Katkat
Back

Estimate free-trial conversion probability

IBMData Scientist · Technical Screen
EasyData ScientistTechnical ScreenAnalytics & Experimentation

Last updated

This question evaluates a data scientist's competency in cohort definition, censored-data handling, segmentation and confounding assessment, and uncertainty quantification for measuring free-trial to paid conversion, and it belongs to the Analytics & Experimentation domain within data science.

Context

A product offers a free trial. You are asked: “What is the probability of conversion for a group of people who started a free trial?”

Data (assume available)

A table of trial starts:

  • user_id
  • trial_start_at (timestamp)
  • trial_length_days (int)
  • country/channel/plan/device (optional segments)

A table of paid conversions:

  • user_id
  • paid_start_at (timestamp, nullable if never converted)
  • revenue (optional)

Task

  1. Define precisely what “conversion probability” means, including the time window and cohort definition.
  2. Show how you would estimate the conversion probability for a cohort of trial starters, including how you would handle:
  • users whose trial has not ended yet (incomplete observation)
  • delayed conversions (convert after trial)
  • segmentation and potential confounding (e.g., channel mix changes)
  1. Provide a way to quantify uncertainty (confidence/credible intervals) and communicate results.
  2. Suggest follow-up analyses/metrics (diagnostics and guardrails) to ensure the estimate is decision-useful.