function calculateSignificance() {
// 1. Get Elements
var cVisInput = document.getElementById('controlVisitors');
var cConvInput = document.getElementById('controlConversions');
var vVisInput = document.getElementById('variantVisitors');
var vConvInput = document.getElementById('variantConversions');
var confLevelInput = document.getElementById('confidenceLevel');
var resultDiv = document.getElementById('result');
// 2. Parse Values
var n1 = parseFloat(cVisInput.value); // Control Visitors
var x1 = parseFloat(cConvInput.value); // Control Conversions
var n2 = parseFloat(vVisInput.value); // Variant Visitors
var x2 = parseFloat(vConvInput.value); // Variant Conversions
var confidenceThreshold = parseFloat(confLevelInput.value);
// 3. Validation
if (isNaN(n1) || isNaN(x1) || isNaN(n2) || isNaN(x2)) {
resultDiv.style.display = 'block';
resultDiv.className = 'result-neutral';
resultDiv.innerHTML = "Error: Please enter valid numbers in all fields.";
return;
}
if (n1 <= 0 || n2 <= 0) {
resultDiv.style.display = 'block';
resultDiv.className = 'result-neutral';
resultDiv.innerHTML = "Error: Visitor count must be greater than zero.";
return;
}
if (x1 > n1 || x2 > n2) {
resultDiv.style.display = 'block';
resultDiv.className = 'result-neutral';
resultDiv.innerHTML = "Error: Conversions cannot be higher than visitors.";
return;
}
// 4. Calculations (Two-tailed Z-Test for Proportions)
var p1 = x1 / n1; // Control CR
var p2 = x2 / n2; // Variant CR
var cr1Percent = (p1 * 100).toFixed(2);
var cr2Percent = (p2 * 100).toFixed(2);
// Relative Uplift
var uplift = 0;
if (p1 > 0) {
uplift = ((p2 – p1) / p1) * 100;
} else {
uplift = (p2 > 0) ? 100 : 0; // Edge case if control is 0
}
var upliftFormatted = uplift.toFixed(2) + "%";
if (uplift > 0) upliftFormatted = "+" + upliftFormatted;
// Pooled Probability
var pPool = (x1 + x2) / (n1 + n2);
// Standard Error
var se = Math.sqrt(pPool * (1 – pPool) * ((1/n1) + (1/n2)));
// Z-Score
var zScore = 0;
if (se > 0) {
zScore = (p2 – p1) / se;
}
// P-Value Calculation (Approximation of standard normal CDF)
// Using a numerical approximation for the cumulative distribution function
function getPValueFromZ(z) {
// Absolute value because it's symmetric for two-tailed
var zAbs = Math.abs(z);
// Constants for approximation
var p = 0.2316419;
var b1 = 0.31938153;
var b2 = -0.356563782;
var b3 = 1.781477937;
var b4 = -1.821255978;
var b5 = 1.330274429;
var t = 1 / (1 + p * zAbs);
var sigma = 1 – (1 / (Math.sqrt(2 * Math.PI)) * Math.exp(-0.5 * zAbs * zAbs) *
(b1 * t + b2 * Math.pow(t, 2) + b3 * Math.pow(t, 3) + b4 * Math.pow(t, 4) + b5 * Math.pow(t, 5)));
// Two-tailed p-value
return 2 * (1 – sigma);
}
var pValue = getPValueFromZ(zScore);
// Determine Confidence
var observedConfidence = 1 – pValue;
var isSignificant = observedConfidence >= confidenceThreshold;
// 5. Output Construction
var resultHTML = "";
var resultClass = "";
var outcomeText = "";
if (isSignificant) {
if (uplift > 0) {
resultClass = "result-success";
outcomeText = "
Test is Statistically Significant!
You can be " + (observedConfidence * 100).toFixed(2) + "% confident that the variation performs better than the control.";
} else {
resultClass = "result-neutral"; // Significant drop
outcomeText = "
The observed difference is not statistically significant at the " + (confidenceThreshold * 100) + "% level. Continue testing or conclude no difference.";
}
resultHTML += outcomeText;
resultHTML += "
Understanding Statistical Significance in A/B Testing
In the world of Conversion Rate Optimization (CRO), data drives decisions. However, raw numbers can be misleading due to random variance. This Conversion Rate Statistical Significance Calculator helps you determine if the difference between your control page (A) and your variation (B) is a genuine result or just statistical noise.
What is Statistical Significance?
Statistical significance is a way of quantifying how likely it is that a result occurred by chance. In A/B testing, if a test is "significant" at a 95% confidence level, it means there is only a 5% probability that the observed difference in conversion rates happened purely by random chance.
Key Concept: The P-Value
The P-value represents the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A lower P-value (typically < 0.05) indicates higher significance.
How This Calculator Works
This calculator uses a two-tailed Z-test for two population proportions. It requires four data points:
Control Visitors: The total number of users who saw the original version.
Control Conversions: The number of users who completed the desired action (sale, signup, click) on the original version.
Variation Visitors: The total number of users who saw the new version.
Variation Conversions: The number of users who completed the action on the new version.
Interpreting the Results
Conversion Rate (CR): Calculated as (Conversions / Visitors) * 100.
Uplift: The percentage increase or decrease in the conversion rate of the variation compared to the control. Positive uplift means the new version is performing better.
Confidence Level:
Most marketers aim for 95% confidence. This is the industry standard.
90%: Lower threshold, higher risk of false positives. Acceptable for low-risk changes.
95%: Standard threshold. Strong evidence of a real difference.
99%: Very high threshold. Required for high-risk or critical infrastructure changes.
Why Sample Size Matters
Statistical significance is heavily dependent on sample size (the number of visitors). Even a massive 50% uplift might not be significant if you only tested it on 10 people. Conversely, a tiny 1% uplift can be highly significant if tested on 1,000,000 people.
Common Pitfall: Calling tests too early. It is tempting to stop a test as soon as the calculator shows "Significant." However, you should usually decide on a fixed sample size beforehand to avoid "peeking" errors, which can inflate your false positive rate.
When Should You Stop a Test?
You should generally stop a test when:
You have reached the pre-calculated sample size required to detect the minimum detectable effect (MDE).
The test has run for at least one or two full business cycles (e.g., 2 full weeks) to account for day-of-week variance.
You have reached statistical significance (typically >95%).