Sample Size And Margin Of Error Calculator Confidence Interval Formula

Sample Size Formula:

\[ n = \frac{z^2 \times SD^2}{MOE^2} \]

Required Sample Size (n):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Sample Size Formula?

The sample size formula calculates the minimum number of participants needed in a study to achieve a desired margin of error for a given confidence level. It's essential for designing statistically valid research studies.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

\[ n = \frac{z^2 \times SD^2}{MOE^2} \]

Where:

\( n \) — Required sample size
\( z \) — Z-score for desired confidence level
\( SD \) — Standard deviation of the population
\( MOE \) — Desired margin of error

Explanation: The formula shows that sample size increases with higher confidence levels (larger z-scores) or greater variability (larger SD), and decreases with larger acceptable margins of error.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure. It's crucial for study validity and ethical research conduct.

4. Using the Calculator

Tips: Enter the z-score corresponding to your desired confidence level (1.96 for 95% CI), estimated standard deviation from pilot data or literature, and acceptable margin of error. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What z-score should I use?
A: Common z-scores are 1.645 (90% CI), 1.96 (95% CI), and 2.576 (99% CI). Choose based on your desired confidence level.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, similar published research, or make an educated estimate based on the measurement scale.

Q3: What's a reasonable margin of error?
A: This depends on your research context. For surveys, ±3-5% is common. For clinical studies, consider clinical significance.

Q4: Does this work for proportions?
A: For proportions (like survey responses), use \( SD = \sqrt{p(1-p)} \) where p is the expected proportion.

Q5: What about finite populations?
A: For populations under 20,000, apply the finite population correction: \( n_{adj} = \frac{n}{1 + \frac{n-1}{N}} \) where N is population size.