Sample Size Calculator
Determine the minimum number of respondents needed for your survey or research study.
Understanding Sample Size Calculation
In statistics, calculating the correct sample size is crucial for ensuring that your research findings are both representative and scientifically valid. A sample size that is too small may lead to inaccurate results, while a sample size that is excessively large wastes time and resources.
Key Variables in Sample Size Calculation
- Confidence Level: This represents how certain you want to be that the population's true margin of error falls within your results. The most common confidence level is 95%, which corresponds to a Z-score of 1.96.
- Margin of Error: Also known as the confidence interval, this is the amount of "wiggle room" you permit. If you have a 5% margin of error and 60% of your sample picks an answer, you can be confident that if you asked the entire population, between 55% and 65% would have picked that answer.
- Population Size: The total number of people in the group you are studying. If you are surveying a specific company with 500 employees, 500 is your population size. If the population is extremely large (like a whole country), it is often treated as "infinite."
- Population Proportion: This is the expected distribution of responses. If you don't know, 50% is the standard choice because it is the most conservative estimate and ensures the largest required sample size.
Example Calculation
Imagine you want to survey a city with 10,000 residents. You decide on a 95% confidence level (Z = 1.96) and a 5% margin of error.
1. First, calculate the sample size for an infinite population using Cochran's Formula:
n = (Z² * p * (1-p)) / e²
n = (1.96² * 0.5 * 0.5) / 0.05² = 384.16
2. Next, adjust for the finite population of 10,000:
n_adjusted = n / (1 + (n-1)/Population)
n_adjusted = 384.16 / (1 + (383.16/10000)) ≈ 370
In this case, you would need to survey 370 people to achieve your desired statistical accuracy.
Why Sample Size Matters
Without a statistically significant sample size, your data may suffer from "sampling bias." This occurs when the individuals sampled do not reflect the diversity or characteristics of the larger group. Using a calculator ensures your survey design is robust and your conclusions are defensible in academic or business environments.