📚 AS Eduqas Statistics: Statistical Enquiry Report Writing Framework and Model Answers | AS Eduqas 统计：统计调查报告写作框架与范文
The AS Eduqas Statistics qualification requires students not only to perform calculations but also to structure clear, logical statistical reports. Whether you are tackling the Statistical Enquiry component or an extended exam question, knowing how to frame a coherent report is essential for top marks. This guide breaks down the writing process step by step, followed by a fully worked model answer based on a hypothesis test and correlation analysis.
AS Eduqas 统计学考试不仅要求学生进行计算，还需要构建清晰、有逻辑的统计报告。无论你是在完成统计调查部分，还是应对扩展性考题，掌握报告写作框架都是获取高分的关键。本指南将逐步拆解写作流程，随后提供一份基于假设检验与相关分析的完整范文。
1. Understanding the Report Structure | 理解报告结构
A statistical enquiry report for Eduqas typically follows the PPDAC cycle: Problem, Plan, Data, Analysis, Conclusion. Each section must flow logically and demonstrate statistical thinking. Examiners reward clear labelling of stages, accurate use of statistical terminology, and thorough interpretation of results in context.
Eduqas 的统计调查报告通常遵循 PPDAC 循环：问题、计划、数据、分析、结论。每个部分必须逻辑连贯，并展现统计思维。考官看重清晰的阶段标注、准确使用统计术语以及在具体情境中全面解释结果。
The report should begin with a clear statement of the problem and hypotheses, followed by a description of the data collection method. Next, present the data using appropriate graphs and summary statistics. The analysis section must include formal statistical tests, such as correlation coefficients or chi-squared tests, and the conclusion should link findings back to the original problem, acknowledging limitations.
报告应以清晰的问题陈述与假设开始，随后描述数据收集方法。然后使用适当的图表和汇总统计来呈现数据。分析部分必须包含正式的统计检验，例如相关系数或卡方检验，而结论应把发现与原始问题联系起来，并承认研究局限。
2. Defining the Problem and Hypotheses | 定义问题与假设
Start by stating the research question. For example: ‘Is there an association between daily screen time and quality of sleep among sixth-form students?’ Then convert this into null and alternative hypotheses. The null hypothesis (H₀) usually states there is no association or no difference, while the alternative (H₁) states there is an association or a difference. Clearly write H₀ and H₁ using statistical notation where possible, such as H₀: ρ = 0 vs H₁: ρ ≠ 0 for a correlation test.
首先陈述研究问题。例如：“高中六年级学生每日屏幕时间与睡眠质量之间是否存在关联？”然后将其转化为零假设与备择假设。零假设 (H₀) 通常表示无关联或无差异，备择假设 (H₁) 则表示存在关联或差异。尽可能用统计符号清晰地写出 H₀ 和 H₁，例如对于相关性检验可写为 H₀: ρ = 0，H₁: ρ ≠ 0。
In the model answer later, we will use a two-tailed test for Pearson’s product-moment correlation coefficient. The hypotheses will be clearly stated at the beginning of the report, ensuring the reader immediately understands the aim of the investigation.
在后续范文中，我们将针对皮尔逊积矩相关系数使用双尾检验。假设将在报告开头明确陈述，确保读者立即理解调查目的。
3. Planning the Data Collection | 规划数据收集
Describe how you obtained the data. Specify the target population, sampling method (e.g., simple random, stratified, opportunity), and sample size. Explain why this method was chosen and how you minimised bias. For instance, you might use a random number generator to select participants from a school register. Also, clearly describe the variables, their types (quantitative continuous, discrete, qualitative) and how they were measured.
描述你如何获取数据。要明确目标总体、抽样方法（例如简单随机、分层、便利抽样）和样本量。解释为何选择该方法，以及你如何减少偏差。例如，你可以使用随机数生成器从学校名册中选取参与者。同时，清晰描述变量、变量类型（定量连续、离散、定性）及其测量方式。
In the model answer, we will use a sample of 25 Year 12 students, collecting data on ‘daily screen time (hours)’ and ‘average sleep duration (hours)’. Screen time will be measured via a validated app, and sleep duration through a questionnaire. The plan section will justify the sample size and address potential ethical issues.
在范文中，我们将使用 25 名十二年级学生的样本，收集“每日屏幕时间（小时）”和“平均睡眠时长（小时）”数据。屏幕时间通过经验证的应用程序测量，睡眠时长通过问卷收集。计划部分将论证样本量的合理性并说明潜在的伦理问题。
4. Presenting Data Graphically | 用图表呈现数据
Select graphs that suit your variables. For investigating the relationship between two quantitative variables, a scatter diagram is ideal. Ensure axes are clearly labelled with units, a title is given, and the graph is accurately scaled. Comment on any visible pattern, trend, or anomalies.
选择适合变量的图表。研究两个定量变量关系时，散点图是理想选择。确保坐标轴清晰标注单位，给出标题，并准确标度。对任何可见的模式、趋势或异常值进行评论。
In our model report, we will present a well-labelled scatter plot showing screen time on the x-axis and sleep duration on the y-axis. The initial visual inspection suggests a negative correlation, which will later be quantified.
