Lesson 1.3: Sampling Methods and Their Evaluation

Introduction

In this lesson, we will explore the various sampling methods used in statistical investigations, both random and non-random. Understanding these methods is crucial for obtaining data that accurately reflects a population. We will also delve into the concept of stratification, learn how to carry out different types of sampling, and evaluate the pros and cons of each method. By the end of this lesson, students will be able to choose appropriate sampling strategies depending on specific research contexts.

Learning Objectives

• Understand random and non-random sampling methods: simple random, systematic, cluster, judgmental (quota or convenience), and snowball sampling.
• Understand the use of stratification in both proportional and disproportional ratios prior to sampling.
• Evaluate the advantages, limitations, and appropriate contexts of each sampling method and discuss practical constraints when collecting unbiased data.
• Learn how to carry out simple random, systematic, cluster, judgmental, and snowball sampling.
• Calculate the numbers required for a proportional stratified sample and justify the use of stratification.

H2: Random Sampling Methods

Random sampling methods are techniques in which each member of a population has a known and equal chance of being selected. This section discusses simple random sampling, systematic sampling, and cluster sampling.

H3: Simple Random Sampling

In simple random sampling, every individual in the population has an equal chance of being selected. This method is often implemented using random number generation or drawing names from a hat.

How to Conduct Simple Random Sampling

1. Define the population you want to study. For example, suppose we want to know the average study hours of students in a school with 500 students.
2. Assign a unique number to each individual in the population (from 1 to 500).
3. Use a random number generator or a table of random numbers to select the sample.
4. For example, if we randomly selected the numbers 23, 45, and 112, these would be the students chosen for our sample.

Example

If we wanted to pick a sample of 10 students from the 500, we could generate 10 random numbers:

1. Using a random number generator, we get: 17, 42, 106, 220, 150, 342, 405, 88, 364, and 485.
2. The corresponding students selected from the population will form our sample.

H3: Systematic Sampling

Systematic sampling selects every $k^{th}$ member of the population after a random starting point. This method can be easier and faster than simple random sampling, particularly for large populations.

How to Conduct Systematic Sampling

1. Decide the size of your sample, say $n$. For example, if we want to select 100 students from 1000.
2. Calculate $k$, where $k = \frac{N}{n}$, with $N$ being the population size. Here, $k = \frac{1000}{100} = 10$.
3. Randomly choose a starting point between 1 and $k$.
4. Select every $k^{th}$ individual from that starting point.

Example

If we start at position 3:

• The sample will be students numbered 3, 13, 23, 33, ..., and so forth up to 1000.

H3: Cluster Sampling

Cluster sampling involves dividing the population into groups or clusters, then randomly selecting entire clusters to form the sample. This method is useful when individuals are spread out over a large area.

How to Conduct Cluster Sampling

1. First, identify clusters within the population (e.g. classes within a school).
2. Use random sampling to select a few clusters.
3. Every individual within the selected clusters is included in the sample.

Example

If a school has 20 classes, and we randomly choose classes 4, 9, and 17, all students within those classes will be sampled.

H2: Non-Random Sampling Methods

Non-random sampling methods do not provide every individual in a population an equal chance of being selected. Basic types include judgmental sampling and snowball sampling.

H3: Judgmental (Quota) Sampling

Judgmental sampling involves selecting individuals based on the researcher’s judgment to meet certain quotas. While this method can provide valuable insights, it may introduce significant biases.

How to Conduct Judgmental Sampling

1. Decide criteria for selection (e.g. age, gender).
2. Choose individuals that fit these criteria until a predetermined quota is achieved.

Example

If a researcher wants to survey opinions on a school policy and has determined they need 50 males and 50 females, they might choose participants based on their acquaintance with suitable individuals.

H3: Snowball Sampling

Snowball sampling is often used when the population is hard to access. In this method, existing study subjects recruit future subjects.

How to Conduct Snowball Sampling

1. Start with a few known participants from the target population.
2. Ask those participants for referrals to other individuals.
3. Continue until the sample size is adequate.

Example

Suppose a researcher is studying the behavior of certain social groups; they might interview one member and ask them to introduce others from their network.

H2: Stratified Sampling

Stratified sampling involves dividing the population into distinct subgroups (strata) that differ in a specific characteristic and subsequently sampling from each stratum.

Proportional vs Disproportional Stratified Sampling

• Proportional Stratified Sampling: Each subgroup is sampled in proportion to its size in the population.
• Disproportional Stratified Sampling: Some subgroups are overrepresented or underrepresented compared to their actual size in the population.

How to Conduct Stratified Sampling

1. Identify the strata relevant to your research.
2. Decide the sample size $n$ to be drawn from each stratum. For proportional sampling:

• Determine the sample size from each stratum by calculating: $n_i = \frac{N_i}{N} \times n$, where $N_i$ is the size of the stratum and $N$ is the total population size.

Example

If a school has 100 seniors, 200 juniors, and 300 sophomores and we want to sample 60 students:

• Seniors: $n_1 = \frac{100}{600} \times 60 = 10$
• Juniors: $n_2 = \frac{200}{600} \times 60 = 20$
• Sophomores: $n_3 = \frac{300}{600} \times 60 = 30$

Conclusion

In this lesson, students has learned about various sampling methods including both random and non-random techniques. It is crucial to evaluate the appropriateness of these methods based on the research context. Random sampling provides strong generalization opportunities but may be resource-intensive. Non-random methods can yield quick results but might introduce bias. Stratified sampling allows for targeted insights but needs careful implementation and justification.

Study Notes

• There are two main types of sampling methods: random and non-random.
• Simple random sampling gives every individual an equal chance of selection.
• Systematic sampling selects every $k^{th}$ individual after a random starting point.
• Cluster sampling uses groups and includes entire groups in the sample.
• Judgmental (quota) sampling is based on researcher judgment.
• Snowball sampling is useful for hard-to-reach populations, relying on referrals.
• Stratification divides the population into strata for targeted sampling, proportional or disproportional.
• Adequate justification and methods must be chosen based on the research objectives.