📚 Year 12 WJEC Statistics: Key Points for Experimental/Practical Assessment | WJEC 12年级统计：实验与实践考核要点
In the Year 12 WJEC Statistics course, the experimental or practical assessment often takes the form of a statistical project where you must plan, carry out, and evaluate an investigation. Success depends on understanding the statistical enquiry cycle, proper sampling, data handling, and clear communication of findings. This guide highlights the essential points you need to master for the practical component.
在 WJEC 12年级统计课程中，实验或实践考核通常以统计项目的形式出现，要求你规划、实施并评估一项调查。成功的关键在于理解统计探究周期、正确抽样、数据处理以及清晰地传达结果。本指南将重点阐述实践部分必须掌握的核心要点。
1. The Statistical Enquiry Cycle | 统计探究循环
The WJEC assessment framework follows a structured cycle: Problem (identify a question), Plan (design the study), Data (collect evidence), Analysis (apply statistical techniques), and Conclusion (interpret and evaluate). You must demonstrate each stage clearly in your project.
WJEC 评估框架遵循一个结构化的循环：问题（确定研究问题）、计划（设计研究方案）、数据（收集证据）、分析（应用统计技术）和结论（解释和评估）。你必须在项目中清晰地展示每个阶段。
Always refer back to the problem statement to ensure your analysis remains relevant.
务必反复回顾问题陈述，确保分析始终切题。
2. Defining the Problem and Hypotheses | 界定问题与假设
Begin with a clear, measurable research question and state null (H₀) and alternative (H₁) hypotheses where applicable. For example: ‘Does a new teaching method improve test scores compared to the traditional method?’ with H₀: μ₁ = μ₂, H₁: μ₁ > μ₂ (where μ₁ is the mean for the new method and μ₂ for the traditional method).
从一个清晰、可测量的研究问题入手，并在适用时陈述原假设 (H₀) 和备择假设 (H₁)。例如：”新教学方法是否比传统方法更能提高考试成绩？” 对应 H₀: μ₁ = μ₂, H₁: μ₁ > μ₂（其中 μ₁ 为新方法的均值，μ₂ 为传统方法的均值）。
Hypotheses must be framed before collecting data to avoid bias.
假设必须在收集数据之前设定，以避免偏差。
3. Sampling Methods and Their Strengths | 抽样方法及其优点
Select an appropriate sampling technique from simple random, stratified, systematic, cluster, or quota sampling. Justify your choice based on the population and practical constraints. For example, stratified sampling ensures representation of key subgroups, reducing sampling error.
从简单随机抽样、分层抽样、系统抽样、整群抽样或配额抽样中选择合适的抽样方法。根据总体和实际限制条件说明你的选择理由。例如，分层抽样确保关键子群体的代表性，减少抽样误差。
| Method | Key Advantage | Disadvantage |
|---|---|---|
| Simple Random | Unbiased, easy | Needs complete list |
| Stratified | Precise for subgroups | Complex to implement |
The table above compares common sampling methods. You should be able to explain how your chosen method addresses potential biases.
上表对比了常用的抽样方法，你需要能够阐述所选方法如何应对潜在偏差。
4. Designing Data Collection Instruments | 设计数据收集工具
Whether using questionnaires, interviews, or experiments, your instrument must collect relevant data without leading questions. Pilot testing is crucial to identify flaws. For experimental designs, consider control groups, randomisation, and replication to ensure validity.
无论是使用问卷、访谈还是实验，你的收集工具必须能够获取相关数据，且不包含诱导性问题。试点测试对于发现缺陷至关重要。对于实验设计，要考虑对照组、随机化和重复，以确保有效性。
For example, in a plant growth experiment, control variables like light, water, and soil type must be held constant.
