Non-Random Sampling Methods Explained | 非随机抽样方法详解

📚 Non-Random Sampling Methods Explained | 非随机抽样方法详解

In statistics, sampling is the process of selecting a subset of individuals from a population to estimate characteristics of the whole population. Random sampling methods give every member of the population a known and equal chance of being selected, which helps reduce bias. Non-random sampling methods, however, do not rely on randomness; they are often used when random sampling is impractical, expensive, or impossible. This article explains the main types of non-random sampling, their uses, and their limitations for A-Level Mathematics students.

在统计学中，抽样是从总体中选取一部分个体来估计总体特征的过程。随机抽样方法使总体中每个成员都有已知且相等的机会被选中，从而有助于减少偏差。然而，非随机抽样方法不依赖随机性，通常用于随机抽样不切实际、成本过高或无法实施的情况。本文面向 A-Level 数学学生，详细解释非随机抽样的主要类型、用途及其局限性。

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1. What Are Non-Random Sampling Methods? | 什么是非随机抽样方法？

Non-random sampling, also called non-probability sampling, is a sampling technique where the samples are selected in a way that does not give every individual in the population an equal chance of being chosen. The selection is often based on the researcher’s judgement, convenience, or the voluntary participation of subjects. As a result, the sample may not be representative of the population, and statistical inference requires caution.

非随机抽样，又称非概率抽样，是一种抽样技术，其选取样本的方式并不给予总体中每个个体均等的入选机会。选择通常基于研究者的判断、便利性或受试者的自愿参与。因此，样本可能无法代表总体，进行统计推断时需要谨慎。

Key characteristics of non-random sampling:

• Selection is subjective or convenience-based.

  选择是主观的或基于便利性。

• Probability of selection is unknown.

  选取概率是未知的。

• Statistical theory of sampling distributions may not apply.

  抽样分布的统计理论可能不适用。

• Often cheaper and faster than random sampling.

  通常比随机抽样更便宜、更快速。

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2. Why Choose Non-Random Sampling? | 为什么选择非随机抽样？

Despite the statistical disadvantages, non-random sampling methods are widely used in real-world research. They are valuable when the population is difficult to access, when time and budget are limited, or when the research is exploratory rather than confirmatory. For A-Level students, understanding these reasons helps evaluate the validity of studies that use such methods.

尽管存在统计上的缺点，非随机抽样方法在现实研究中仍被广泛使用。当总体难以接触、时间和预算有限，或研究属于探索性而非验证性时，这些方法很有价值。对于 A-Level 学生来说，理解这些原因有助于评估使用此类方法的研究的有效性。

Common reasons to use non-random sampling:

• Insufficient time or funding for a full random sample.

  没有足够的时间或资金进行完整的随机抽样。

• No complete list of the population (sampling frame).

  没有完整的总体名单（抽样框）。

• The research aims to test a hypothesis quickly or to gain initial insights.

  研究旨在快速检验假设或获取初步见解。

• The target population is rare or hidden, such as drug users or homelessness groups.

  目标总体是稀有的或隐藏的，例如吸毒者或无家可归者群体。

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3. Convenience Sampling | 便利抽样

Convenience sampling involves selecting individuals who are easiest to reach or who are available at the time of the study. For example, a student conducting a school survey might interview classmates in the cafeteria because they are readily accessible. This method is simple and inexpensive, but it is highly prone to bias because the sample may not reflect the entire population.

便利抽样是指选择最容易接触或在研究时可用到的个体。例如，一名学生在学校食堂采访同学进行问卷调查，因为他们最容易接触到。这种方法简单且成本低，但极易产生偏差，因为样本可能无法反映整个总体。

Advantages of convenience sampling:

• Very quick and easy to carry out.

  非常快速且易于实施。

• Low financial cost.

  财务成本低。

• Useful for pilot studies or preliminary exploration.

  适用于试点研究或初步探索。

Disadvantages:

• Severe risk of under-representation of certain groups.

  某些群体被严重低估的代表性风险。

• Results cannot be generalised reliably to the whole population.

  结果无法可靠地推广到整个总体。

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4. Voluntary Response Sampling | 自愿回应抽样

Voluntary response sampling, also known as self-selection sampling, occurs when individuals choose to participate in a survey or study on their own initiative. Common examples include online polls, phone-in votes, and questionnaires posted on social media. The respondents are often those with strong opinions, which leads to bias.

自愿回应抽样，又称自我选择抽样，是指个体主动选择参与调查或研究。常见的例子包括在线投票、电话投票以及发布在社交媒体上的问卷。回应者往往是那些观点强烈的人，这会导致偏差。

For A-Level students, it is important to recognise that voluntary response samples tend to over-represent people with extreme views or high motivation. This makes the sample unrepresentative of the general public.

