📚 Year 13 CIE Statistics: Experimental/Practical Assessment Key Points | Year 13 CIE 统计：实验/实践考核要点
In the Cambridge International A Level Statistics (0390) course, the practical component, tested through Paper 3 Statistical Enquiry, challenges you to plan, execute, and report on a real statistical investigation. This article distils the key points you need to master experimental design, data handling, hypothesis testing, and evaluation to achieve top marks in your practical assessment.
在剑桥国际 A Level 统计学（0390）课程中，实践部分通过 Paper 3 统计调查进行考核，要求你规划、执行并报告一项真实的统计研究。本文提炼了实验设计、数据处理、假设检验和评估等关键要点，帮助你掌握这些技能，在实践考核中取得优异成绩。
1. Understanding the Assessment Objectives | 理解考核目标
The practical paper assesses your ability to formulate a statistical problem, design an appropriate sampling or experimental strategy, collect and process data, select and apply statistical models, and critically interpret the findings in context. Each stage carries marks for planning, methodology, analysis, and evaluation.
实践试卷评估你提出统计问题、设计合适的抽样或实验策略、收集和处理数据、选择并应用统计模型，以及在情境中批判性解读结果的能力。每个阶段都对应计划、方法、分析和评估的分数。
You must demonstrate competence in using statistical software or a graphic calculator to generate outputs, yet the focus remains on meaningful interpretation, not just computation. Examiners expect clear evidence of the statistical enquiry cycle.
你必须展示使用统计软件或图形计算器生成输出的能力，但重点始终是有意义的解释，而不仅仅是计算。考官期望看到清晰的统计调查循环的证据。
2. Planning a Statistical Enquiry | 规划统计调查
Begin with a well-defined research question or hypothesis that is testable with the resources available. Break down the problem into measurable variables and ensure the question is focused enough to allow a thorough analysis within the word or page limit.
从一个明确、可检验的研究问题或假设入手，并考量可用的资源。将问题分解为可测量的变量，确保问题足够聚焦，能在字数或页数限制内完成深入分析。
Consider ethical issues, such as informed consent, anonymity, and data protection, especially when dealing with human participants. A strong plan includes a timeline, a description of the target population, and a justification for the chosen methodology.
考虑伦理问题，如知情同意、匿名性和数据保护，特别是在涉及人类参与者时。一个完善的计划应包括时间表、目标人群的描述，以及对所选方法的论证。
3. Designing the Experiment or Survey | 设计实验或调查
If you conduct an experiment, incorporate the principles of randomisation, replication, and control. Randomly assign subjects to treatment groups to minimise bias; use blocking where necessary to account for confounding variables. Clearly define the response variable and the factor levels.
如果进行实验，要纳入随机化、重复和对照的原则。将受试者随机分配到处理组以最小化偏差；必要时使用区组来考虑混杂变量。明确界定响应变量和因子水平。
For a survey, design unbiased questions and pilot them. Avoid leading or ambiguous wording. Decide on closed or open-ended formats and plan how responses will be coded for analysis. A pilot study reveals flaws in questionnaire design before the main data collection.
对于调查，要设计无偏的问题并进行预测试。避免引导性或模糊的措辞。确定封闭式还是开放式题型，并计划如何对回答进行编码以供分析。预研究能在主要数据收集前揭示问卷设计的缺陷。
4. Sampling Methods and Randomisation | 抽样方法和随机化
Select a probability sampling method when possible: simple random sampling ensures every unit has an equal chance of selection, often using random number tables or software-generated random numbers. Stratified sampling improves representativeness by dividing the population into homogeneous strata and sampling proportionally.
尽可能选择概率抽样方法：简单随机抽样确保每个单位有相同的被选机会，通常使用随机数表或软件生成的随机数。分层抽样通过将总体划分为同质层并按比例抽样，提高了代表性。
Avoid convenience or quota sampling unless justified by severe practical constraints, as they introduce selection bias. Always explain the sampling frame and any deviations from an ideal method, as this feeds into your evaluation of reliability.
