Advanced Sample Size Calculator
How to Use:
- Select your desired Confidence Level. This reflects how sure you want to be that the true population parameter falls within your margin of error.
- Enter the Margin of Error (E) as a decimal (e.g., 0.05 for 5%). This is the acceptable amount of error in your estimate.
- Enter the Estimated Population Proportion (p) as a decimal (e.g., 0.5 if unknown, which maximizes sample size). This is your best guess of the proportion in the population.
- Optionally, enter the Population Size (N) if it's known and relatively small. This allows for a finite population correction. Leave blank if the population is very large or unknown.
- Click "Calculate Sample Size".
- The required sample size will be displayed. Click "Show Details" for formulas, theory, and step-by-step calculations.
Enter as a decimal (e.g., 0.03 for 3%)
Enter as a decimal (0-1). Use 0.5 if unsure.
For finite population correction.
Calculation Result:
Required Sample Size (n): -
Formulas Used:
For Infinite Population (or N is very large/unknown):
n₀ = (Z² * p * (1-p)) / E²
For Finite Population (Finite Population Correction - FPC):
n = n₀ / (1 + ((n₀ - 1) / N))
Where:
Z = Z-score for the confidence level
p = Estimated population proportion
E = Margin of error
N = Population size
n₀ = Sample size for infinite population
Theory:
Calculating the appropriate sample size is crucial for research and surveys. Too small a sample may lead to unreliable conclusions, while too large a sample can be costly and time-consuming.
- Confidence Level: The probability that the sample statistic (e.g., sample proportion) will accurately reflect the true population parameter within the margin of error. A 95% confidence level means that if the study were repeated many times, 95% of the calculated confidence intervals would contain the true population parameter. The Z-score is derived from the standard normal distribution corresponding to this confidence level.
- Margin of Error (E): The maximum expected difference between the true population parameter and the estimate from your sample. It's often expressed as a plus or minus percentage (e.g., ±5%).
- Population Proportion (p): An estimate of the proportion of a characteristic or attribute in the population. If unknown, 0.5 is typically used because it yields the maximum possible sample size, ensuring the study is adequately powered.
- Population Size (N): The total number of individuals in the group you are studying. The Finite Population Correction (FPC) adjusts the sample size downwards when the sample size is a significant fraction (usually >5%) of the population size, as sampling without replacement from a smaller population provides more information per observation.