对于 A-Level 学生而言，重要的一点是要认识到自愿回应样本往往过度代表持有极端观点或高动机的人。这使得样本无法代表普通公众。

Example: A local radio station asks listeners to text in their opinion about a new policy. Only listeners who feel strongly enough will respond, so the results do not reflect the entire community.

例如：某广播电台请听众通过短信表达对新政策的看法。只有那些感受足够强烈的听众才会回应，因此结果不能反映整个社区。

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5. Purposive (Judgement) Sampling | 目的性（判断）抽样

Purposive sampling, also called judgement sampling, relies on the researcher’s expertise to select individuals who are deemed most useful or representative for the study. For instance, a researcher studying expert opinions on climate change might deliberately select climate scientists from different regions. This method ensures that the sample contains relevant expertise, but it is subjective because the researcher decides who is “typical” or “informative”.

目的性抽样，又称判断抽样，依赖研究者根据专业知识选择被认为对研究最有用或最具代表性的个体。例如，研究气候变化专家意见的研究者可能会特意选择来自不同地区的气候科学家。这种方法确保样本包含相关的专业知识，但具有主观性，因为由研究者决定谁是“典型的”或“有信息量的”。

Purposive sampling is often used in qualitative research, case studies, and when a specific subgroup is of interest. However, it does not allow statistical estimation of population parameters because selection is non-random.

目的性抽样通常用于定性研究、案例研究以及针对特定亚群的研究。然而，由于选择是非随机的，不能对总体参数进行统计估计。

Types of purposive sampling:

• Maximum variation sampling – captures a wide range of perspectives.

  最大差异抽样——涵盖广泛的视角。

• Homogeneous sampling – focuses on one particular subgroup.

  同质抽样——专注于某一个特定亚群。

• Typical case sampling – selects cases that are “average” or normal.

  典型案例抽样——选择“平均”或正常的案例。

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6. Snowball Sampling | 雪球抽样

Snowball sampling is a technique where existing study subjects recruit future subjects from among their acquaintances. This method is especially useful for hidden or hard-to-reach populations, such as illegal drug users, individuals with rare diseases, or undocumented immigrants. The sample grows like a snowball rolling downhill.

雪球抽样是一种由现有研究对象从其熟人网络中招募未来研究对象的技术。这种方法对隐藏的或难以接触的总体尤其有用，例如非法药物使用者、患罕见病者或无证移民。样本像滚下山的雪球一样越滚越大。

How it works:

1. Initial participants are identified through convenience or purposive sampling.

   通过便利抽样或目的性抽样确定初始参与者。

2. Each participant refers other eligible individuals.

   每位参与者引荐其他符合条件的人。

3. This process continues until the desired sample size is reached.

   该过程持续到达到所需样本量为止。

Snowball sampling is effective for reaching hidden populations, but it introduces bias because participants share similar social networks, which may lead to over-representation of certain characteristics.

雪球抽样在接触隐藏群体方面很有效，但它会引入偏差，因为参与者具有相似的社会网络，这可能导致某些特征被过度代表。

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7. Quota Sampling | 配额抽样

Quota sampling is a non-random technique similar to stratified sampling, but the selection within each stratum is not random. The researcher first divides the population into mutually exclusive groups (quotas) based on characteristics such as age, gender, or income. Then interviewers are instructed to fill each quota using judgement or convenience.

配额抽样是一种类似于分层抽样的非随机技术，但每个层内的选择不是随机的。研究者首先根据年龄、性别或收入等特征将总体划分为互斥的组（配额）。然后访问员被指示使用判断或便利方式来填满每个配额。

For example, a market researcher may need 100 respondents, with 50 males and 50 females. The interviewer can approach anyone who fits the gender quota, without using random selection. This guarantees proportional representation of certain groups, but it does not remove selection bias because the interviewer chooses who to approach.

例如，市场研究员可能需要 100 名受访者，其中 50 名男性和 50 名女性。访问员可以接触任何符合性别配额的人，而不进行随机选择。这保证了某些群体的比例代表性，但并不能消除选择偏差，因为访问员决定接触谁。

Comparison: In stratified random sampling, participants within each stratum are chosen randomly; in quota sampling, they are chosen non-randomly.

比较：在分层随机抽样中，每个层内的参与者是随机选择的；而在配额抽样中，他们是非随机选择的。

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8. Non-Random vs Random Sampling | 非随机与随机抽样对比

To understand the value of non-random sampling, it is helpful to compare it directly with random sampling methods such as simple random sampling, systematic sampling, and stratified random sampling. The table below summarises the key differences.

