📚 Year 13 WJEC Statistics: Writing Framework and Model Answer | Year 13 WJEC 统计：论文写作框架与范文
The Statistical Enquiry is the central assessment component of Year 13 WJEC Statistics, requiring you to plan, conduct, analyse and evaluate an independent investigation. Your report must demonstrate a clear logical structure, correct application of statistical techniques and critical reflection. This guide breaks down the writing framework and provides a model answer to help you reach the highest mark bands.
统计调查是 Year 13 WJEC 统计课程的核心评估部分，要求学生独立完成规划、实施、分析和评价。报告必须展现清晰的逻辑结构、正确的统计方法应用以及批判性反思。本文拆解写作框架并提供范文，帮助你冲击最高评分等级。
1. Understanding the Statistical Enquiry Task | 理解统计调查任务
Begin by carefully reading the task brief. Identify the population of interest, the key variables and whether the aim is to compare groups, test for association or estimate a parameter. Every WJEC investigation expects you to frame a precise research question that can be answered with data.
首先要仔细阅读任务说明。明确目标总体、关键变量，判断是要比较组间差异、检验关联性还是估计参数。WJEC 每次调查都要求你提出一个能用数据回答的精确研究问题。
Your question should be measurable and realistic given the data you can collect. For example, ‘Does the mean time spent on revision differ between male and female Year 13 students?’ is far stronger than a vague ‘Is there a difference in revision habits?’.
研究问题应可测量且在你所能收集数据范围内切合实际。例如，“男女生在复习时间上的平均值是否存在差异？”就远比模糊的“复习习惯有差异吗？”更有力。
2. Planning and Formulating Hypotheses | 规划与提出假设
Translate your research question into formal null and alternative hypotheses. For a two-sample t-test, write H₀: μ₁ = μ₂ and H₁: μ₁ ≠ μ₂ or a one-sided equivalent. The hypotheses must be stated clearly before any data collection.
将研究问题转化为正式的零假设和备择假设。对于双样本 t 检验，应写出 H₀: μ₁ = μ₂ 和 H₁: μ₁ ≠ μ₂ 或相应的单侧形式。假设必须在数据收集前明确陈述。
Also specify your significance level α (usually 0.05) and decide whether you will use a p-value approach or critical region. WJEC reports that explicitly mention these planning decisions score highly on ‘statistical reasoning’.
同时明确显著性水平 α（通常为 0.05），并决定采用 p 值法还是临界域法。WJEC 报告中若能明确提及这些计划决策，会在“统计推理”方面获得高分。
3. Data Collection Methods | 数据收集方法
Describe how you obtained your sample. State the sampling method (simple random, stratified, opportunity, etc.) and discuss why it was chosen. Acknowledge any practical constraints, such as time or access, and link them to potential bias.
描述你如何获取样本。说明抽样方法（简单随机、分层、方便抽样等）并讨论选择理由。坦诚说明时间、访问权限等实际约束，并将其与潜在偏差联系起来。
If you used a questionnaire, include a copy in the appendix and explain how you piloted it. For secondary data, cite the source precisely and comment on its reliability and relevance to your research question.
如果使用了问卷，请在附录中附上副本，并说明如何进行了试点测试。若使用二手数据，应准确引用来源，并评论其可靠性及与研究问题的相关性。
4. Data Cleaning and Descriptive Statistics | 数据清洗与描述性统计
Before analysis, check the dataset for anomalies or missing values. Document any data cleaning steps, such as removing obvious entry errors or deciding how to handle missing responses. Transparency is valued in WJEC marking.
分析前检查数据集是否存在异常或缺失值。记录所有数据清洗步骤，例如删除明显的录入错误，或如何处理缺失回答。WJEC 评分很看重透明度。
Present descriptive statistics in a neat table: sample size n, mean x̄, median, standard deviation s, range and any other relevant measures. Always include units and label your tables. This provides the first layer of insight into your data.
用整洁的表格展示描述性统计：样本量 n、均值 x̄、中位数、标准差 s、极差和其他相关指标。务必包含单位并给表格加标题。这将提供数据的第一层洞察。
5. Graphical Presentation | 图形展示
Use box plots to compare distributions across groups, histograms to show shape, and scatter diagrams for bivariate data. Every graph must have a title, labelled axes and, where appropriate, a key. Do not simply paste screenshots; generate clean plots in software like GeoGebra or Excel and export them as images.
