Lecture Notes: Types of Biased Samples and Simple Random Sampling

Introduction

• Welcome to the second lecture.
• Recap of the previous lecture on biased samples.

Biased Samples

• Definition: A biased sample shows favoritism to one outcome over others.

Types of Biased Samples

1. Convenience Sample

   • Information collected easily from accessible sources.
   • Example: Sampling only friends or familiar individuals.
   • Issue: Does not represent the wider population.

2. Voluntary Response Sample

   • Participation is self-selected by subjects.
   • Result: Dominated by individuals with strong opinions.
   • Issue: Not representative of the entire population.

Simple Random Sampling (SRS)

• Definition: A sampling technique where every sample has an equal chance of being selected.
• Denoted as RS.

Understanding Sample Sizes

• Population Size (N): Denoted by capital N. Example: Total student population = 27,000.
• Sample Size (n): Denoted by small n. Example: Sample of 3 students.

Characteristics of a Simple Random Sample

• Every possible sample of size n has an equal chance of selection.
• Example Method:
  • Write names on cards, place in a basket, mix, and draw randomly.

Practical Steps to Create a Simple Random Sample

1. Labeling Subjects

   • For population size up to 100: Use labels 01, 02, ..., 99.
   • For population size up to 1,000: Use three-digit labels 000, 001, ..., 999.

2. Using Random Number Tables

   • Utilize Table B for random digits.
   • Random digits are computer-generated and distributed equally.

Random Number Table

• Structure: A continuous string of numbers starting from line reference 101.
• Generation: Computer randomizes digits (0-9) to ensure equal selection probability.

Summary

• Key takeaway is understanding and differentiating between biased and unbiased sampling methods.
• Simple Random Sampling ensures unbiased representation by giving each subject an equal selection chance.