在范文报告中，我们将展示一张标注完整的散点图，x 轴为屏幕时间，y 轴为睡眠时长。初步目测显示存在负相关，后续将进行量化。
5. Calculating Summary Statistics | 计算汇总统计
Present relevant statistics such as the mean, median, standard deviation, and range for each variable. Use a table to display these clearly. The table should include both measures of location and spread. Show the formulas used, even if the calculations were done on a calculator, so the examiner can follow your reasoning.
呈现相关统计量，例如每个变量的均值、中位数、标准差和极差。使用表格清晰展示，应包括位置量数和离散量数。即使计算由计算器完成，也需展示所用公式，以便考官理解你的推理过程。
- Mean: x̄ = Σx / n
- Standard deviation (sample): s = √[ Σ(x – x̄)² / (n – 1) ]
In the model answer,
| Statistic | Screen Time (hrs) | Sleep Duration (hrs) |
|---|---|---|
| Mean (x̄) | 6.4 | 7.2 |
| Sample SD (s) | 1.8 | 1.2 |
| Total (n=25) | 160 | 180 |
Note: Show one example calculation for mean and standard deviation.
注意：应展示一个均值和标准差的计算示例。
6. Performing the Hypothesis Test | 执行假设检验
Calculate the test statistic using the formula for Pearson’s correlation coefficient r:
r = Sxy / √(Sxx × Syy)
where Sxy = Σ(x – x̄)(y – ȳ), Sxx = Σ(x – x̄)², Syy = Σ(y – ȳ)². Clearly state the computed value, for example r = -0.68. Then compare this with the critical value from the product-moment correlation coefficient table for n=25 at a 5% significance level (two-tailed). The critical value for ν = 23 degrees of freedom is approximately 0.396. Since |r| > critical value, you reject H₀.
使用皮尔逊相关系数 r 的公式计算检验统计量：r = Sxy / √(Sxx × Syy)，其中 Sxy = Σ(x – x̄)(y – ȳ)，Sxx = Σ(x – x̄)²，Syy = Σ(y – ȳ)²。清晰陈述计算值，例如 r = -0.68。然后将其与皮尔逊积矩相关系数临界值表进行比较，在 5% 显著性水平（双尾）下，n=25 时自由度 ν = 23 的临界值约为 0.396。由于 |r| > 临界值，拒绝 H₀。
Always interpret the rejection in the context of the problem: ‘There is sufficient evidence at the 5% level to suggest a significant negative linear correlation between daily screen time and sleep duration.’
始终结合具体情境解释拒绝结果：“在 5% 的显著性水平下，有足够证据表明每日屏幕时间与睡眠时长之间存在显著的负线性相关。”
7. Analysing Correlation vs. Causation | 分析相关与因果
One of the most important skills in the report is discussing the difference between correlation and causation. Emphasise that even a strong correlation does not imply that increased screen time causes reduced sleep. Other factors, such as academic stress or caffeine intake, could influence both variables. Mentioning confounding variables strengthens the evaluation.
报告中最重要的技能之一是讨论相关与因果的区别。要强调即使存在强相关，也不意味着屏幕时间增加导致睡眠减少。其他因素，如学业压力或咖啡因摄入量，可能对两个变量都有影响。提及混杂变量能增强评估部分的深度。
In the model answer, we will explicitly state: ‘A significant negative correlation exists, but this does not establish causation. An observational study cannot control for all extraneous variables.’
在范文中，我们将明确陈述：“存在显著的负相关，但这并不能建立因果关系。观察性研究无法控制所有额外变量。”
8. Drawing Conclusions | 得出结论
Summarise the findings concisely. State whether the initial hypothesis was supported and reiterate the strength and direction of the relationship. Link the statistical evidence back to the original research question. For example: ‘Students with higher daily screen time tend to have shorter sleep durations, with a moderately strong negative linear correlation (r = -0.68, p < 0.05).'
简明总结研究发现。陈述初始假设是否得到支持，并重申关系的强度和方向。将统计证据与原始研究问题关联起来。例如：“每日屏幕时间较长的学生睡眠时长往往较短，两者呈中等强度的负线性相关（r = -0.68，p < 0.05）。”
Also mention any practical implications, but keep them measured. Avoid overstating the findings.
还应提及任何实际应用意义，但要保持克制，避免夸大研究结论。
9. Evaluating the Enquiry | 评估调查
A high-mark report must include a thorough evaluation. Discuss limitations of the sampling method (e.g., small sample size, opportunity sampling from one school limits generalisability). Comment on possible measurement errors: self-reported sleep data might be unreliable. Suggest improvements, such as using a larger, more diverse sample and objective sleep trackers. Also, evaluate the choice of statistical test — was Pearson’s r appropriate? Could Spearman’s rank have been better if the relationship appeared non-linear?
