Populations, Samples, and Slovin's Formula

Respondents of the Study

Population

• Refers to the entire group about which conclusions are drawn
• Reports from this group are true representations of information
• A parameter is a numeric characteristic of a population

Sample

• A subset representing the entire population
• It's the group from which data will be collected
• A statistic is a numeric characteristic of a sample

Sampling

• The process of selecting a representative sample from a population, to make inferences about the population

Sample Size

• Determining the acceptable sample size is important
• Larger samples lead to more reliable study results

Universal Sampling

• When a population is equal to or less than 100, the entire population can serve as the sample size

Slovin's Formula

• Used to calculate sample size: n = N / (1 + Ne^2)
• n = sample size
• N = population size
• e = margin of error

Example of Slovin's Formula Application

• If N (population) = 168 and e (margin of error) = 0.05, then:
• n = 168 / (1 + 168 * (0.05)^2)
• n ≈ 119

Sample Size Calculator

• Online tools are available to calculate sample size

Sampling Techniques

• Probability Sampling: Employs randomization to ensure every population member has an equal chance of selection; also referred to as scientific sampling
• Non-probability Sampling: Does not rely on randomization, often used when randomization is not feasible, aiming to obtain a representative sample

Variations of Probability Sampling

• Simple Random Sampling: Each member has an equal chance of being selected
• Stratified Random Sampling: The population is divided into subgroups (strata), and members are randomly selected from each subgroup proportionately
• Systematic Random Sampling: Uses a specific system, such as selecting every 3rd person from a list; the sampling interval = N/n
• Cluster Random Sampling: The population is divided into clusters, and entire clusters are selected as samples

Example of Proportionate Stratified Sampling

• In a junior high school with 600 students:
  • 180 in Grade 7
  • 160 in Grade 8
  • 150 in Grade 9
  • 110 in Grade 10
• If the computed sample size is 240, then the proportionate sampling would be:
  • Grade 7: (180/600) * 240 = 72 students
  • Grade 8: (160/600) * 240 = 65 students
  • Grade 9: (150/600) * 240 = 60 students
  • Grade 10: (110/600) * 240 = 43 students
  • Total: 240 respondents (100%)

Variations of Non-Probability Sampling

• Convenience (or Accidental) Sampling: Members are selected based on availability
• Purposive Sampling: Members of a specific group are deliberately sought
• Proportional and Non-Proportional Quota Sampling: Members are sampled until exact proportions of certain data types are obtained or until sufficient data is collected in different categories
• Diversity Sampling: Members are intentionally selected across possible response types to capture all possibilities
• Snowball Sampling: Initial members are sampled, then asked to identify other potential members, continuing until enough samples are collected