3 Fieldwork Investigation | 实地调查

📚 3 Fieldwork Investigation | 实地调查

In the context of A-Level Mathematics (Edexcel), a fieldwork investigation refers to the systematic collection of real-world data through surveys, observations, or experiments to explore statistical relationships or test hypotheses. This process is a practical application of the statistical enquiry cycle and helps students understand the challenges and techniques involved in obtaining reliable data.

在A-Level数学（爱德思）中，实地调查指的是通过调查、观察或实验系统地收集真实世界的数据，以探索统计关系或检验假设。这一过程是统计探究周期的实际应用，有助于学生理解获取可靠数据所涉及的挑战与技巧。

1. What is Fieldwork Investigation? | 什么是实地调查？

A fieldwork investigation is a structured process of gathering first-hand data outside a laboratory or classroom setting. In statistics, it often involves designing a study, selecting participants, and using questionnaires or measurements to collect information about a population.

实地调查是在实验室或教室之外收集第一手数据的结构化过程。在统计学中，它通常涉及设计研究、选择参与者，并利用问卷或测量来收集关于总体的信息。

Unlike secondary data obtained from existing sources, fieldwork provides raw data that can be tailored to specific research questions, allowing students to apply statistical methods such as hypothesis testing and correlation analysis directly to real situations.

与从现有来源获得的二手数据不同，实地调查提供了可针对特定研究问题定制的原始数据，使学生能够将假设检验和相关分析等统计方法直接应用于真实情境。

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2. Planning the Investigation | 规划调查

A successful fieldwork investigation starts with clear aims and objectives. You should identify the variables of interest, formulate a null hypothesis H₀ and an alternative hypothesis H₁, and decide what data is needed to test them.

成功的实地调查始于明确的目的和目标。你应该确定感兴趣的变量，提出原假设 H₀ 和备择假设 H₁，并决定需要哪些数据来检验它们。

For example, if you want to investigate whether a study program affects exam scores, you need to define the independent variable (program participation) and the dependent variable (exam score). You must also consider potential confounding variables such as student motivation.

例如，如果要调查学习计划是否影响考试成绩，你需要定义自变量（是否参与计划）和因变量（考试成绩）。你还必须考虑潜在的混杂变量，如学生的学习动机。

A detailed plan should include the type of data, sampling method, sample size, and ethical considerations. This planning ensures the reliability and validity of the investigation.

详细的计划应包括数据类型、抽样方法、样本量和伦理考量。这样的规划确保了调查的可靠性和有效性。

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3. Defining the Population and Sample | 定义总体和样本

The population is the complete set of individuals or items that are of interest in an investigation. A sample is a subset of the population selected for the actual study. A key goal is to make the sample representative so that statistical inferences about the population are valid.

总体是调查中感兴趣的所有个体或项目的完整集合。样本是从总体中选出的用于实际研究的子集。一个关键目标是使样本具有代表性，以便对总体的统计推断有效。

Parameters are numerical values that describe a population (e.g., population mean μ, population standard deviation σ). Statistics describe a sample (e.g., sample mean x̄, sample standard deviation s). The process of using sample statistics to estimate population parameters is the core of statistical inference.

参数是描述总体的数值（如总体均值 μ、总体标准差 σ）。统计量描述样本（如样本均值 x̄、样本标准差 s）。使用样本统计量来估计总体参数的过程是统计推断的核心。

Sample mean: x̄ = (Σxᵢ)/n

样本均值：x̄ = (Σxᵢ)/n

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4. Sampling Techniques | 抽样方法

Choosing the right sampling technique is crucial to avoid bias and ensure the sample reflects the population. Common methods include simple random sampling, stratified sampling, systematic sampling, quota sampling, and opportunity sampling.

选择正确的抽样方法对于避免偏差和确保样本反映总体至关重要。常见方法包括简单随机抽样、分层抽样、系统抽样、配额抽样和机会抽样。

Simple random sampling gives every member of the population an equal chance of being selected, often using random number generators. It is the most straightforward method but may be impractical for large populations.

简单随机抽样使总体中的每个成员都有相等的机会被选中，通常使用随机数生成器。它是最直接的方法，但对于大规模总体可能不切实际。

Stratified sampling divides the population into distinct strata (e.g., age groups) and selects a random sample from each stratum in proportion to its size. This guarantees representation of all subgroups and reduces variability.

分层抽样将总体划分为不同的层（如年龄组），并按各层大小比例从中随机抽取样本。这保证了所有子群体的代表性，并减少了变异性。

Systematic sampling selects every k-th member from a list of the population, where k is calculated as population size divided by desired sample size. This is simple but may introduce bias if there is an underlying pattern in the list.

