Unequal Sample Sizes on AB Testing

Solution & Explanation

1. Understanding the Problem

The primary concern with unequal sample sizes in an AB test is the potential for bias and the impact on statistical power and significance. In the given scenario, one group has 50,000 users and the other has 200,000 users, leading to an 80:20 split.

2. Key Considerations

• Random Assignment: Ensure that users are randomly assigned to each variant. Randomization helps mitigate selection bias and ensures that the only difference between groups is the treatment itself.
• Duration of the Test: If both groups were exposed to the test for the same duration, it reduces temporal biases.
• Variance and Power: The smaller group, despite having fewer users, still contains 50,000 observations, which is substantial. This would typically provide enough power to detect meaningful effects, assuming the effect size is not minuscule.

3. Potential Biases

• Sampling Bias: If the assignment was not truly random, or if specific demographics were overrepresented in one group, the results could be biased.
• Statistical Significance and Power: Larger groups tend to have narrower confidence intervals, which could lead to detecting statistically significant differences more easily, even if they are not practically significant.

4. Statistical Testing

• Binomial Test: For two conditions, use a binomial test to check if the observed distribution significantly deviates from expected proportions.
• Chi-Squared Test: For multiple conditions, this test can highlight significant differences in group distributions.

5. Practical Steps

• Check Randomization: Review the randomization process to ensure it's robust and unbiased.
• Analyze Variance: Compare the variances between groups to ensure they are similar, which would indicate proper randomization.
• Downsampling: Consider downsampling the larger group to match the smaller group's size if variances are significantly different, to maintain balance in comparison.

6. Conclusion

While unequal sample sizes can introduce potential biases, the size of the smaller group here is large enough to provide a powerful test, minimizing concerns about power and variance. However, ensuring random assignment and equal treatment duration is crucial to maintaining the validity of the test results. Conducting statistical tests to confirm randomization and balance is essential before drawing any conclusions from the AB test.