body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-container {
background: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
margin-bottom: 40px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
@media (max-width: 600px) {
.calc-grid {
grid-template-columns: 1fr;
}
}
.form-group {
margin-bottom: 15px;
}
label {
display: block;
margin-bottom: 5px;
font-weight: 600;
font-size: 0.9em;
}
input, select {
width: 100%;
padding: 10px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
box-sizing: border-box;
}
input:focus, select:focus {
border-color: #4dabf7;
outline: none;
box-shadow: 0 0 0 3px rgba(77, 171, 247, 0.2);
}
.btn-calculate {
background-color: #228be6;
color: white;
border: none;
padding: 12px 20px;
font-size: 16px;
border-radius: 4px;
cursor: pointer;
width: 100%;
margin-top: 10px;
font-weight: bold;
transition: background-color 0.2s;
}
.btn-calculate:hover {
background-color: #1c7ed6;
}
.results-container {
margin-top: 25px;
padding-top: 20px;
border-top: 2px solid #dee2e6;
display: none;
}
.result-box {
background: white;
padding: 20px;
border-radius: 6px;
text-align: center;
border: 1px solid #dee2e6;
margin-bottom: 15px;
}
.result-label {
color: #6c757d;
font-size: 0.9em;
text-transform: uppercase;
letter-spacing: 0.5px;
margin-bottom: 5px;
}
.result-value {
font-size: 2.5em;
font-weight: 700;
color: #228be6;
}
.result-sub {
font-size: 0.9em;
color: #868e96;
margin-top: 5px;
}
.error-msg {
color: #e03131;
font-weight: bold;
text-align: center;
margin-top: 10px;
display: none;
}
.article-content h1 { font-size: 2.2em; color: #343a40; margin-bottom: 0.5em; }
.article-content h2 { font-size: 1.6em; color: #495057; margin-top: 1.5em; border-bottom: 2px solid #e9ecef; padding-bottom: 10px; }
.article-content h3 { font-size: 1.3em; color: #495057; margin-top: 1.2em; }
.article-content p { margin-bottom: 1.2em; }
.article-content ul { margin-bottom: 1.2em; padding-left: 20px; }
.article-content li { margin-bottom: 0.5em; }
.highlight-box { background-color: #e7f5ff; padding: 15px; border-left: 4px solid #228be6; margin: 20px 0; }
function calculateSampleSize() {
var popInput = document.getElementById('populationSize').value;
var z = parseFloat(document.getElementById('confidenceLevel').value);
var marginRaw = parseFloat(document.getElementById('marginOfError').value);
var nonRespRaw = parseFloat(document.getElementById('nonResponseRate').value);
var errorDiv = document.getElementById('errorMsg');
var resultsDiv = document.getElementById('resultsContainer');
// Reset display
errorDiv.style.display = 'none';
resultsDiv.style.display = 'none';
// Validation
if (isNaN(marginRaw) || marginRaw <= 0) {
errorDiv.textContent = "Please enter a valid Margin of Error greater than 0.";
errorDiv.style.display = 'block';
return;
}
if (isNaN(nonRespRaw) || nonRespRaw = 100) {
errorDiv.textContent = "Please enter a valid Non-Response Rate between 0 and 99%.";
errorDiv.style.display = 'block';
return;
}
var p = 0.5; // Standard deviation proportion (0.5 yields maximum sample size)
var e = marginRaw / 100;
// 1. Calculate Base Sample Size (Infinite Population)
// Formula: SS = (Z^2 * p * (1-p)) / e^2
var ss = (Math.pow(z, 2) * p * (1 – p)) / Math.pow(e, 2);
// 2. Finite Population Correction (if population provided)
if (popInput && popInput.trim() !== "") {
var pop = parseFloat(popInput);
if (pop > 0) {
// Formula: NewSS = SS / (1 + (SS – 1) / Pop)
ss = ss / (1 + ((ss – 1) / pop));
}
}
// Round up required completed surveys
var targetCompleted = Math.ceil(ss);
// 3. Adjust for Non-Response Rate
// Formula: Invitations = TargetCompleted / (1 – NonResponseRate)
var nonRespDecimal = nonRespRaw / 100;
var requiredInvites = targetCompleted / (1 – nonRespDecimal);
requiredInvites = Math.ceil(requiredInvites);
// Update UI
document.getElementById('sampleSizeResult').textContent = targetCompleted.toLocaleString();
document.getElementById('invitationsResult').textContent = requiredInvites.toLocaleString();
document.getElementById('displayNonResp').textContent = nonRespRaw;
resultsDiv.style.display = 'block';
}
Sample Size Calculator with Non-Response Rate
Designing a research study or survey requires precision. Simply knowing how many responses you need isn't enough; you must also account for the reality that not everyone invited will participate. This Sample Size Calculator with Non-Response Rate helps you determine exactly how many invitations you need to send to achieve statistically significant results.
Why Non-Response Rate Matters: If you need 385 completed surveys but only send 385 invitations, you will likely fail to reach your quota. Accounting for the non-response rate ensures your dataset is large enough to be valid.
How to Calculate Sample Size with Non-Response
Calculating the required invitations involves a two-step process: determining the base sample size and then adjusting for the expected drop-off.
1. Determine Base Sample Size
First, we use standard statistical formulas (typically Cochran's formula) to find the number of completed surveys needed based on your population parameters:
- Confidence Level (Z): The probability that your sample accurately reflects the population (usually 95%).
- Margin of Error (e): The acceptable range of deviation (typically +/- 5%).
- Population Size (N): The total number of people in the group you are studying.
2. Adjust for Non-Response
Once you have the target number of completed surveys, you must divide this number by the expected response rate to find the total invitation count.
Formula:
Total Invitations = Required Sample Size / (1 – Non-Response Rate)
Definitions of Calculator Inputs
Population Size
The total number of individuals in the group you intend to study. If you are surveying a massive group (e.g., "all US citizens"), you can leave this blank to use an infinite population assumption.
Confidence Level
This indicates how sure you can be that your results are accurate. A 95% confidence level is the industry standard, meaning if you repeated the survey 100 times, 95 of them would yield results within your margin of error.
Margin of Error
Also known as the confidence interval. If your survey finds that 50% of people like a product with a 5% margin of error, the "true" value is likely between 45% and 55%. Lower margins of error require significantly larger sample sizes.
Estimated Non-Response Rate
This is the percentage of people you invite who will not complete the survey. This includes bounces, unopened emails, and people who start but do not finish.
- Example: If you expect a 20% response rate, your Non-Response Rate is 80%.
- Average Rates: Internal employee surveys often see 30-40% non-response, while external email marketing surveys can see 80-95% non-response.
Real-World Example
Imagine you are surveying a company of 5,000 employees to determine satisfaction with a new policy.
- Parameters: You want a 95% Confidence Level and a 5% Margin of Error.
- Base Calculation: The calculator determines you need 357 completed surveys.
- Non-Response Adjustment: You know from past surveys that 40% of employees ignore these emails (Non-Response Rate = 40%).
- Final Calculation: 357 / (1 – 0.40) = 595.
You must send at least 595 invitations to ensure you receive the necessary 357 responses.