1. What is the A/B Test Z-Score?

The Z-score measures how many standard deviations the difference between two proportions is from zero. It helps determine if the observed difference in an A/B test is statistically significant or due to random chance.

2. How Does the Calculator Work?

The calculator uses the Z-score formula for proportion comparison:

Where:

• \( p_1 \) — Proportion of success in group 1
• \( p_2 \) — Proportion of success in group 2
• \( n_1 \) — Sample size of group 1
• \( n_2 \) — Sample size of group 2
• \( p \) — Pooled proportion = \( \frac{x_1 + x_2}{n_1 + n_2} \)

Explanation: The formula compares the difference between two proportions relative to the expected variability if there were no true difference.

3. Importance of Statistical Significance

Details: Statistical significance helps determine if the results of an A/B test are reliable and not due to random variation. A higher absolute z-score indicates stronger evidence against the null hypothesis.

4. Using the Calculator

Tips: Enter proportions as values between 0 and 1, and sample sizes as positive integers. Typically, a z-score beyond ±1.96 indicates statistical significance at the 95% confidence level.

5. Frequently Asked Questions (FAQ)

Q1: What is a good z-score for statistical significance?
A: Typically, |z| > 1.96 indicates significance at α=0.05, |z| > 2.58 at α=0.01.

Q2: Can this calculator be used for any A/B test?
A: This is specifically for proportion comparisons (conversion rates, click-through rates, etc.).

Q3: What if my z-score is negative?
A: A negative z-score means group 2 performed better than group 1. The absolute value determines significance.

Q4: Are there sample size requirements?
A: Larger sample sizes provide more reliable results. Generally, each group should have at least 30-50 observations.

Q5: What's the relationship between z-score and p-value?
A: The z-score can be converted to a p-value using the standard normal distribution. Lower p-values correspond to higher absolute z-scores.