Scenario: Suppose we have a website and want to test whether a new button color (Version B) performs better than the current one (Version A) in terms of click-through rate (CTR).

  1. Define Hypotheses:

    • (H_0): The CTR of Version B ≤ the CTR of Version A.
    • (H_1): The CTR of Version B > the CTR of Version A (one-tailed test).

  2. Group Assignment:

    • Randomly assign 1,000 users to each version (A and B), and record the number of clicks.

  3. Data Collection:

    • Version A: 10% click-through rate (100 clicks out of 1,000).
    • Version B: 12% click-through rate (120 clicks out of 1,000).

  4. Statistical Analysis:

    • Use a binomial test to compare the click-through rates.
    • Calculate the p-value to determine whether the difference is statistically significant.
    • If the p-value is less than 0.05, conclude that Version B performs significantly better.