例如，在植物生长实验中，光照、水分和土壤类型等控制变量必须保持不变。
5. Managing Bias and Data Quality | 管理偏差与数据质量
Awareness of bias types—selection bias, measurement bias, non-response bias—is essential. Describe steps taken to minimise each. Data quality dimensions include accuracy, timeliness, completeness, and relevance. Always check for outliers and anomalies.
认识到偏差的类型——选择偏差、测量偏差、无响应偏差——是至关重要的。描述你采取的减少每种偏差的措施。数据质量维度包括准确性、及时性、完整性和相关性。务必检查异常值和异常情况。
Use a pilot study to test procedures and refine your instruments before the main data collection.
在正式数据收集之前，通过试点研究测试流程并完善你的工具。
6. Organising and Presenting Data | 整理与呈现数据
Raw data must be cleaned and organised into frequency tables or stem-and-leaf diagrams. Choose appropriate graphical displays: bar charts for categorical data, histograms for continuous data, box plots for comparing distributions, and scatter diagrams for bivariate relationships.
原始数据必须经过清理，整理成频率表或茎叶图。选择合适的图形展示：条形图用于分类数据，直方图用于连续数据，箱线图用于比较分布，散点图用于双变量关系。
Always label axes, include a title, and provide a key if needed. The visualisation should highlight the patterns relevant to your hypothesis.
始终标记坐标轴、包含标题，并在需要时提供图例。可视化应突出与假设相关的模式。
7. Descriptive Statistics and Summary Measures | 描述性统计与汇总度量
Calculate measures of central tendency (mean, median, mode) and dispersion (range, interquartile range, standard deviation). For example, standard deviation s = √[ Σ(x – x̄)² / (n-1) ]. Use these to describe the data’s shape and spread.
计算集中趋势的度量（均值、中位数、众数）和离散程度（极差、四分位距、标准差）。例如，标准差 s = √[ Σ(x – x̄)² / (n-1) ]。使用这些度量描述数据的形态和离散程度。
A box plot can effectively show the five-number summary: minimum, Q₁, median, Q₃, maximum.
箱线图可以有效地展示五数概括：最小值、第一四分位数、中位数、第三四分位数、最大值。
8. Probability Distributions for Inference | 用于推断的概率分布
In Year 12 WJEC Statistics, you often use the Binomial distribution B(n, p) and the Normal distribution N(μ, σ²). Check conditions: for binomial, fixed number of trials, independent, same probability; for normal, symmetric bell-shaped data or using Central Limit Theorem for means.
在 WJEC 12年级统计中，你经常会用到二项分布 B(n, p) 和正态分布 N(μ, σ²)。检查条件：二项分布需要固定试验次数、独立性、相同概率；正态分布要求数据对称钟形或利用中心极限定理处理均值。
Perform hypothesis tests using test statistics: for binomial, find P(X ≤ k | p=p₀) or use critical regions; for normal, compute Z = (x̄ – μ₀) / (σ/√n) and compare to critical values.
使用检验统计量进行假设检验：对于二项分布，计算 P(X ≤ k | p=p₀) 或使用临界区域；对于正态分布，计算 Z = (x̄ – μ₀) / (σ/√n) 并与临界值比较。
9. Interpreting Results and Drawing Conclusions | 解释结果与得出结论
Relate your statistical findings back to the original problem. If the p-value is less than the significance level (e.g., 0.05), reject H₀ and support the alternative hypothesis. Otherwise, fail to reject H₀. Discuss the practical significance, not just statistical significance.
将统计发现与原问题联系起来。如果 p 值小于显著性水平（如 0.05），则拒绝 H₀ 并支持备择假设。否则，无法拒绝 H₀。要讨论实际意义，而不仅仅是统计显著性。
Include a discussion of limitations, such as sample size, potential confounding variables, and generalisability of results.
要包含对局限性的讨论，例如样本量、潜在的混杂变量以及结果的推广性。
10. Report Structure and Communication | 报告结构与沟通
A well-organised report includes: introduction (problem/hypothesis), methodology (sam
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