文化资本（知识、品味、文凭）可以转换为经济资本和社会资本。教育系统将文化资本视为天赋能力，从而使这种转换合法化。
Thus, middle-class children who possess the dominant cultural codes are at an advantage, while working-class children’s lived culture is devalued, reproducing class inequality through symbolic violence.
因此，拥有主导文化符码的中产阶级子女占据优势，而工人阶级子女的生活文化被贬低，通过符号暴力再生产阶级不平等。
12. McDonaldization Theorem (Ritzer) | 麦当劳化定理 (瑞泽尔)
Ritzer’s McDonaldization theorem: The principles of the fast-food restaurant—efficiency, calculability, predictability, and control—are coming to dominate more sectors of society through rationalization. This process is an extension of Weber’s theory of rationalization and can lead to the ‘irrationality of rationality’.
瑞泽尔的麦当劳化定理：快餐店的原则——效率、可计算性、可预测性和控制——正通过合理化主导越来越多的社会领域。这一过程是韦伯合理化理论的延伸，并可能导致“理性的非理性化”。
As globalization spreads, local cultures are homogenised into a predictable, standardized form, diminishing human creativity and diversity.
随着全球化蔓延，地方文化被同化为一种可预测的、标准化的形式，削弱了人类的创造力和多样性。
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