Sample Size Calculator
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Sample Size Calculator
Determine the minimum sample size required for your study based on statistical parameters.
Required Sample Size:
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Understanding Sample Size Calculation
Determining the appropriate sample size is a crucial step in designing any research study, survey, or experiment. A sample size that is too small may not yield statistically significant results, while a sample size that is too large can be wasteful of resources and time. This calculator helps you estimate the minimum number of participants or observations needed to achieve reliable and valid conclusions.
The Formula (Cochran's Formula with Finite Population Correction)
The most common formula used for calculating sample size for proportions, especially in survey research, is Cochran's formula. For finite populations, it's often adjusted with a finite population correction factor. A widely accepted approach for a large population, assuming maximum variability (which yields the largest sample size), is:
Formula for Infinite Population:
n₀ = (Z² * p * (1-p)) / e²
Where:
- n₀ = Initial sample size estimate
- Z = Z-score corresponding to the desired confidence level (e.g., 1.96 for 95% confidence)
- p = Estimated proportion of the attribute in the population. If unknown, use 0.5 for maximum variability.
- e = Margin of error (e.g., 0.05 for ±5%)
Adjusted Formula for Finite Population:
n = n₀ / (1 + (n₀ – 1) / N)
Where:
- n = Final adjusted sample size
- n₀ = Initial sample size estimate from the infinite population formula
- N = Population size
Key Parameters Explained:
- Population Size (N): The total number of individuals or items in the group you are interested in studying. If the population is very large or unknown, a finite population correction might not be strictly necessary, but it's good practice to include it.
- Margin of Error (e): This is the acceptable range of error in your results. A smaller margin of error (e.g., 3% instead of 5%) requires a larger sample size. It represents the precision you want in your estimates.
- Confidence Level: This indicates the probability that the true population parameter falls within your confidence interval. Common levels are 90%, 95%, and 99%. A higher confidence level requires a larger sample size. The Z-score reflects this level (e.g., Z=1.645 for 90%, Z=1.96 for 95%, Z=2.576 for 99%).
- Estimated Proportion (p): This is your best guess of the proportion of the population that has the characteristic you are measuring. If you have no prior information, using p=0.5 (50%) will result in the largest required sample size, ensuring your sample is large enough regardless of the true proportion.
How to Use This Calculator:
- Enter your estimated Population Size (N).
- Specify your desired Margin of Error (e) as a decimal (e.g., 0.05 for 5%).
- Select your desired Confidence Level from the dropdown.
- Input the Estimated Proportion (p). If you don't know, use 0.5.
- Click "Calculate Sample Size".
The result will be the minimum number of participants or observations required for your study to meet the specified statistical criteria. Remember that this is an estimate, and factors like expected response rates or study design complexity might necessitate further adjustments.
function getZScore(confidenceLevel) {
var z = 0;
if (parseFloat(confidenceLevel) === 0.90) {
z = 1.645;
} else if (parseFloat(confidenceLevel) === 0.95) {
z = 1.96;
} else if (parseFloat(confidenceLevel) === 0.99) {
z = 2.576;
}
return z;
}
function calculateSampleSize() {
var N = parseFloat(document.getElementById("populationSize").value);
var e = parseFloat(document.getElementById("marginOfError").value);
var confidenceLevel = document.getElementById("confidenceLevel").value;
var p = parseFloat(document.getElementById("estimatedProportion").value);
var resultElement = document.getElementById("result-value");
resultElement.textContent = "–"; // Reset result
// Input validation
if (isNaN(N) || N <= 0) {
alert("Please enter a valid Population Size greater than 0.");
return;
}
if (isNaN(e) || e = 1) {
alert("Please enter a valid Margin of Error between 0 and 1 (e.g., 0.05 for 5%).");
return;
}
if (isNaN(p) || p 1) {
alert("Please enter a valid Estimated Proportion between 0 and 1 (e.g., 0.5 for 50%).");
return;
}
var z = getZScore(confidenceLevel);
if (z === 0) {
alert("Invalid confidence level selected.");
return;
}
// Calculate initial sample size (n₀) for infinite population
var n0_numerator = Math.pow(z, 2) * p * (1 – p);
var n0_denominator = Math.pow(e, 2);
var n0 = n0_numerator / n0_denominator;
// Adjust for finite population (n)
var n_numerator = n0;
var n_denominator = 1 + (n0 – 1) / N;
var n = n_numerator / n_denominator;
// Ensure sample size is at least 1 and round up to the nearest whole number
var finalSampleSize = Math.ceil(Math.max(1, n));
resultElement.textContent = finalSampleSize.toLocaleString();
}