使用箱线图比较组间分布，直方图展示形状，散点图用于双变量数据。每张图必须有标题、带标签的坐标轴，必要时还要有图例。不要直接粘贴截图；应在 GeoGebra 或 Excel 等软件中生成整洁的图形并导出为图像。
Comment on what the graph reveals. For example, ‘The box plot suggests that the median spending for Group A is higher, but the interquartile range shows greater variability.’ Avoid generic statements; link every visual to your hypothesis.
评论图形所揭示的信息。例如，“箱线图表明 A 组的中位数支出更高，但四分位距显示出更大的变异。”避免笼统语句；把每个视觉展示与假设联系起来。
6. Choosing and Applying Inferential Statistics | 选择与运用推断统计
Justify the test you select by checking assumptions. For a two-sample t-test, confirm approximate normality using histograms or the sample size (Central Limit Theorem) and check for equal or unequal variances. If assumptions are violated, consider a Mann-Whitney U test as a non-parametric alternative.
通过检验假设来论证所选检验的合理性。对于双样本 t 检验，利用直方图或样本量（中心极限定理）确认近似正态性，并检查方差齐性或不齐性的情况。若假设不满足，考虑使用曼-惠特尼 U 检验作为非参数替代。
Perform the calculation step by step. Show the formula, substitute the numbers and give the test statistic. Then report the p-value (or compare with critical value) using the correct degrees of freedom. WJEC examiners expect you to handle both equal-variance and Welch-Satterthwaite approaches correctly.
逐步完成计算。写出公式，代入数值并给出检验统计量。然后使用正确的自由度报告 p 值（或与临界值比较）。WJEC 考官期望你正确运用等方差和 Welch-Satterthwaite 两种处理方法。
7. Interpreting Results and Drawing Conclusions | 结果解释与结论
State clearly whether you reject or do not reject H₀. Then interpret the result in the context of the original research question. Avoid saying ‘the null hypothesis is proved’; instead use phrases like ‘there is insufficient evidence to suggest a difference’.
清晰说明是否拒绝 H₀。然后在原始研究问题的背景下解释结果。避免说“证明了零假设”；而应使用“没有足够证据表明存在差异”等表述。
Discuss the practical significance, not just statistical significance. A p-value below 0.05 does not automatically mean the effect is important. Report the effect size (e.g., Cohen’s d) if relevant, and connect your findings to the real-world scenario you investigated.
讨论实际显著性，而不仅是统计显著性。p 值低于 0.05 不一定意味着效应重要。如相关，报告效应量（例如 Cohen’s d），并将发现与你调查的现实情境联系起来。
8. Model Answer: A Hypothesis Test Analysis | 范文：假设检验分析
The following excerpts are from an investigation comparing the mean time (minutes) spent on weekly homework by students following two different study programmes.
以下段落选自一项比较两种不同学习方案学生每周作业平均时间（分钟）的调查报告。
Hypothesis statement: We wish to test if there is a difference in mean homework time. H₀: μ₁ = μ₂, H₁: μ₁ ≠ μ₂ at the 5% significance level. Both groups have more than 30 observations, so the Central Limit Theorem assures normality of the sampling distribution. A two-sample t-test assuming unequal variances (Welch) will be used.
假设陈述：我们想检验平均作业时间是否有差异。H₀: μ₁ = μ₂，H₁: μ₁ ≠ μ₂，显著性水平 5%。两组样本量均超过30，因此中心极限定理保证抽样分布的正态性。将使用假定方差不相等的双样本 t 检验（Welch 检验）。
Calculation: Group A: n₁ = 35, x̄₁ = 48.2, s₁ = 12.5. Group B: n₂ = 40, x̄₂ = 44.6, s₂ = 14.0. The test statistic is t = (48.2 – 44.6) / √(12.5²/35 + 14.0²/40) = 3.6 / 3.242 = 1.110. Using the Welch-Satterthwaite equation, the degrees of freedom are approximately 72. The two-tailed p-value from the t-distribution is 0.2708.