高分报告必须包含全面的评估。讨论抽样方法的局限性（例如样本量小、仅在一所学校使用便利抽样限制了推广性）。评论可能的测量误差：自报睡眠数据可能不可靠。提出改进建议，例如使用更大、更多样化的样本和客观的睡眠追踪设备。同时，评估所选择的统计检验——皮尔逊 r 是否合适？如果关系看起来非线性，秩相关系数是否会更好？
This critical reflection demonstrates higher-order thinking and is explicitly rewarded by Eduqas examiners.
这种批判性反思展现了高阶思维能力，Eduqas 考官会明确给予加分。
10. Model Answer: Introduction & Methodology | 范文：引言与方法
Enquiry Question: Is there a relationship between daily screen time and average nightly sleep duration for Year 12 students at A Level College?
Hypotheses: H₀: ρ = 0 (no linear correlation between screen time and sleep duration). H₁: ρ ≠ 0 (there is a linear correlation). Significance level: 5%, two-tailed test.
Methodology: A questionnaire was distributed to 25 randomly selected Year 12 students aged 16-17. Screen time was recorded as the average hours per day based on phone screen-time apps over one week. Sleep duration was self-reported average hours per night over the same week. Participation was voluntary and anonymous.
调查问题：A Level 学院十二年级学生的每日屏幕时间与平均夜间睡眠时长之间是否存在关系？
假设：H₀: ρ = 0（屏幕时间与睡眠时长无线性相关）。H₁: ρ ≠ 0（存在线性相关）。显著性水平：5%，双尾检验。
方法：向 25 名随机选择的 16-17 岁十二年级学生发放问卷。屏幕时间根据手机屏幕时间应用记录的过去一周每日平均小时数来计量。睡眠时长是同一周内自报的平均每晚睡眠小时数。参与是自愿且匿名的。
This section is concise but covers all required planning elements. Notice the clear labelling of hypotheses and the justification of data collection.
此部分简明扼要却涵盖了所有必需的规划要素。注意假设的清晰标注和数据收集的依据。
11. Model Answer: Analysis & Conclusion | 范文：分析与结论
Data Analysis: A scatter diagram (Figure 1) shows a negative trend. Summary statistics: mean screen time = 6.4 hrs, SD = 1.8 hrs; mean sleep = 7.2 hrs, SD = 1.2 hrs. The computed Pearson correlation coefficient r = -0.68. The critical value for n=25 at the 5% level (two-tailed) is 0.396. Since |-0.68| > 0.396, we reject H₀. There is sufficient evidence to conclude a significant negative linear correlation. The coefficient of determination r² = 0.4624 indicates that about 46.2% of the variation in sleep duration can be accounted for by variation in screen time.
Conclusion: The investigation found a moderately strong, statistically significant negative correlation between screen time and sleep duration among Year 12 students. However, this does not prove causation; factors like stress and physical activity could also influence sleep. The sample was limited to one school, affecting generalisability. Future studies should track participants longitudinally across multiple schools.
数据分析：散点图（图 1）显示负向趋势。汇总统计：屏幕时间均值 = 6.4 小时，标准差 = 1.8 小时；睡眠均值 = 7.2 小时，标准差 = 1.2 小时。计算得到的皮尔逊相关系数 r = -0.68。在 5% 显著性水平（双尾）下，n=25 的临界值为 0.396。由于 |-0.68| > 0.396，拒绝 H₀。有足够证据得出存在显著的负线性相关。决定系数 r² = 0.4624 表明睡眠时长变异中约有 46.2% 可由屏幕时间变异来解释。
结论：本次调查发现，十二年级学生的屏幕时间与睡眠时长之间存在中等偏强、统计显著的负相关。但这并不证明因果关系；压力和身体活动等因素也可能影响睡眠。样本仅限于一所学校，影响了推广性。未来研究应在多所学校对参与者进行纵向追踪。
This model answer seamlessly integrates calculations, statistical inference, and critical evaluation — exactly what Eduqas examiners seek.
这篇范文无缝融合了计算、统计推断和批判性评估——正是 Eduqas 考官所追求的标准。
12. Final Tips for Report Writing | 报告写作的最后技巧
Always use precise statistical language. Avoid vague phrases like ‘the data suggests’. Instead, say ‘the evidence at the 5% significance level suggests reject H₀’. Present all graphs and tables with numbered captions. Check your calculations and critical values carefully. Finally, leave time to write a meaningful evaluation — it often differentiates a Grade A from a Grade C.
始终使用精确的统计语言。避免“数据表明”这类模糊表述，而应说“在 5% 显著性水平下，证据表明拒绝 H₀”。所有图表都需添加带编号的标题。仔细检查计算和临界值。最后，预留时间写一篇有意义的评估——这往往是区分 A 等和 C 等的关键。
Practise by writing short reports under timed conditions. Use real data sets from past Eduqas papers, and always follow the PPDAC structure. With consistent practice, the report framework will become second nature.
通过限时练习撰写简短报告来巩固。使用 Eduqas 历年真题中的真实数据集，并始终遵循 PPDAC 结构。经过反复练习，报告框架将变为你的第二天性。
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