Probability Sampling and Slovin's Formula

Simple Random Sampling

• Uses two methods: Table of Random Numbers (traditional approach) or the lottery (fishbowl) method
• Both methods are used to determine individual samples/respondents

Systematic Sampling

• Choosing every kth name on the list
• kth stands for a number between 0 and the size of the sample that you want to select
• Often preferred due to ease and less trouble
• However, it is less precise and violates the assumption of each member having an equal chance to be selected

Stratified Sampling

• Used to ensure fair representation of strata in the population
• Strata can be entities grouped accordingly, such as class sections, year levels, barangays, etc.

Cluster Sampling

• Used when the population is large and spread over a large area
• Divides the population into segments, and then selects several segments at random
• Also known as area sampling, often applied on a geographical basis

Multi-Stage Sampling

• Selection of the sample is done in two or more steps
• Population is divided into first-stage units, then a sample is drawn
• Further stages involve dividing the population into a hierarchy of sampling units

Probability Sampling

• Requires determining the population size to compute the sufficient sample size
• The Slovin's formula is commonly used: n = 𝑁 / (1 + 𝑁𝑒2)
• Another formula is Lynch, et.al.'s: n = 𝑁𝑧2.𝑝(1−𝑝) / (𝑁𝑑2 + 𝑧2.𝑝(1−𝑝))
• The computed sample size is the minimum required, and the researcher may add more but not less

Sample Size Formulae

• Slovin's formula: n = 𝑁 / (1 + 𝑁𝑒2)
• Lynch, et.al.'s formula: n = 𝑁𝑧2.𝑝(1−𝑝) / (𝑁𝑑2 + 𝑧2.𝑝(1−𝑝))

Simple Random Sampling (Under Probability Sampling)

• Each member of the population has an equal and independent chance of being selected
• Equal chance due to no bias, and independent chance due to the choice of one person not affecting the choice of another
• Characteristics of the sample should be close to that of the population