计算：A 组：n₁ = 35, x̄₁ = 48.2, s₁ = 12.5。B 组：n₂ = 40, x̄₂ = 44.6, s₂ = 14.0。检验统计量为 t = (48.2 – 44.6) / √(12.5²/35 + 14.0²/40) = 3.6 / 3.242 = 1.110。使用 Welch-Satterthwaite 公式，自由度约为 72。t 分布的双尾 p 值为 0.2708。
Conclusion: Since p = 0.271 > 0.05, we do not reject H₀. There is no statistically significant evidence of a difference in mean homework time between the two programmes. However, the wide confidence interval (-2.8, 10.0) suggests the study would benefit from a larger sample to detect smaller effects.
结论：由于 p = 0.271 > 0.05，我们不拒绝 H₀。没有统计上显著的证据表明两种方案在平均作业时间上存在差异。然而，置信区间较宽（-2.8，10.0），表明该研究需增大样本量才能发现较小的效应。
9. Evaluation and Limitations | 评估与局限性
Critically reflect on every stage of your enquiry. Discuss sampling limitations, measurement error, potential confounding variables and the extent to which conclusions can be generalised. High-scoring reports treat evaluation as an integral section, not an afterthought.
对调查的每个阶段进行批判性反思。讨论抽样局限性、测量误差、潜在混杂变量以及结论能被推广的程度。高分报告把评估视为不可或缺的部分，而非事后补充。
Suggest concrete improvements: a larger stratified sample, a more precise measuring instrument, or the inclusion of additional background variables in a multiple regression model. Link these suggestions back to the weaknesses you identified.
提出具体的改进建议：更大的分层样本、更精确的测量工具、或在多元回归模型中纳入更多背景变量。将这些建议与你发现的弱点结合起来。
10. Report Structure and Checklist | 报告结构与清单
A well-organised report makes it easy for the examiner to award marks. Follow this typical WJEC investigation structure:
结构良好的报告能让考官轻松给分。请遵循以下典型的 WJEC 调查报告结构：
| Section | Key Contents | 主要内容 |
|---|---|---|
| 1. Introduction | Research question, rationale, hypotheses | 研究问题、理由、假设 |
| 2. Data Collection | Sampling method, sample size, ethics, pilot | 抽样方法、样本量、伦理、试点 |
| 3. Data Presentation | Tables, graphs, descriptive statistics | 表格、图形、描述性统计 |
| 4. Statistical Analysis | Choice of test, assumptions, calculations, p-value | 检验选择、假设、计算、p 值 |
| 5. Interpretation & Conclusion | Contextual conclusion, effect size, limitations | 情境化结论、效应量、局限性 |
| 6. Evaluation & Appendices | Reflection, improvements, raw data, questionnaire | 反思、改进、原始数据、问卷 |
11. Common Pitfalls and Tips for High Marks | 常见错误与高分技巧
Mistake: using inappropriate graphs, such as a pie chart for continuous data. Tip: always match the graph type to the variable type and the question you are exploring.
错误：使用不当图形，例如用饼图展示连续数据。技巧：始终将图形类型与变量类型及所探究的问题相匹配。
Mistake: reporting a p-value without stating the hypothesis or significance level. Tip: write the hypothesis and α explicitly before every test. This shows you understand the framework of statistical testing.
错误：在未说明假设或显著性水平的情况下直接报告 p 值。技巧：每次检验前明确写出假设和 α，这能体现你对统计检验框架的理解。
Mistake: ignoring assumptions. Even if you do not perform formal tests, comment on normality and variance visually or using rules of thumb. High marks go to students who discuss why the chosen test is appropriate.
错误：忽略假设。即便不进行正式检验，也应通过图形或经验法则对正态性和方差进行评述。能讨论所选检验为何恰当的学生更容易得高分。
Mistake: drawing over-confident conclusions. Always use cautious language such as ‘suggests’, ‘provides weak evidence’ or ‘indicates a possible trend’. This demonstrates statistical maturity.
错误：得出过于确定的结论。要始终使用谨慎的语言，如“表明”、“提供较弱证据”或“指出可能的趋势”。这将展示统计思维的成熟度。
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