Sampling Techniques: An Overview

• Sampling is a set of statistical techniques used to select a representative subset of a population to draw conclusions about the entire population

Introduction to Sampling

• Society's need for and availability of information is increasing.
• Ideally, a study involves analyzing every individual in a population, known as a census.
• However, censuses are often unfeasible due to economic or time constraints.
• Sampling selects a subset to represent the whole and statistical methods are used to ensure it is representative.
• The goal is to select an appropriate sample for analyzing a population.
• Sampling methods vary depending on the population (finite or infinite) and the approach (probabilistic or non-probabilistic).
• Selected samples must be representative, with each unit representing characteristics from a known quantity within the population.

Basic Sampling Concepts

• Unit of Observation: The object or individual being studied.
• Population: The collection of all individuals/objects of interest.
• Sample: A subset of the population.
• Population Size: The total number of individuals in the population and can be large, unknown or infinite.
• Sampled Population: The set of objects/individuals selected from the population to be in the sample.
• Sample Size: The number of individuals included in the sample and is much smaller than the population size.
• Sampling Unit: Each element or unit included in the sample, representing either a single element or a group.
• Parameter: A functional of a variable of interest that is the average, proportion variance etc.
• Sampling involves selecting a sample from the target population and gathering data on variables of interest.
• Population parameters, are estimated from the sample through estimators.
• For example, estimating the average spending of individuals from Spain on clothes in December.
• A sample of individuals are selected and data on clothes expenditure in December collected is used to estimate the population parameter.
• A framework, or MARCO is generally needed to select a sample, it is a list of the sampling units.

Sampling Frame

• The sampling frame is a list of elements or materials providing information about the population under study, such as people, businesses or households.
• Population units included in the sample, are extracted from the framework.
• The frame should match the target population, but discrepancies can occur due to errors, outdated information or omissions.
• Accessing frames with elementary units is difficult, frames with composed units is easier, such as streets, municipalities or familiar units.
• For population studies, the National Statistics Institute (Instituto Nacional de Estadística) uses the Census or the Municipal Register as sampling frames.
• Sampling frames may be unknown or outdated, making it difficult to create a list for a tourist study in a reasonable time.
• The list of individuals may not be current or may contain errors, so frame refinement is necessary.

Key Advantages and Limitations

• A census is necessary when individual data is required and when the population is small and can be analyzed in its entirety.
• Sampling is needed in these scenarios:
• When the population is infinite or very large
• When time or economic resources are limited
• When observation destroys the observation is destructive

Estimators

• Estimators of population parameters, such as average spending of individuals, proportions of individuals allergic to seafood, are calculated from sample data.
• Estimators are mathematical functions used to approximate the value of a population parameter from data.
• The sample mean X is a estimator of the population mean E[X] and depends on the type of sampling used.
• Weights are necessary when observations from the sample are from an optimal estimator.
• In inference, an estimator is a random variable and the sample mean obtained from a simple random sample, has a normal distribution.
• It's important to give the value of the point estimation on the sample and a measure of error or variability.
• Variance or typical deviation is studied to study the estimator.
• Basic estimators used are the sample mean, total sample, proportion sample, etc.
• Estimating a parameter θ of a variable of interest (X) involves taking a random sample (X1, ..., Xn) and getting an estimator of the parameter.
• Important properties to study an estimator are:
• Bias: Difference between the expected value of the estimator and the parameter.
• Efficiency: Achieved with minimum variance.
• Consistency: An estimator is consistent if it converges in probability to the when the sample size increases to infinity, asymptotically unbiased and its variance approaches zero.
• The bias and variance of an estimator are known when the distribution of the estimator is known.
• To determine all potential values of an estimator, all samples have to be extracted from the population and analyzing all results.
• In real life, only one sample is selected from a population and so real variance isn't known and only the estimation is shown.
• Several estimators will be reviewed for different sampling methods later in the course, as well as expression the expression for the variance and estimating.

Main Errors in Sampling

• Sampling Error: Occurs by analyzing only a subset of the population and it gauges the precision of estimates.
• The amount is related to sample size and method .
• Generally correlated with the typical deviation.

Selection Bias

• Occurs when a part of the population is inaccessible.
• If a study aims to gauge public opinion for a certain population being unable to be reached skews the findings.
• Interviewer selecting certain individuals over other can affect the results.

Measurement Bias

• Occurs through errors when collecting data.
• Common when studies depend on measuring equipment, can happen from the individuals doing the studies, or not telling the truth.
• Control questions are introduced to identify lies.

Non-Response Bias

• Inability to analyze due to external factor, can affect the results of the study.
• Studies can have absence of observations depending on the group and cause the results.

Designing a Sampling Study

• Steps include:
• Determine the population being studied
• Describe the population, if it is finite or not and if all the population is known
• Decide what information is desired
• Select the sampling method
• Work in the field to collect data
• Data processing and purification
• Analyze and interpretate

Types of Sampling

Probabilistic Sampling

• Probability of an being included in the sample is known from the start.
• Allows for calculating the range of error, controlling population parameters.
• Types of Probabilistic Sampling include Simple Random, Conglomerates, Stratified and Multistage.

Non-Probabilistic Sampling

• Likelihood of the inclusion is unknown.
• Presents biases impossible to measure.
• Extrapolation not possible to the entire population.

Convenience Sampling

• Researchers select sample without following probabilistic standards.
• Results cannot be generalized.
• For example data from a doctor analyzing patient data.

Quota Sampling

• Used in types of election studies.
• Researchers have a limited of surveys and divide proportionally.

Accidental or Snowball Sampling

• Used where it is difficult to access the individuals.
• A sample of individual and successive individuals identified by them
• Frequently used in studies by social media

Technical Specifications

• Creating a file technique is necessary when completing a sampling study with basic information:
• Target Population of study
• Sampled Unit
• Geographical Area
• Timing
• Sampling frame: listing used to get the sample
• Margin of Error and Confidence Levels
• Sampling Method
• Selection method for sampling
• Type of Questionnaire
• Technique in collecting information.
• Chief Investigator
• Title
• Data Source

Examples of Sample Designs

• Technical data for the CIS Barometer (Center for Sociological Research) and conducts personal surveys via telephone.
• National Scope survey in individuals 18+
• 4,000 individuals size sample
• The estates are formed by size of a population with some areas in range for example 2001 to 10,000
• Under simple random it is at +- 1.6

Technical Population Survey

• Continual survey of trimester periodicity
• Population that live in family housing
• National territory scope
• Quarter of results reported
• Personal interview method with population of 130,000 individuals

Consumer Price Index

• Continuing survey of monthly periodicity
• Base period of 2021
• Sample of 177 municipalities
• Various articles surveyed monthly