为了理解非随机抽样的价值，将其与随机抽样方法（如简单随机抽样、系统抽样和分层随机抽样）直接比较是有帮助的。下表总结了主要区别。

Feature	Random Sampling	Non-Random Sampling
Selection basis | 选择基础	Chance / random mechanism | 机会/随机机制	Judgement, convenience, or self-selection | 判断、便利或自我选择
Probability of selection | 选取概率	Known and non-zero | 已知且非零	Unknown | 未知
Representativeness | 代表性	Usually high | 通常较高	Often low | 通常较低
Bias | 偏差	Minimised | 最小化	Likely to be present | 很可能存在
Cost and time | 成本和时间	Higher | 较高	Lower | 较低
Ability to estimate sampling error | 估计抽样误差的能力	Yes | 可以	No | 不可以

In random sampling, the Central Limit Theorem and other statistical tools allow researchers to calculate confidence intervals and test hypotheses. In non-random sampling, these tools are invalid because the sample selection mechanism is not probability-based.

在随机抽样中，中心极限定理和其他统计工具使研究者能够计算置信区间和检验假设。而在非随机抽样中，这些工具是无效的，因为样本选择机制并非基于概率。

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9. Bias and Limitations | 偏倚与局限性

The main limitation of non-random sampling is bias. Bias occurs when some members of the population are more likely to be selected than others, leading to a sample that systematically differs from the population. This reduces the accuracy of estimates and weakens the credibility of conclusions.

非随机抽样的主要局限性是偏倚。当总体中某些成员比其他成员更有可能被选中时，就会产生偏倚，导致样本系统性地偏离总体。这会降低估计的准确性，削弱结论的可信度。

Types of bias common in non-random sampling:

• Selection bias – the researcher or the method systematically excludes certain groups.

  选择偏倚——研究者或方法系统性地排除了某些群体。

• Volunteer bias – self-selected participants have different characteristics from non-participants.

  志愿者偏倚——自我选择的参与者与非参与者具有不同的特征。

• Referral bias – in snowball sampling, participants are linked socially, so the sample may not represent isolated individuals.

  引荐偏倚——在雪球抽样中，参与者之间存在社会联系，因此样本可能无法代表孤立的个体。

A-Level students should always ask whether a sample was obtained randomly when assessing the validity of a statistical study. If non-random methods were used, any conclusions should be treated as indicative, not definitive.

A-Level 学生在评估统计研究的有效性时，应始终询问样本是否通过随机方式获得。如果使用了非随机方法，任何结论都应视为指示性的，而非确定性的。

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10. When to Use Non-Random Sampling | 何时使用非随机抽样

Although non-random sampling has limitations, there are situations where it is the only viable option. A researcher might use non-random sampling when the goal is to explore a topic, develop a questionnaire, or study a hard-to-reach population. In such cases, the speed and low cost outweigh the lack of statistical generalisability.

尽管非随机抽样存在局限，但在某些情况下它是唯一可行的选择。研究者在目标为探索主题、编制问卷或研究难以接触的总体时，可能会使用非随机抽样。在这种情况下，速度和低成本超过了统计上缺乏可推广性的缺点。

Appropriate situations include:

• Pilot studies before a large-scale random survey.

  大规模随机调查之前的试点研究。

• Exploratory research where relationships are not yet well understood.

  关系尚不明确的探索性研究。

• Studying hidden populations for which no sampling frame exists.

  研究不存在抽样框的隐藏群体。

• Qualitative studies focused on depth of understanding rather than statistical inference.

  注重理解深度而非统计推断的定性研究。

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11. Summary | 总结

Non-random sampling methods offer practical alternatives to random sampling when constraints exist. Convenience sampling and voluntary response sampling are easy to implement but highly biased. Purposive sampling allows researchers to select informative cases, while snowball sampling helps reach hidden populations. Quota sampling ensures group proportions but not random selection within groups. Each method has its own strengths and weaknesses, and the choice of method must be justified by the research context.

非随机抽样方法在存在限制时为随机抽样提供了实用的替代方案。便利抽样和自愿回应抽样容易实施但偏倚较大。目的性抽样允许研究者选择有信息量的案例，而雪球抽样有助于接触隐藏群体。配额抽样保证了组的比例，但不保证组内随机选择。每种方法都有其优缺点，方法的选择必须根据研究背景来论证。

For A-Level Mathematics and Statistics examinations, students need to identify these methods, understand their biases, and explain why a particular sampling method might be chosen in a given scenario. The ability to criticise sampling methods is a key skill in statistical literacy.

对于 A-Level 数学和统计学考试，学生需要识别这些方法，理解其偏倚，并解释在给定情境下为何可能选择某种抽样方法。批判性评价抽样方法的能力是统计素养中的关键技能。

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Published by TutorHao | Mathematics Revision Series | aleveler.com

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