除非受到严重的实际限制并给出合理解释，否则避免使用便利抽样或配额抽样，因为它们会引入选择偏差。始终说明抽样框架以及与理想方法的任何偏差，因为这将纳入对可靠性的评估。
5. Data Collection Tools and Techniques | 数据收集工具与技术
Use primary data where the investigation demands direct measurement, but secondary data from official databases or previous studies can be valuable if its provenance is sound. Document all instruments – rulers, digital sensors, questionnaires – and note their precision.
如果调查需要直接测量，应使用一手数据；但如果来源可靠，来自官方数据库或以往研究的二手数据也同样有价值。记录所有工具——尺子、数字传感器、问卷——并注明其精度。
For any measurement, record the units and the possible sources of measurement error. When using technology, such as data loggers or online survey platforms, describe the setup precisely so that the enquiry could be replicated.
对于任何测量，记录单位和可能的测量误差来源。使用数据记录器或在线调查平台等技术时，要准确描述设置，以便该调查可以被重复。
6. Organising and Presenting Data | 数据整理与呈现
Organise raw data into clear frequency tables or summary tables before attempting any graphical display. Use box plots to compare distributions, histograms for continuous data, and scatter diagrams to explore relationships. Always label axes, include units, and provide a descriptive title.
在尝试任何图形显示之前，将原始数据整理成清晰的频数表或摘要表。使用箱线图比较分布，直方图用于连续数据，散点图用于探索关系。务必标注坐标轴、单位和描述性标题。
Descriptive statistics – mean, median, standard deviation, interquartile range – give numerical summaries that complement visual ones. Report them alongside graphs to strengthen the initial stage of analysis.
描述性统计量——均值、中位数、标准差、四分位距——提供与图形相辅相成的数值摘要。在图形旁报告它们，以加强分析的初始阶段。
7. Selecting Appropriate Statistical Tests | 选择适当的统计检验
Match the test to the type of data and the research question. For comparing two means, the two-sample t-test requires approximately normal data and independent samples, while a paired t-test suits matched data. The table below summarises common scenarios.
根据数据和问题类型匹配合适的检验。对于两个均值的比较，双样本 t 检验要求数据近似正态且样本独立，而配对 t 检验适用于配对数据。下表总结了常见情形。
| Test | Typical use | Key condition(s) |
|---|---|---|
| One-sample t-test | Comparing sample mean to a known value | Normality; n < 30 use t, large n use CLT |
| Two-sample t-test | Difference of two independent means | Normality in each group; equal variances (can use Welch's) |
| Chi-squared test for independence | Association between two categorical variables | Expected frequencies at least 5 |
| Chi-squared goodness-of-fit | Whether observed frequencies follow a theoretical distribution | Same as above; df = k-1 |
| Pearson's correlation | Strength of linear relationship | Bivariate normality; linearity |
Always check assumptions with residual plots, normal probability plots, or goodness-of-fit tests before stating your conclusions. Non-parametric alternatives like the Mann-Whitney U test can be used when normality is violated.
在陈述结论之前，务必用残差图、正态概率图或拟合优度检验检查假设。当正态性被违反时，可使用曼-惠特尼 U 检验等非参数替代方法。
8. Hypothesis Testing in Practice | 实践中的假设检验
State the null hypothesis H₀ and the alternative H₁ precisely. Choose a significance level α (commonly 0.05) before looking at the data. Calculate the test statistic using the appropriate formula, for example:
准确陈述零假设 H₀ 和备择假设 H₁。在查看数据之前选定显著性水平 α（通常为 0.05）。用相应公式计算检验统计量，例如：
t = (x̄ − μ₀) / (s/√n)
Then find the p-value or compare the statistic with the critical value. If p < α, reject H₀ in favour of H₁. Always state the conclusion in the context of the original problem and avoid causal language unless supported by the design.
然后查找 p 值或将统计量与临界值比较。若 p < α，则拒绝 H₀ 而支持 H₁。始终在原问题的情境中陈述结论，除非设计允许，否则避免使用因果性语言。
Be aware of Type I error (rejecting a true H₀) and Type II error (failing to reject a false H₀). In your evaluation, comment on the power of the test and whether the sample size was sufficient to detect a meaningful effect.
