Free Shipping Impact on Conversion Rates

Solution & Explanation

Steps to Analyze the Results:

1. Define the Hypotheses:

   • Null Hypothesis (H0): Surfacing free shipping has no significant effect on conversion rates, i.e., the conversion rates of the control and experiment groups are equal.
   • Alternative Hypothesis (Ha): Surfacing free shipping significantly increases conversion rates, i.e., the conversion rate of the experiment group is higher than that of the control group.

2. Calculate Conversion Rates:

   • Control Group Conversion Rate: $p_1 = \frac{1413}{3056} \approx 0.462$
   • Experiment Group Conversion Rate: $p_2 = \frac{1533}{2947} \approx 0.520$

3. Determine the Pooled Proportion:

   • $p_{pooled} = \frac{1413 + 1533}{3056 + 2947} \approx 0.490$

4. Check Conditions for Normal Approximation:

   • Ensure that $n_1 \times p_{pooled}, n_2 \times p_{pooled} > 10$. This condition holds, indicating that the normal approximation is valid.

5. Calculate the Standard Error (SE):

   • $SE = \sqrt{p_{pooled} \times (1 - p_{pooled}) \times \left( \frac{1}{n_1} + \frac{1}{n_2} \right)} \approx 0.0129$

6. Compute the Z-Statistic:

   • $Z = \frac{p_2 - p_1}{SE} = \frac{0.520 - 0.462}{0.0129} \approx 4.4939$

7. Determine the Critical Value and Compare:

   • At a 5% significance level, the critical Z-value is approximately 1.645.
   • Since $Z = 4.4939$ is greater than 1.645, we reject the null hypothesis.

8. Conclusion:

   • The test confirms, with 95% confidence, that highlighting free shipping significantly increases conversion rates.
   • Confidence Interval for Difference: Calculate the confidence interval for the difference in conversion rates:
     • $CI = (p_2 - p_1) \pm Z_{critical} \times SE$
     • $CI = 0.058 \pm 1.645 \times 0.0129$
     • $CI = [0.0347, 0.0853]$
   • Since the interval does not include 0, the increase in conversion rate is statistically significant.

Additional Considerations:

1. Practical Significance:

   • Evaluate whether the observed increase in conversion rate translates into sufficient revenue growth to justify the implementation of the change.

2. Sanity Checks:

   • Ensure there was no selection bias in assigning users to the control and experiment groups.
   • Confirm that external factors (e.g., holidays, promotions) did not influence the results.

3. Long-Term Effects:

   • Consider running the test for a longer period to rule out novelty effects and to ensure consistent results over time.

4. Representative Sample:

   • Ensure that the sample is representative of the entire customer base to generalize the findings.

By following these steps and considerations, you can confidently determine the success of the A/B test and make informed decisions on implementing free shipping notifications on the checkout page.