📊Sampling Surveys Unit 2 – Sampling Design and Techniques

Introduction to Sampling

• Sampling involves selecting a subset of individuals from a population to estimate characteristics of the entire population
• Enables researchers to gather data efficiently and cost-effectively when studying large populations
• Allows for inferential statistics, drawing conclusions about the population based on the sample
• Requires careful design and execution to ensure the sample is representative of the population
• Sampling techniques are used in various fields (market research, public opinion polling, quality control)
• Proper sampling minimizes bias and sampling error, leading to more accurate results
• Sampling is a fundamental concept in statistics and is essential for making data-driven decisions

Population vs. Sample

• A population is the entire group of individuals, objects, or events that a researcher wants to study and draw conclusions about
  • Populations can be large and diverse (all registered voters in a country)
  • Populations can be specific and well-defined (all students enrolled in a particular university)
• A sample is a subset of the population selected for study
  • Samples are used to estimate characteristics of the population
  • Samples should be representative of the population to minimize bias
• Population parameters are the true values of characteristics in the entire population
• Sample statistics are the values calculated from the sample data, used to estimate population parameters
• Inferential statistics allows researchers to make conclusions about the population based on the sample data
• The quality of the sample determines the accuracy of the inferences made about the population

Sampling Methods Overview

• Sampling methods are techniques used to select a sample from a population
• The choice of sampling method depends on factors (population size, variability, available resources)
• Probability sampling involves random selection, where each unit has a known, non-zero chance of being selected
  • Probability sampling allows for the calculation of sampling error and the use of inferential statistics
  • Examples of probability sampling include simple random sampling, stratified sampling, and cluster sampling
• Non-probability sampling involves non-random selection, where the probability of selecting each unit is unknown
  • Non-probability sampling is often used when probability sampling is not feasible or practical
  • Examples of non-probability sampling include convenience sampling, snowball sampling, and quota sampling
• The sampling frame is a list of all units in the population from which the sample is drawn
• Sampling bias occurs when the sample does not accurately represent the population, leading to inaccurate estimates
• Sampling error is the difference between a sample statistic and the corresponding population parameter

Probability Sampling Techniques

• Simple random sampling (SRS) is a probability sampling technique where each unit has an equal chance of being selected
  • In SRS, a random number generator or a random number table is used to select units from the sampling frame
  • SRS is easy to implement and analyze, but it may not be practical for large or geographically dispersed populations
• Stratified sampling involves dividing the population into homogeneous subgroups (strata) and selecting a random sample from each stratum
  • Stratification variables are characteristics used to divide the population (age, gender, income level)
  • Stratified sampling ensures that all subgroups are represented in the sample, reducing sampling error
• Cluster sampling involves dividing the population into clusters, randomly selecting a subset of clusters, and sampling all units within the selected clusters
  • Clusters are naturally occurring groups (city blocks, schools, hospitals)
  • Cluster sampling is useful when a complete list of individual units is not available or when units are geographically dispersed
• Systematic sampling involves selecting units at regular intervals from the sampling frame
  • The first unit is selected randomly, and then every kth unit is selected, where k is the sampling interval
  • Systematic sampling is simple to implement but may lead to bias if there is a hidden pattern in the population

Non-Probability Sampling Techniques

• Convenience sampling involves selecting units that are easily accessible or willing to participate
  • Convenience sampling is quick and inexpensive but may not be representative of the population
  • Examples of convenience sampling include surveying people at a shopping mall or using a volunteer sample
• Snowball sampling involves initially selecting a small group of participants who then recruit additional participants from their networks
  • Snowball sampling is useful when studying hard-to-reach or hidden populations (drug users, homeless individuals)
  • Snowball sampling relies on referrals, which may lead to bias if the initial participants are not diverse
• Quota sampling involves selecting units based on predetermined quotas for specific characteristics
  • Quotas are set to ensure that the sample has the same proportions of characteristics as the population
  • Quota sampling is non-random, as the researcher selects units to fill the quotas
• Purposive sampling involves selecting units based on the researcher's judgment and the study's objectives
  • Purposive sampling is useful when the researcher needs to select units with specific characteristics or expertise
  • Examples of purposive sampling include selecting key informants or extreme cases

Sample Size Determination

• Sample size is the number of units selected from the population for the study
• The required sample size depends on factors (population variability, desired precision, confidence level)
• Larger sample sizes generally lead to more precise estimates and smaller sampling errors
• The margin of error is the maximum expected difference between the sample statistic and the population parameter
  • The margin of error decreases as the sample size increases, holding other factors constant
• The confidence level is the probability that the true population parameter falls within the confidence interval
  • Common confidence levels are 90%, 95%, and 99%
  • Higher confidence levels require larger sample sizes to maintain the same margin of error
• Sample size calculators or formulas can be used to determine the appropriate sample size for a given study
  • The formula for calculating the sample size for a proportion is: $n = \frac{Z^2 p(1-p)}{e^2}$, where $Z$ is the z-score, $p$ is the expected proportion, and $e$ is the margin of error
• Practical considerations (budget, time, resources) may limit the achievable sample size

Dealing with Bias and Error

• Bias is a systematic error that leads to inaccurate estimates of population parameters
• Selection bias occurs when the sampling method favors certain units over others
  • Examples of selection bias include undercoverage (excluding certain units) and self-selection (participants choosing to participate)
• Non-response bias occurs when there are systematic differences between those who respond and those who do not respond to a survey
  • Non-response bias can be reduced by increasing response rates through incentives, reminders, or multiple contact attempts
• Measurement bias occurs when the data collection process systematically distorts the responses
  • Examples of measurement bias include leading questions, social desirability bias, and recall bias
• Sampling error is the random variation in sample statistics due to the sampling process
  • Sampling error can be reduced by increasing the sample size or using more efficient sampling methods
• To minimize bias and error, researchers should:
  • Use probability sampling methods when possible
  • Ensure the sampling frame is complete and up-to-date
  • Pretest and validate survey instruments
  • Train interviewers to minimize interviewer bias
  • Use weighting techniques to adjust for non-response or undercoverage

Practical Applications and Case Studies

• Market research: Sampling is used to gather data on consumer preferences, brand awareness, and product satisfaction
  • Example: A company conducts a stratified sample of consumers to evaluate the potential demand for a new product
• Public opinion polling: Sampling is used to estimate population opinions on various topics (politics, social issues, consumer confidence)
  • Example: A polling organization conducts a national survey using random digit dialing to estimate voter preferences before an election
• Quality control: Sampling is used to monitor the quality of products or services in manufacturing or service industries
  • Example: A factory uses systematic sampling to select a sample of products for inspection to ensure they meet quality standards
• Healthcare research: Sampling is used to study the prevalence of diseases, the effectiveness of treatments, and patient satisfaction
  • Example: A hospital conducts a cluster sample of patients to assess the quality of care and identify areas for improvement
• Environmental studies: Sampling is used to monitor pollution levels, assess biodiversity, and evaluate the impact of human activities on ecosystems
  • Example: Researchers use stratified sampling to estimate the population of a rare species in a large nature reserve
• Case study: The Gallup Organization's use of quota sampling in the 1936 U.S. presidential election
  • Gallup used quota sampling to accurately predict the election outcome, while the Literary Digest's mail-in survey, which used a non-representative sample, famously predicted the wrong winner
• Case study: The use of cluster sampling in the World Health Organization's Expanded Programme on Immunization (EPI) surveys
  • The EPI surveys use a two-stage cluster sampling design to estimate vaccination coverage and other health indicators in developing countries, providing valuable data for public health decision-making