Statistical Sampling: Core Concepts and Essential Elements

Sampling Process and Principles

To ensure a sample accurately represents the population under investigation, its size and the methodology used must adhere to specific principles.

Core Sampling Concepts

Population (Universe)

The population, or universe, is defined as the complete set of elements existing within a specific space and time, all of which are affected by the same problem under study, and from which information is desired.

Sample

A sample is a representative fraction of the population. From the sample, we can infer or estimate the characteristics of the entire population.

Sampling

Sampling is the procedure for selecting a subset of elements (the sample) from a larger group (the population) in order to make inferences about the population. For well-conducted sampling, it is essential that the chosen elements adequately represent the population. If the sample fails to fulfill this task, it is considered biased.

Sampling Units

Sampling units are the individual elements available for selection. These units may or may not coincide with the ultimate units of the population being studied.

Sampling Frame (Random Basis)

The sampling frame is the list of all sampling units from which the sample will be drawn. A robust sampling frame should meet the following criteria:

• It should contain every element of the target population.
• Each element should appear only once (no duplicates).
• It should only contain elements that belong to the population under study.

In a broader sense, the sampling frame encompasses all information that can be used to select the sample, yielding results comparable to those obtained from a comprehensive list.

Essential Elements in Statistical Sampling

Beyond the fundamental concepts, several other elements are crucial for effective statistical sampling:

• Sample Size (n)

  The sample size (n) refers to the total number of sampling units that constitute the sample.

• Population Size (N)

  The population size (N) represents the total number of elements that make up the entire population.

• Parameter

  A parameter is a numerical value of the population, typically unknown, that represents a specific characteristic of the population (e.g., the population mean, the population proportion). The parameter is the value intended for estimation, and this estimate is known as an estimator.

• Standard Deviation

  The standard deviation (σ) is derived from the population variance (σ²) by taking its square root. It is used to determine the sample size; a more uniform population (smaller standard deviation) generally allows for a smaller sample size.

• Estimation Error

  Estimation error is defined as the difference between the estimated value (from the sample) and the true, unknown value (the population parameter). Represented by Epsilon (ε), this error arises because a sample does not provide comprehensive information about the entire population. In this context, it is often called sampling error or random error. Sampling error can typically be reduced by increasing the sample size. In finite populations (e.g., 10,000 inhabitants), a common convention considers the sampling error to be approximately two standard deviations.

• Confidence Level

  The confidence level defines the probability that the true population parameter falls within a specified range (the confidence interval) around the sample estimate. It is expressed as a percentage. For example:

  • A sampling error of ±2 standard deviations corresponds to approximately a 95% confidence level.
  • A sampling error of ±3 standard deviations corresponds to approximately a 99% confidence level.