Sampling Methods and Bias in Data Collection

1.4 Other Effective Sampling Methods

Overview of Sampling Techniques

Sampling is a fundamental process in statistics used to select a subset of individuals from a population for study. While simple random sampling is the most basic method, there are several other effective techniques that help ensure representative samples and address practical constraints.

• Simple Random Sampling: Every possible sample of size n from a population of size N has an equally likely chance of occurring.

• Stratified Sampling: The population is divided into non-overlapping groups called strata, and a simple random sample is taken from each stratum. Individuals within each stratum should be similar in some way. Example: A college divides its community into students, staff, and faculty to survey campus safety, then randomly samples from each group.

• Systematic Sampling: Every kth individual is selected from the population, starting from a randomly chosen number between 1 and k. Example: A grocery store owner surveys every 7th customer, starting with a randomly chosen 5th customer, then the 12th, 19th, etc., until the desired sample size is reached.

• Cluster Sampling: The population is divided into groups (clusters), a simple random sample of clusters is selected, and all individuals within the chosen clusters are surveyed. Example: A university treats each online class as a cluster, randomly selects some classes, and surveys all students in those classes.

Comparison: Stratified vs. Cluster Sampling

Both methods involve dividing the population into groups, but differ in how samples are selected:

• Stratified Sampling: Random samples are taken from each group (stratum).

• Cluster Sampling: Some groups (clusters) are randomly selected, and all individuals in those groups are surveyed.

Sampling Identification Example

Consider the following scenario:

• A sales manager wants to obtain a sample of 12 clients from a list of 100. He randomly selects a number from 1 to 8 (obtaining 7), then includes the 7th client and every 8th client thereafter. The selected clients are: 7, 15, 23, 31, 39, 47, ...

• Type: Systematic Sampling

1.5 Bias in Sampling

Understanding Bias in Sampling

Bias occurs when a sample does not accurately represent the population, leading to misleading results. Recognizing and minimizing bias is essential for valid statistical inference.

• Sampling Bias: The sampling technique favors one part of the population over another. Example: Phone-in surveys exclude individuals without phones, leading to unrepresentative results.

• Nonresponse Bias: Individuals selected for the sample who do not respond may have different opinions from those who do respond. Example: A mail-in questionnaire is not returned by some recipients, potentially skewing results.

• Response Bias: Survey answers do not reflect the true feelings of respondents, often due to the way questions are asked or the presence of interviewers. Example: Uniformed police officers conducting door-to-door surveys may influence respondents to answer favorably about the police department.

Summary Table: Types of Sampling and Bias

Sampling Method	Description	Example
Simple Random	Every sample of size n has equal chance	Randomly select students from a list
Stratified	Divide into strata, sample from each	Sample students, staff, faculty separately
Systematic	Select every k-th individual	Survey every 7th customer
Cluster	Randomly select clusters, survey all in cluster	Survey all students in selected online classes

Type of Bias	Description	Example
Sampling Bias	Technique favors part of population	Phone-in survey excludes those without phones
Nonresponse Bias	Non-respondents differ from respondents	Mail-in questionnaire not returned
Response Bias	Answers do not reflect true feelings	Police officers survey public opinion

Key Formulas

• Systematic Sampling Formula: To select every k-th individual, start at a random number r between 1 and k, then select individuals at positions: $r, r+k, r+2k, \ldots$ Example: If r = 7 and k = 8, selected positions are 7, 15, 23, 31, ...

Additional info: Academic context and examples were expanded for clarity and completeness.