Sats 2-3 simple-random-and-systematic-random-sampling-8

Introduction to Sampling Methods

  • Focus: Simple Random Sampling and Systematic Random Sampling

  • Objective: Ensure every individual in the population has an equal chance of participation.

Simple Random Sample (SRS)

  • Definition: A sampling method ensuring that every individual and every sample has an equal chance of selection.

  • Analogy: Comparable to a raffle where tickets are mixed and drawn randomly.

  • Example: Selecting billiard balls from a hat to illustrate randomness.

  • Key Point: Each sample is equally probable, regardless of the selection order.

    • Observations:

      • The same item can appear in different samples (e.g., a solid yellow billiard ball appearing in multiple samples).

      • Unusual samples are just as likely as common samples.

      • raffel

Methods for Simple Random Sampling

1a. Random Number Generator

  • Usage: When manpower for manual selection is limited.

  • Process: Assign unique numbers to individuals within the population.

  • Example: Selecting 100 people from a population of 2000.

    • Steps:

      • Use technology or a calculator to generate random numbers.

      • Enter the range (1-2000 in this example) and the number of samples needed (e.g., 100).

      • If repeats occur in selection, ignore and redo until 100 unique numbers are achieved.

1b. Random Number Table

  • Use Context: Alternatives when technology isn’t readily available.

  • Distinctive Features: All individuals must have numbers with the same digits length.

    • Example Implementation:

      • Numbering individuals from 0001 to 2000.

      • Picking numbers from a table of random digits to select corresponding individuals.

    • Challenges:

      • Time-consuming due to the need to avoid unassigned and duplicate numbers.

Systematic Random Sampling

  • Definition: Involves selecting every k-th individual from a predefined population list.

  • Important Note: This method is not inherently random; sorting beforehand is crucial.

  • Employing Systematic Sampling:

    • Assign a value, k, to decide the selection interval.

    • Example: To select a sample of 25 from 500 individuals, take every 20th individual (500/25 = 20).

Contextual Example

  • Example from a classroom:

    • Counting off every 4th student for participation, showing how specific counting impacts sample selection.

    • If students are alphabetized, choosing specific individuals influences the subsequent selections (e.g., picking Adamson impacts nearby students).

    • The nice thing about a systematic sample is that it can be tailored to fit your sample size. If you wanted a sample of 25 from 500 individuals, you could sample every 20th person since 500 divided by 25 equals 20. So, you would obtain your sample of 25 by sampling every 20th person.

Summary of Key Terms

  • Simple Random Sample (SRS): A method ensuring that every subset of individuals has the same chance of being selected.

  • Random Number Generator: A technological tool for random sampling that assigns numbers to individuals.

  • Random Number Table: A non-technical way to select individuals based on pre-assigned numbers.

  • Systematic Random Sample: A method selecting every k-th individual, emphasizing the necessity for initial random sorting of the sample.