注意第一类错误（拒绝了一个为真的 H₀）和第二类错误（未能拒绝一个为假的 H₀）。在评估中，对检验的效能以及样本量是否足以检测有意义的效应加以评论。
9. Using Technology and Software | 使用技术与软件
CIE expects you to be fluent with a statistical package or a graphing calculator. Enter data into Excel, GeoGebra, or a dedicated statistics app. Use software to produce graphs, compute descriptive statistics, and run inferential tests, ensuring that you understand the output rather than treating it as a black box.
CIE 希望你熟练使用统计软件包或图形计算器。将数据输入 Excel、GeoGebra 或专门的统计应用程序。利用软件生成图表、计算描述性统计量并运行推断检验，并确保你理解输出，而非单纯将其当作黑箱。
Always report the software or calculator model and the commands employed. Copy key tables and charts into your report, but trim excessive output. Annotate software-generated results to show how they link to your hypothesis and conclusions.
始终报告所使用的软件或计算器型号以及用到的指令。将关键表格和图表复制到报告中，但要删减过多的输出。对软件生成的结果进行注释，以显示它们如何与你的假设和结论相关联。
10. Interpreting Results and Drawing Conclusions | 解释结果并得出结论
Move beyond a simple 'reject' or 'do not reject' statement. Interpret the effect size, e.g. the difference in means, and provide a confidence interval where appropriate. A confidence interval gives a range of plausible values for the parameter and indicates the precision of the estimate.
不要仅仅停留在“拒绝”或“不拒绝”的陈述上。解释效应大小，如均值之差，并在适当情况下给出置信区间。置信区间给出了参数的合理范围，并表明估计的精度。
Link your findings back to the original research question. Discuss whether the results are practically significant, not just statistically significant. A very large sample might make a tiny difference statistically significant even if it has no real-world importance.
将你的发现与最初的研究问题联系起来。讨论结果是否具有实际显著性，而不仅仅是统计显著性。一个极大的样本可能使一个微小的差异达到统计显著，即使它在现实世界中无足轻重。
11. Evaluating Limitations and Reliability | 评估局限性与可靠性
Identify the main sources of variability and bias. Were there any confounding variables that were not controlled? Did non-response or missing data affect the results? Could measurement errors have influenced the outcome? A candid evaluation shows high-level understanding.
识别主要的变异来源和偏差。是否存在未加控制的混杂变量？无应答或缺失数据是否影响了结果？测量误差是否可能影响结局？坦诚的评估显示出高层次的认知。
Assess the generalisability of your conclusions. If you used a convenience sample of students from one school, clearly state that the findings may not extend to other populations. Discuss how future enquiries could improve the design – for example, by increasing sample size or using random allocation.
评估结论的普适性。如果你从一所学校便利抽取了学生样本，应明确说明这些发现可能无法推广到其他人群。讨论未来的调查如何改进设计——例如，增大样本量或采用随机分配。
12. Report Writing and Communication | 报告撰写与沟通
Structure your report with clear sections: Introduction (research question, rationale), Methodology (design, sampling, data collection), Analysis (descriptive and inferential statistics, graphs), Discussion (interpretation, evaluation), and Conclusion. Use subheadings to guide the reader.
运用清晰的章节结构撰写报告：引言（研究问题、理由）、方法（设计、抽样、数据收集）、分析（描述性和推断性统计、图表）、讨论（解释、评估）和结论。使用小标题引导读者。
Write in a precise, academic style, avoiding personal anecdotes. Reference any secondary data sources and acknowledge the software used. Proofread for accuracy in numbers, graphs, and statements – a single misplaced decimal point can undermine credibility.
采用准确、学术的风格，避免个人轶事。引用任何二手数据源并说明所使用的软件。校对数字、图表和陈述的准确性——一个小数点的差错就可能损害可信度。
Published by TutorHao | Statistics Revision Series | aleveler.com
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