Non-random Sampling | 非随机抽样

📚 Non-random Sampling | 非随机抽样

In Edexcel A-Level Mathematics, the statistics component requires you to understand how data is collected. Sampling methods are divided into random and non-random methods. This article focuses on non-random sampling, especially quota sampling and opportunity sampling, which frequently appear in exam questions asking for advantages, disadvantages, and comparisons.

在 Edexcel A-Level 数学的统计部分，你需要理解数据的收集方式。抽样方法分为随机抽样和非随机抽样。本文重点讨论非随机抽样，特别是配额抽样和便利抽样，这些方法常在考试中要求分析优缺点或与随机抽样进行比较。

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1. What Is Non-random Sampling? | 什么是非随机抽样？

Non-random sampling is any method where members of the population are not selected by chance. Instead, the researcher uses judgement, convenience, or quotas to decide who is included. Because not every member has a known or equal chance of selection, the sample may not represent the population fully.

非随机抽样是指样本成员不是通过随机机制选出的方法。研究者根据判断、便利性或配额来决定谁被选入样本。由于不是每个成员都有已知或均等的入选概率，样本可能无法完全代表总体。

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2. Why Use Non-random Sampling? | 为什么使用非随机抽样？

Non-random sampling is often quicker, cheaper, and easier than random methods. It does not require a complete sampling frame, so it can be used when no list of the population exists. It is useful for pilot studies or when time and resources are limited.

非随机抽样通常比随机方法更快捷、更省钱、更容易实施。它不需要完整的抽样框，因此当总体名单不存在时也可以使用。它适用于试点研究或时间和资源有限的情况。

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3. Quota Sampling | 配额抽样

Quota sampling is a non-random method in which the researcher sets quotas for different subgroups, such as age, gender, or income. Interviewers then select people to fill each quota until the required numbers are met. The quotas are often chosen to match known population proportions.

配额抽样是一种非随机方法，研究者为不同子群（如年龄、性别或收入）设定配额。调查员随后选择符合条件的人来填满每个配额，直到达到所需人数。配额通常按已知的总体比例设定。

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4. How Quota Sampling Works | 配额抽样如何实施

Suppose a college has 60% male and 40% female students, and a sample of 50 is needed. The researcher sets quotas of 30 males and 20 females. Interviewers approach students in the cafeteria and choose enough of each group, but the final choice within each quota is not random.

假设一所大学有 60% 的男生和 40% 的女生，需要抽取 50 人。研究者设定配额为 30 名男生和 20 名女生。调查员在食堂接近学生并选择足够的每组人数，但在每个配额内最终选择谁并不是随机的。

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5. Advantages of Quota Sampling | 配额抽样的优点

Quota sampling does not require a sampling frame, so it can be used when a list of the population is unavailable. It is relatively fast and cheap because researchers can stop once quotas are filled. It also ensures that key subgroups are represented in the sample.

配额抽样不需要抽样框，因此在无法获得总体名单时仍可使用。它相对快速且成本较低，因为配额一满就可以停止。它还能确保关键子群在样本中得到代表。

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6. Disadvantages of Quota Sampling | 配额抽样的缺点

The main disadvantage is that selection within quotas is not random, so interviewer bias can occur. For example, an interviewer might avoid people who look busy or choose those who seem friendly. This can produce a sample that is not representative, even if the quotas match population proportions. Quota sampling also cannot be used to calculate a meaningful margin of error because it is not probability-based.

主要缺点是配额内的选择不是随机的，因此可能产生调查员偏差。例如，调查员可能会避开看起来很忙的人，或选择看起来友好的人。这样得到的样本可能不具代表性，即使配额比例与总体一致。配额抽样还不能计算有意义的误差范围，因为它不是基于概率的方法。

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7. Opportunity Sampling | 便利抽样

Opportunity sampling, also called convenience sampling, involves selecting people who are available at the time of the study. For example, a researcher standing outside a train station might ask the first 50 passers-by. There is no randomness and no attempt to meet quotas.

