ES

Sampling Concepts and Methods Notes

Context of Sampling in Everyday Communication with Numbers

  • Research workflow: address a research question or hypothesis

  • Identify variables: independent vs. dependent

  • Determine how to measure variables

  • Plan data collection

  • Purpose: Statistical inference to answer the research question

  • Scope: On whom? And how?

Key Concepts: Population, Sample, and Inference

  • Population: The entire pool from which a statistical sample is drawn

  • Sample: A subset of the population used for analysis

  • Sample Frame: A list of all individuals in the population who can be sampled; sometimes not fully attainable

  • Sampling: A process where a predetermined number of observations are taken from a larger population

  • Population parameter: A specific value that describes a characteristic of the population (unknown until measured)

  • Sample statistic: A numerical value calculated from the sample to estimate the population parameter

  • Statistical inference: Using sample data to make conclusions about the population

  • Confidence interval: A range of values used to estimate the population parameter

  • 95% confidence interval: A commonly used interval level; interpretation depends on repeated sampling

  • Interpretation is important: CI conveys uncertainty and reliability of the estimate

Complete Enumeration vs. Sampling

  • Complete enumeration (studying the population directly)

    • Strength: Provides a precise answer to the research question

    • Weakness: Time, energy, and money required

  • Sampling (studying a subset of the population)

    • Strength: Saves time, energy, and money

    • Weakness: Provides an estimate rather than an exact population value

  • Important generalization: With properly drawn random and representative samples, estimation can be very accurate; otherwise, estimates can be far from the truth

  • Sampling can be done using probabilistic or non-probabilistic techniques

Probability vs. Non-Probability Sampling

  • Probability sampling (random sampling)

    • Every member of the defined population has an equal chance of being selected

    • Also called unbiased or representative sampling

    • Requires a sampling frame (at least partially)

    • Goals: Generalize findings to a broader population; maximize representativeness

    • Common methods: Simple random, systematic, stratified

  • Non-probability sampling (non-random sampling)

    • Does not give all individuals equal chances of selection

    • Some members are more likely to be included than others

    • Also called biased or unrepresentative sampling

    • Often chosen to save resources or when generalization is not the primary goal

    • Common methods: Volunteer, Convenience, Purposive, Snowball, Quota

Probability Sampling Methods

  • A probability sampling method uses some form of random selection; every defined population member has an equal chance of being chosen

  • Requires a sampling frame (or partial frame)

  • Three main methods:

    • Simple Random Sampling

    • Systematic Random Sampling

    • Stratified Random Sampling

Simple Random Sampling

  • Basic technique: select a group of subjects from a larger group where every unit has an equal chance of being selected

  • 3 steps:

    1. Get a list of everyone in the population (with identifiers)

    2. Generate appropriate random numbers (e.g., using random number generators)

    3. Select individuals whose identifiers match the random numbers

Systematic Random Sampling

  • Sample members are selected according to a random starting point and a fixed, periodic interval

  • Four steps:

    1. Get a list of everyone in the population

      • Calculate skip interval = Population size/sample size

      • k = N / n (formula)

        k = The skip interval (or sampling interval).

      • N = The total population size.

      • n = The desired sample size. 

      • To select a sample, randomly choose a starting point between 1 and k, then select every k-th element from the population until the sample size n is achieved.

    2. Pick a random starting point between 1 and the skip interval

    3. A constant interval is selected to facilitate participant
      selection
      • 8,18,28,38,48,...

      This method is known as systematic sampling and is effective for producing a representative sample when the population is ordered.

Stratified Random Sampling

  • Population can be partitioned into subpopulations (strata) of similar units

  • Within each stratum, apply the same random selection process as simple random sampling

  • Rationale: ensures representation from each subpopulation

Non-Probability Sampling Methods

  • Non-probability sampling: samples are gathered in a process that does not give all individuals equal chances of being selected

  • Five common methods:

    • Volunteer Sampling

    • Convenience Sampling

    • Purposive Sampling

    • Snowball Sampling

    • Quota Sampling

Volunteer Sampling

  • Participants self-select into the study

  • Often those with a strong interest in the topic

  • Examples: Research on healing power of prayer; firearms regulation surveys conducted by phone

Convenience Sampling

  • Also called grab, accidental, opportunity, or haphazard sampling

  • Sample drawn from the part of the population closest at hand

  • Example: Interviewing people outside a coffee shop

Purposive (Judgmental) Sampling

  • Selecting participants based on specific characteristics or study objectives

  • Nonrandom

  • Examples: Attending political rallies for interviews; Native Hawaiian family narratives

Snowball (Network) Sampling

  • Existing subjects recruit future subjects from among their acquaintances

  • Useful when potential participants are hard to locate

  • Example: Researching experiences in Alcoholics Anonymous (AA)

Quota Sampling

  • Assemble a sample that has the same proportions as the population for known characteristics (demographics, etc.)

  • Similar to stratified sampling but non-random

  • Example: Studying experiences of different ethnic groups with discrimination

  • Important note: Non-random selection and no use of a sampling frame

Strengths and Weaknesses of Non-Probability Sampling

Strengths

  • Save time, energy, and money

  • Convenient and often feasible

Weaknesses

  • Not all individuals have equal chances of being selected

  • Results are not generally generalizable to a broader population

  • Example: A study based on a sample of UH undergraduates may not generalize to U.S. adults

  • The sample can be systematically different from the population (bias)

  • May over- or under-represent certain outcomes

  • Limited by resources (time, energy, money, etc.) and lack of a sampling frame

  • Not inherently bad; suitability depends on research objective

  • Example in practice: Hawaiian Identity through family narratives (topic-sensitive, not necessarily generalizable)

Concrete Example: UH Manoa Sample Scenario

  • Population (N): 17,490

  • Sample size (n): 100

  • Sample gender breakdown: Male 60%, Female 40%

  • Population gender breakdown: Male 60%, Female 40%

  • Example numbers: 10,494 males (60%), 6,996 females (40%) in population; 60 males, 40 females in the sample

  • Purpose of the example: show proportional stratified-like allocation within a simple random framework

Practical Implications and Takeaways

  • Probability sampling yields representative samples when frames exist and sampling is executed properly

  • Randomized methods (simple, systematic, stratified) enable generalization and accurate statistical inference if framed correctly

  • Non-probability methods are valuable for feasibility, exploratory work, or when generalization is not the primary goal

  • Always consider the objective of the study when choosing a sampling method

Recap and Core Principles

  • Complete enumeration vs. sampling: trade-off between precision and resources

  • Probability methods (Simple, Systematic, Stratified): aim for generalizability and representativeness; require frames

  • Non-probability methods (Volunteer, Convenience, Purposive, Snowball, Quota): resource-efficient; limit generalizability

  • Key terms to remember: Population, Sample, Sampling Frame, Population Parameter, Sample Statistic, Confidence Interval (e.g., 95%), and the importance of interpretation

  • Fundamental formulas:

    • Skip interval in systematic sampling:
      Population size/sample size

    • Skip interval in systematic sampling: Population size / Sample size; used to determine how many elements to skip in the sampling process. These concepts form the basis for understanding sampling techniques and their application in research.

  • Practical note: Always align sampling design with research goals, resource constraints, and the level of generalizability required for the study