Populations, Samples & Sample Size: Slovin's Formula

Population and Sample

• Population: The entire group a researcher wants to draw conclusions about.
• Sample: A subset of the population that represents the entire group. Data is collected from the sample.

Parameters and Statistics

• Parameter: A numerical characteristic of a population.
• Statistic: A numerical characteristic of a sample.

Sample Size Determination

• Larger samples generally lead to more reliable study results.
• Determining the acceptable sample size is essential for research.
• If the total population is 100 or less, the total population can be the sample size.

Slovin's Formula

• Formula used to calculate sample size:
  • n = N / (1 + Ne²), where:
    • n = sample size
    • N = population size
    • e = margin of error

Example Using Slovin's Formula

• If the population (N) is 168 and the margin of error (e) is 0.05, the sample size (n) is 119.

Available Online Calculators

• Online sample size calculators are available.

Sampling Techniques

• Probability Sampling:

  • Uses randomization to ensure all population members have a chance of selection.
  • Also called scientific sampling.

• Non-Probability Sampling:

  • Doesn’t rely on randomization techniques.
  • Used when randomization isn't possible in order to obtain a representative sample, specifically in areas not possible to randomize.

Variations of Probability Sampling

• Simple Random Sampling: Every member has an equal chance.
• Stratified Random Sampling: Divides the population into subgroups, and members are selected randomly from each group.
• Systematic Random Sampling: Uses a specific system for selection, like every 3rd person on a list.
• Cluster Random Sampling: Divides the population into clusters, and every member from a selected cluster is considered a sample.

Variations of Non-Probability Sampling

• Convenience Sampling: Members are selected based on availability.
• Purposive Sampling: Members of a specific group are selected purposefully.
• Proportional and Non-proportional Quota Sampling: Members are sampled until exact proportions of certain data types are obtained, or until sufficient data in certain categories is collected.
• Diversity Sampling: Intentionally selecting members across different types of responses.
• Snowball Sampling: Sampled members help identify other members to be sampled until enough samples are collected.

Understand populations, samples, parameters, and statistics in research. Learn how to calculate sample size using Slovin's Formula and determine appropriate sample sizes for research studies. This is suitable for statistics and research methods courses.