A/B Two-Proportion Z-Test Calculator
Computes a pooled two-proportion z-score and two-sided normal-approximation p-value for supplied A/B conversion counts; the 95% flag is p < 0.05 and does not establish experiment validity.
About this a/b two-proportion z-test calculator
Computes a pooled two-proportion z-score and two-sided normal-approximation p-value for supplied A/B conversion counts; the 95% flag is p < 0.05 and does not establish experiment validity Enables rapid evaluation of advertising efficiency and campaign economics without transmitting proprietary media budget figures.
Metrics formula & attribution logic
The execution engine processes input tokens and applies transformations in the browser sandbox. Specifically, Calculation and parameter relationship: p̄=(conversionsA+conversionsB)/(visitorsA+visitorsB); z=(conversionsB/visitorsB−conversionsA/visitorsA)/√(p̄(1−p̄)(1/visitorsA+1/visitorsB)); twoSidedPValue=2×(1−Φ(|z|)); significantAt95=(twoSidedPValue<0.05) The normal-approximation win estimate is Φ((pB−pA)/SE_unpooled); the 95% confidence interval for the conversion-rate difference is (pB−pA) ± 1.959963984540054×SE_unpooled.
Worked campaign analytics example
Scenario: Use the following data to evaluate A/B Two-Proportion Z-Test Calculator
Sample input:
Processing: Calculation and parameter relationship: p̄=(conversionsA+conversionsB)/(visitorsA+visitorsB); z=(conversionsB/visitorsB−conversionsA/visitorsA)/√(p̄(1−p̄)(1/visitorsA+1/visitorsB)) For each arm, s² = p̂(1−p̂)×n/(n−1) when n > 1; expected counts below 5 prompt caution. The 95% interval is an unpooled Wald interval for pB−pA. The win estimate is Φ((pB−pA)/SE_unpooled), a normal approximation, not a posterior or causal probability. The decision is significant only when the two-sided pooled z-test has p < 0.05.
Illustrative output:
Input parameters & edge case boundaries
Parameter domains and units: conversionsA,conversionsB,visitorsA,visitorsB ∈ ℤ; 0 ≤ conversionsA < visitorsA; 0 ≤ conversionsB < visitorsB; visitorsA,visitorsB > 0; [rateA] = [rateB] = %. This is a pooled, normal-approximation two-sided test for the supplied counts; it does not establish randomization, independence, practical importance, or multiple-testing control. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. If the pooled standard error is zero, the z-test is undefined and the input is rejected. Sample variance is estimated separately for each Bernoulli arm. The prompt flags any expected success or failure count below 5; this is a normal-approximation check, not proof of model validity. The win estimate is an approximation, not a Bayesian posterior or a probability of causal success. The conclusion uses the pooled two-sided z-test and p < 0.05.
Marketing metrics in A/B Two-Proportion Z-Test Calculator implement standard industry formulas (IAB/MRC). External ad platform reporting may differ slightly due to time zone cutoffs or attribution windows.
Local metrics evaluation boundary
Formula calculations and numeric evaluations in A/B Two-Proportion Z-Test Calculator run synchronously in the browser JavaScript engine with zero server telemetry.
Advertising industry standards & specifications
Interactive Advertising Bureau (IAB) measurement guidelines and Media Rating Council (MRC) reporting standards:
A/B Two-Proportion Z-Test Calculator verification · Audit standards
How to use it
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
Which calculation does A/B Two-Proportion Z-Test Calculator perform?+
Calculation and parameter relationship: p̄=(conversionsA+conversionsB)/(visitorsA+visitorsB); z=(conversionsB/visitorsB−conversionsA/visitorsA)/√(p̄(1−p̄)(1/visitorsA+1/visitorsB)); twoSidedPValue=2×(1−Φ(|z|)); significantAt95=(twoSidedPValue<0.05) The normal-approximation win estimate is Φ((pB−pA)/SE_unpooled); the 95% confidence interval for the conversion-rate difference is (pB−pA) ± 1.959963984540054×SE_unpooled.
What input can I paste into A/B Two-Proportion Z-Test Calculator?+
Paste the following input exactly, preserving JSON field names where present: {"conversionsA":100,"visitorsA":1000,"conversionsB":120,"visitorsB":1000}
Which parameter limits and units apply to A/B Two-Proportion Z-Test Calculator?+
Parameter domains and units: conversionsA,conversionsB,visitorsA,visitorsB ∈ ℤ; 0 ≤ conversionsA ≤ visitorsA; 0 ≤ conversionsB ≤ visitorsB; visitorsA,visitorsB > 0; [rateA] = [rateB] = %.
What result does this A/B Two-Proportion Z-Test Calculator example produce?+
The example produces these values in the raw output: { "rateA": 10, "rateB": 12, "zScore": 1.4293008498232314, "twoSidedPValue": 0.1529178732524119, "significantAt95": false, "winProbabilityVariantHigherPercent": 92.36459493759028, "difference95CiLowerPercentagePoints": -0.7411481998019945, "difference95CiUpperPercentagePoints": 4.741148199801993, "sampleVarianceA": 0.0900900900900901, "sampleVarianceB": 0.1057057057057057, "sampleVarianceCheckCode": "adequate", "conclusionCode": "not_significant" }