系统抽样从总体名单中每隔 k 个成员选取一个，k 等于总体大小除以所需样本大小。这种方法简单，但如果名单中存在某种模式，可能会引入偏差。

Quota sampling involves choosing a predetermined number of individuals with specific characteristics, but the selection is non-random (e.g., interviewers choose whoever is available). This is cheap but prone to interviewer bias.

配额抽样涉及选择具有特定特征的预定数量的个体，但选择是非随机的（例如，采访者选择任何可用的对象）。这种方法成本低廉，但容易受到采访者偏差的影响。

Opportunity sampling (convenience sampling) selects participants based on ease of access, such as friends or passers-by. It is the least reliable method because it is unlikely to represent the target population.

机会抽样（便利抽样）基于获取的方便性选择参与者，例如朋友或路人。这是最不可靠的方法，因为它不太可能代表目标总体。

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5. Types of Data | 数据类型

Data collected during fieldwork can be classified as quantitative or qualitative. Quantitative data are numerical and can be further divided into discrete (countable, e.g., number of siblings) and continuous (measurable, e.g., height).

实地调查中收集的数据可分为定量和定性两类。定量数据是数值型的，可进一步分为离散型（可数的，如兄弟姐妹数）和连续型（可测量的，如身高）。

Qualitative data are non-numerical and describe attributes or categories. They can be ordinal (categories with a natural order, like satisfaction ratings) or nominal (categories without order, like eye colour).

定性数据是非数值的，描述属性或类别。它们可以是有序的（具有自然顺序的类别，如满意度评级）或是名义的（没有顺序的类别，如眼睛颜色）。

Understanding data types is essential for choosing the right summary statistics and graphs. For example, you would use mean and standard deviation for continuous data but mode and bar charts for nominal data.

了解数据类型对于选择合适的汇总统计量和图表至关重要。例如，连续数据使用均值和标准差，而名义数据则使用众数和条形图。

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6. Designing Questionnaires | 设计问卷

Questionnaires are a common tool in fieldwork investigations. Good question design is vital to collect accurate data. Questions should be clear, unbiased, and easy to answer. They can be closed-ended (multiple choice, rating scales) or open-ended (free-text responses).

问卷是实地调查中的常用工具。良好的问题设计对于收集准确数据至关重要。问题应清晰、无偏见且易于回答。它们可以是封闭式的（多项选择、评分量表）或开放式的（自由文本回答）。

Closed-ended questions are easier to analyse numerically, while open-ended questions provide richer qualitative information but are harder to code. Avoid leading questions that suggest a particular answer, and ensure the questionnaire is not too long to prevent respondent fatigue.

封闭式问题在数值上更容易分析，而开放式问题则提供更丰富的定性信息，但更难以编码。避免引导性问题（暗示特定答案），并确保问卷不太长，以防止受访者疲劳。

An example of a good closed-ended question: ‘How many hours do you exercise per week? (a) 0-2 (b) 3-5 (c) 6-8 (d) more than 8’. A poor question would be: ‘Don’t you agree that exercise is good for health?’, which is leading.

一个好的封闭式问题示例：“你每周锻炼多少小时？(a) 0-2 (b) 3-5 (c) 6-8 (d) 8 小时以上”。一个糟糕的问题会是：“你难道不同意锻炼有益健康吗？”，这是引导性的。

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7. Avoiding Bias | 避免偏差

Bias is a systematic error that leads to incorrect estimates of population parameters. Selection bias occurs when the sampling method over- or under-represents certain groups. For example, using an online survey excludes those without internet access.

偏差是一种系统性误差，会导致对总体参数的错误估计。当抽样方法过度或不足地代表某些群体时，就会发生选择偏差。例如，使用在线调查会排除无法上网的人。

Non-response bias arises when a large proportion of selected participants do not respond, and their characteristics differ from those who do. Measurement bias occurs when data collection instruments systematically overstate or understate true values, e.g., a faulty scale.

无应答偏差发生在大部分选定的参与者没有回应，且他们的特征与应答者不同的情况下。测量偏差则发生在数据收集工具系统性地夸大或缩小真实值时，例如一个有故障的秤。

To minimise bias, use a random sampling method, ensure anonymity to encourage honest answers, pilot test questionnaires, and calibrate measuring instruments.

为了减少偏差，应使用随机抽样方法，确保匿名以鼓励诚实回答，试点测试问卷，并校准测量仪器。

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8. Pilot Studies | 试点研究

A pilot study is a small-scale trial run of the investigation before the main data collection. Its purpose is to check the feasibility of the methodology, identify confusing questions, and estimate the time needed.

