Sample Size Calculation in Quantitative Research

Introduction

• Importance of determining sample size in quantitative research.
• A census is often impractical for large populations due to time and cost.
• A sample is a subset of the population.

Key Considerations for Sample Size

1. Population Size

   • Identify how many people fit in the demographic.
   • Example: Surveying mothers' willingness to get vaccinated in a specific area requires sampling rather than a census.

2. Margin of Error

   • Defines how much higher or lower than the population mean the sample mean can fall.
   • Often expressed as a percentage (e.g., ±5%).
   • Example: If 70% of students prefer modular learning with a ±5% margin of error, the actual population percentage lies between 65% and 75%.

3. Confidence Level

   • Indicates the level of certainty that the actual mean falls within the confidence interval.
   • Common confidence levels: 90%, 95%, 99%.
   • A higher confidence level means that the sample mean is more likely to reflect the true population value.

4. Degree of Variability

   • Refers to the expected variance in responses.
   • If unknown, a conservative estimate of 0.5 is often used to ensure a larger sample size.

Sample Size Calculation

• Cochran's Formula (1963)

  • Equation: N₀ = (Z² * p * (1-p)) / e²
  • Where:
    • N₀ = computed sample size
    • Z = critical value of the desired confidence level
    • e = desired margin of error
    • p = estimated proportion of an attribute in the population
  • Example:
    • Population is large, p = 0.5, desired confidence level = 95% (Z = 1.96), margin of error = ±5%.
    • Required sample size = 385 (farming technology adoption).

• Imani's Formula (1967)

  • Equation: n = (N * Z² * p * (1-p)) / (N * e² + Z² * p * (1-p))
  • Example:
    • Population size = 2,000 farmers, margin of error = ±5%.
    • Required sample size = 333 farmers.

Conclusion

• Summarized the importance and methods for calculating sample size in quantitative studies.