便利抽样（又称机会抽样）是指选择在研究时容易接触到的人。例如，站在火车站外的研究者可能会询问最先经过的 50 名路人。这种方法没有随机性，也不设定配额。

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8. Advantages and Disadvantages of Opportunity Sampling | 便利抽样的优缺点

Opportunity sampling is the quickest and cheapest method, needing no planning, no sampling frame, and very little effort. For classroom experiments or initial opinion gathering, it is often practical.

便利抽样是最快、最便宜的抽样方法，几乎不需要计划、不需要抽样框，操作非常省力。对于课堂实验或初步意见收集，它通常很实用。

However, opportunity samples are highly vulnerable to bias. People available in one location at one time may have similar characteristics, such as shoppers on a weekday morning being mostly retirees. The sample is unlikely to represent the wider population, and results cannot be generalised reliably.

然而，便利样本极易产生偏差。在同一时间、同一地点出现的人可能具有相似特征，例如工作日上午的购物者大多是退休人员。样本不太可能代表更广泛的总体，结果也无法可靠地推广。

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9. Comparing Non-random and Random Sampling | 非随机抽样与随机抽样比较

Random methods, such as simple random sampling, give each member an equal chance of selection and reduce selection bias. Non-random methods are faster and cheaper but carry higher risk of bias. In Edexcel exams, you should be prepared to explain why a given method may be suitable or unsuitable in context.

随机方法（如简单随机抽样）使每个成员都有相等的入选机会，并能减少选择偏差。非随机方法更快、更便宜，但偏差风险更高。在 Edexcel 考试中，你应能解释在具体情境中某种方法为何合适或不合适。

Feature | 特征	Quota sampling | 配额抽样	Opportunity sampling | 便利抽样
Selection basis | 选择依据	Quotas for subgroups | 子群配额	Availability | 方便获取
Sampling frame needed | 是否需要抽样框	No | 否	No | 否
Main risk | 主要风险	Interviewer bias within quotas | 配额内调查员偏差	Unrepresentative location or time | 地点或时间不具代表性

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10. Bias in Non-random Sampling | 非随机抽样中的偏差

Bias arises because human choice replaces chance. Quota sampling can reduce some imbalance by controlling subgroup sizes, but it does not remove bias within each subgroup. Opportunity sampling may over-represent people who are easy to reach. To reduce bias, researchers can combine quotas with clear instructions or use random selection where possible.

偏差产生的原因是人为选择取代了随机机制。配额抽样可以通过控制子群规模来减少某些不平衡，但无法消除每个子群内部的选择偏差。便利抽样可能会过多地代表容易接触到的人群。为了减少偏差，研究者可以将配额与明确的操作指引结合起来，或者尽可能使用随机选择。

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11. Exam-style Example Question | 考试风格例题

“A market researcher wants to survey 100 adults about shopping habits. She stands outside a supermarket on a Tuesday morning and interviews the first 100 adults who enter. Identify the sampling method and explain one disadvantage.” This is opportunity sampling; one disadvantage is that weekday morning shoppers may not represent all adults, so the sample is biased.

题干大意：“一名市场研究员想调查 100 名成年人的购物习惯。她周二上午站在超市外，采访前 100 名进入超市的成年人。判断抽样方法并解释一个缺点。”这是便利抽样；一个缺点是工作日上午的购物者可能不能代表所有成年人，因此样本存在偏差。

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12. Key Exam Tips | 关键考试技巧

When answering Edexcel questions, always name the sampling method precisely: “quota sampling” or “opportunity sampling”. Link advantages and disadvantages to the given context, rather than writing generic lists. Use words like “sampling frame”, “representative”, and “bias” to show technical understanding.

在回答 Edexcel 题目时，要准确写出抽样方法名称：“配额抽样”或“便利抽样”。将优缺点与题目情境联系起来，而不是写泛泛的列表。使用“抽样框”、“代表性”和“偏差”等术语来体现专业理解。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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