试点研究是在主要数据收集之前进行的小规模试运行。其目的是检查方法的可行性，识别令人困惑的问题，并估计所需时间。

If a pilot reveals that respondents misunderstand a key term, the questionnaire can be revised. It also helps determine the required sample size for a desired margin of error using the formula:

如果试点研究显示受访者误解了某个关键术语，就可以修改问卷。它还有助于使用公式确定所需样本大小以达到期望的误差范围：

Approximate margin of error ≈ 1/√n for large samples at 95% confidence

大样本、95% 置信度下近似误差范围 ≈ 1/√n

Based on the pilot results, adjustments can be made to improve the final investigation’s quality.

根据试点结果，可以进行调整以提高最终调查的质量。

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9. Data Collection Methods | 数据收集方法

Fieldwork data can be collected in several ways depending on the research question. Observations involve watching and recording behaviours or phenomena without direct interaction. This is useful for studying natural behaviours but may suffer from observer bias.

实地调查数据可根据研究问题以多种方式收集。观察涉及在不直接互动的情况下观看和记录行为或现象。这对于研究自然行为很有用，但可能存在观察者偏差。

Interviews can be structured (fixed questions), semi-structured, or unstructured. They allow deep exploration but are time-consuming. Experiments involve manipulating an independent variable to measure its effect on a dependent variable under controlled conditions.

访谈可以是结构化的（固定问题）、半结构化的或非结构化的。它们允许深入探究，但很耗时。实验涉及操控自变量以测量其在受控条件下对因变量的影响。

Questionnaires are self-administered and can reach a large audience quickly. Each method has trade-offs between cost, depth, and potential biases.

问卷是自填式的，可以快速覆盖大量受众。每种方法在成本、深度和潜在偏差之间都有权衡。

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10. Ethical Considerations | 伦理考虑

Ethical practice is essential in any fieldwork investigation. Participants must give informed consent; they should understand the purpose of the study and that participation is voluntary. Anonymity and confidentiality must be maintained to protect personal data.

在任何实地调查中，伦理实践都是必不可少的。参与者必须给出知情同意；他们应了解研究的目的，并知道参与是自愿的。必须保持匿名和保密以保护个人数据。

Researchers must avoid causing harm or distress. In studies involving vulnerable groups (e.g., children), additional safeguards are required. Data should be stored securely and used only for the stated research purpose.

研究人员必须避免造成伤害或痛苦。在涉及弱势群体（如儿童）的研究中，需要额外的保障措施。数据应安全存储，并仅用于所述的研究目的。

After collecting data, participants have the right to withdraw their responses. Ethical approval may be needed from an institutional review board before commencing.

在收集数据后，参与者有权撤回他们的回答。在开始之前，可能需要获得机构审查委员会的伦理批准。

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11. Recording and Organising Data | 记录与整理数据

Raw data must be recorded systematically, often in a data table or spreadsheet. Each row typically represents one case or respondent, and each column represents a variable. This layout makes it easy to apply statistical formulas and create graphs.

原始数据必须系统地记录，通常采用数据表或电子表格。每行通常代表一个个案或受访者，每列代表一个变量。这种布局便于应用统计公式和创建图表。

For qualitative responses, coding converts text into numerical categories for analysis. For example, ‘yes’ may be coded as 1 and ‘no’ as 0. It is crucial to keep a code book to avoid confusion.

对于定性回答，编码将文本转换为数值类别以供分析。例如，“是”可编码为 1，“否”编码为 0。保留编码簿以避免混淆至关重要。

Organised data can then be summarised using measures of central tendency (mean, median, mode) and measures of spread (range, interquartile range, standard deviation) appropriate to the data type.

整理后的数据可以使用集中趋势度量（均值、中位数、众数）和离散度量（极差、四分位距、标准差）进行汇总，这些度量要适合数据类型。

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12. Limitations and Evaluation | 局限与评价

Every fieldwork investigation has limitations. Small sample sizes reduce the precision of estimates and limit the generalisability of findings. Non-random sampling introduces bias. The measurement tool may lack validity if it does not measure what it intends to.

任何实地调查都有局限性。小样本量降低了估计的精度，并限制了研究结果的推广性。非随机抽样会引入偏差。如果测量工具未能测量其旨在测量的内容，它可能缺乏效度。

Reliability refers to the consistency of results if the investigation is repeated. Using standardised procedures and multiple trials can improve reliability. Validity is about the accuracy of the conclusions. Triangulation (using multiple methods) can enhance validity.

信度指的是如果重复进行调查，结果的一致性。使用标准化程序和多次试验可以提高信度。效度是关于结论的准确性。三角验证（使用多种方法）可以增强效度。

Evaluating the process helps identify sources of error and suggests improvements for future studies. This critical reflection is an integral part of the statistical enquiry cycle.

评估过程有助于识别误差来源，并为未来的研究提出改进建议。这种批判性反思是统计探究周期不可或缺的一部分。

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