Sample Size Calculation

Understanding how we determined the optimal sample size for our survey of Adventist Young Professionals in the Philippines.

95% Confidence Level

5% Margin of Error

1.5M Population Size

Important Note on Population Changes

Please note that the growth of the Adventist Church and the population in the Philippines may have changed since this survey was initiated. This analysis is based on the numbers identified at the time of the survey's conception. While we acknowledge these potential changes, the survey methodology and sample size calculations were determined using the population figures available during the survey's planning phase.

Data Limitations and Assumptions

The total population of Adventist members in the Philippines presented some challenges in data collection. While sources such as Wikipedia and the SSD website provide estimates, they show inconsistencies ranging from 1 million to 1.8 million members. To proceed with the survey, we adopted a conservative estimate of 1.4 million members.

Additionally, there is no official registry or concrete data source for the number of Adventist Young Professionals in the Philippines. Given this limitation, we estimated that approximately 30% of the total Adventist population consists of Young Professionals. This estimation formed the basis for our sample size calculation, allowing us to proceed with the survey while acknowledging these inherent limitations in the available data.

Calculation Details

Step-by-Step Calculation Process

A detailed breakdown of how we arrived at our required sample size using statistical methods.

Input Parameters

Population Size (N): 1,500,000
Confidence Level: 95% → Z = 1.96
Margin of Error (e): 5% → e = 0.05
Population Proportion (p): 0.3 (30%)

Formula Used

We use the finite population correction formula for proportions:

$$n = \frac{Z^2 \cdot p \cdot (1-p)}{e^2} \div \left(1 + \frac{Z^2 \cdot p \cdot (1-p)}{e^2 \cdot N}\right)$$

Calculation Steps

1. Calculate Initial Term

$$Z^2 \cdot p \cdot (1-p) = (1.96)^2 \cdot 0.3 \cdot 0.7 = 0.806736$$

2. Divide by e²

$$\frac{0.806736}{0.05^2} = \frac{0.806736}{0.0025} = 322.6944$$

3. Apply FPC

$$1 + \frac{0.806736}{3750} = 1.00021513$$

Final Result

323

Required Sample Size

This calculation takes into account:

Population proportion of 30%
Finite population of 1.5M
95% confidence level
5% margin of error