Patriarchy in Statistical Analysis | 统计分析中的父权制

📚 Patriarchy in Statistical Analysis | 统计分析中的父权制

In Edexcel A-Level Mathematics, statistical methods are often tested through real-world contexts. One such context is the study of patriarchy, where we can examine gender-based differences in earnings, education or representation. This article uses the theme of patriarchy to revise key S1 and S2 topics: sampling, descriptive statistics, probability, the normal distribution, hypothesis testing and regression.

在 Edexcel A-Level 数学中，统计方法经常通过现实背景来考查。其中一个背景就是父权制研究，我们可以通过它来审视收入、教育或代表性方面的性别差异。本文以父权制为主题，复习 S1 和 S2 中的关键内容：抽样、描述性统计、概率、正态分布、假设检验和回归。

1. Defining the Context: Patriarchy as a Data Theme | 定义背景：父权制作为数据主题

In statistical work, a “context” is the real-world setting that gives meaning to numbers. Patriarchy refers to social structures in which men hold disproportionate power, and it can be studied quantitatively using data on wages, promotions, household labour or political representation. For Edexcel S1/S2, you do not need to evaluate patriarchy itself, but you must be able to describe data, choose suitable diagrams and carry out inferences.

在统计工作中，“背景”是赋予数字意义的现实场景。父权制指的是男性掌握不成比例权力的社会结构，可以通过工资、晋升、家务劳动或政治代表性等数据来定量研究。对于 Edexcel S1/S2，你不需要评价父权制本身，但必须能够描述数据、选择合适的图表并进行推断。

• Typical variables: hourly wage, promotion time, years of education, percentage of female managers.
• 典型变量：时薪、晋升时间、受教育年限、女性管理者百分比。

2. Sampling and Bias in Gender Research | 性别研究中的抽样与偏差

Before any inference, you need a sample that is representative. If a survey on the gender pay gap only samples full-time employees in one industry, it may not generalise to all workers. A census is often impractical, so random sampling methods are used. Common methods include simple random sampling, stratified sampling and cluster sampling.

在进行任何推断之前，你需要一个有代表性的样本。如果一项关于性别薪酬差距的调查只抽取一个行业的全职员工，它可能无法推广到所有劳动者。普查通常不切实际，因此使用随机抽样方法。常见方法包括简单随机抽样、分层抽样和整群抽样。

• Simple random sampling: every member has an equal chance of selection.
• 简单随机抽样：每个成员都有相等被选中的机会。
• Stratified sampling: divide into gender groups and sample proportionally.
• 分层抽样：按性别分组并按比例抽样。
• Quota sampling: non-random, may introduce bias if interviewers choose participants.
• 配额抽样：非随机，如果访员选择参与者可能引入偏差。

3. Descriptive Statistics: Mean, Median and Spread | 描述性统计：均值、中位数与离散程度

For a data set on female and male earnings, the mean gives the arithmetic average, while the median is the middle value when data are ordered. If the distribution is skewed by a few very high male salaries, the median may be a better measure of central tendency. The sample mean is calculated as x̄ = (Σxᵢ)/n.

对于女性和男性收入数据集，均值给出算术平均值，而中位数是数据排序后的中间值。如果分布受少数极高的男性薪资影响而偏斜，中位数可能是更好的集中趋势度量。样本均值计算为 x̄ = (Σxᵢ)/n。

x̄ = (Σxᵢ)/n

Spread is measured by range, interquartile range (IQR) and standard deviation. The sample standard deviation uses n – 1 in the denominator to give an unbiased estimate: s = √[Σ(xᵢ – x̄)² / (n – 1)].

离散程度用全距、四分位距（IQR）和标准差来衡量。样本标准差使用 n – 1 作为分母以给出无偏估计：s = √[Σ(xᵢ – x̄)² / (n – 1)]。

s = √[Σ(xᵢ – x̄)² / (n – 1)]

4. Box Plots and Outliers | 箱线图与异常值

A box plot is useful for comparing male and female salary distributions side by side. It shows the minimum, lower quartile Q₁, median Q₂, upper quartile Q₃ and maximum. Outliers are often defined as values below Q₁ – 1.5 × IQR or above Q₃ + 1.5 × IQR. If the female salary distribution has a lower median and a smaller IQR, that suggests a concentration around lower pay levels.

箱线图对于并排比较男性和女性薪资分布很有用。它显示最小值、下四分位数 Q₁、中位数 Q₂、上四分位数 Q₃ 和最大值。异常值通常定义为低于 Q₁ – 1.5 × IQR 或高于 Q₃ + 1.5 × IQR 的值。如果女性薪资分布有较低的中位数和较小的 IQR，这表明薪资集中在较低水平。

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