The Impact of Simpson’s Paradox on A/B Testing #DataAnalysis #SimpsonsParadox

Simpson’s Paradox and its effect on A/B testing | by Pradeepa Balasubramanian | Feb, 2024

Simpson’s Paradox is a statistical phenomenon where a trend in a population can emerge or disappear when the population is divided into smaller subpopulations. This paradox is important for product analysts to note because it can significantly affect decision-making. For example, when comparing two modes of communication for lead generation, such as WhatsApp and calling, the paradox can impact decision-making.

The paradox was illustrated through an example where WhatsApp initially showed higher conversion rates for new customers, but when extended to the old customer base, it still performed better than calling. However, at the company level, WhatsApp showed poorer performance than calling. This paradox occurred due to the weighted average of WhatsApp being higher in the population with a lower overall conversion rate, violating the principles of A/B testing, and the disproportionate contribution of new and old customer bases to the overall population.

To avoid the effect of confounding variables in A/B tests, it is important to conduct the test only after dividing the population into meaningful segments. It is also crucial to generate treatment using proportionately stratified random sampling and not change any condition of the experiment midway through the test.

Simpson’s Paradox also has implications for building machine learning models, where segmentation, feature selection, and variable importance, along with domain expertise, play a major role in interpreting results. In conclusion, the paradox reemphasizes the importance of human element and domain expertise in decision-making in the age of artificial intelligence.

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