Start by clearly defining all variables and units, then compute the baseline monthly gross fraud loss. Next, apply the rule's recall to find the prevented loss, subtract from baseline to get remaining loss, and finally subtract false-positive operational costs to find net savings. Show every formula step-by-step with units.
Pro tip: Always state your assumptions explicitly (e.g., that false positives incur a fixed cost per alert) and consider edge cases like recall=0 or 1. This demonstrates rigor and prevents miscommunication.
List all given values: monthly transaction volume, average fraud amount, recall, false positive rate, and cost per false positive. Ensure units are consistent (e.g., dollars, counts).
Calculate the total fraud loss without the rule: monthly transaction volume × fraud rate × average fraud amount. If fraud rate is not given, derive it from recall and false positive rate if possible, or state assumptions.
The rule catches a fraction (recall) of fraud, so remaining loss = baseline loss × (1 - recall). Show the formula and units.
Calculate the number of false positives: monthly transaction volume × false positive rate. Multiply by cost per false positive to get total operational cost.
Net savings = baseline loss - remaining loss - false-positive operational costs. Present the final result with units and interpret the business impact.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the metric definition and distributional assumptions (e.g., fraud loss per 1,000 credits is continuous, likely skewed, so use a t-test or bootstrap). Then derive the per-arm sample size using the standard formula for comparing two means, incorporating the 15% relative reduction, 5% significance, and 80% power. Finally, justify your modeling choice by discussing robustness to non-normality and practical considerations like randomization unit and duration.
Pro tip: Mention that you would pre-register the analysis plan and use a sequential testing framework or CUPED to increase sensitivity, showing awareness of practical experimentation pitfalls beyond the basic sample size calculation.
Clarify that the metric is fraud loss per 1,000 credits, a continuous variable. Assume independent observations, equal variances, and approximate normality (or rely on CLT for large n).
State null hypothesis (no difference) and alternative (15% relative reduction). Specify significance level (α=0.05, two-sided) and power (1-β=0.80).
Use the formula for two independent means: n per arm = 2*(z_{α/2}+z_β)^2 * σ^2 / Δ^2, where Δ is the absolute effect corresponding to 15% relative reduction.
Estimate σ from historical data or pilot. Compute Δ = 0.15 * μ_control, where μ_control is the baseline mean fraud loss per 1,000 credits.
Plug in values to get n per arm. Justify using t-test or bootstrap if normality is questionable, and discuss practical adjustments like unequal allocation or clustering.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Wilson interval instead of Wald, which is the right call at low prevalence.
First, compute the Wilson confidence interval for the given prevalence using the formula, then interpret the interval in the context of a go/no-go decision by comparing it to a predefined threshold. Emphasize that the interval provides a range of plausible values for the true fraud rate, which helps assess risk and uncertainty.
Pro tip: When interpreting the interval, consider the practical significance: even if the upper bound is above the threshold, the actual fraud rate might still be acceptable if the cost of fraud is low relative to the benefits. Also, mention that Wilson interval is preferred for small proportions because it has better coverage than the normal approximation.
Compute the observed prevalence: p_hat = 240,000 / 100,000,000 = 0.0024 (or 0.24%). Note that the given 0.12% might be a typo; clarify with the interviewer if needed.
Use the Wilson score interval formula: (p_hat + z^2/(2n) ± z * sqrt((p_hat*(1-p_hat) + z^2/(4n))/n)) / (1 + z^2/n), where z = 1.96 for 95% confidence.
Plug in the numbers: n = 100,000,000, p_hat = 0.0024, z = 1.96. Calculate the lower and upper bounds. The interval will be very narrow due to the large sample size.
Explain that we are 95% confident the true fraud prevalence lies within this interval. Compare the interval to a decision threshold (e.g., if the upper bound is below the acceptable fraud rate, go; if the lower bound is above, no-go; if it straddles, consider more data or risk tolerance).
Based on the interval and business context, provide a clear go/no-go recommendation, acknowledging uncertainty and potential next steps.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by acknowledging the multiple testing problem and the need to control the family-wise error rate (FWER) or false discovery rate (FDR). Then propose a sequential testing framework such as group sequential boundaries (e.g., O'Brien-Fleming) or alpha spending functions, and outline stopping rules for efficacy and futility. Finally, discuss how early stopping can inflate effect sizes and introduce bias, and suggest adjustments like bias-corrected estimators or Bayesian methods.
Pro tip: Mention that while early stopping controls Type I error, it often leads to overestimated effect sizes due to the 'winner's curse'; consider using a Bayesian approach with posterior probabilities for more intuitive decision-making.
Explain that daily peeking at results inflates Type I error if no adjustment is made. Mention that the overall alpha must be controlled across all interim analyses.
Propose a method like group sequential design with alpha spending (e.g., O'Brien-Fleming or Pocock boundaries) or sequential probability ratio test (SPRT). Describe how it allocates alpha across looks.
Specify stopping boundaries for efficacy (reject null) and futility (accept null). Include both statistical and practical considerations (e.g., minimum sample size, business impact).
Discuss how early stopping can bias the estimated effect size (usually upward) and reduce power for secondary metrics. Mention the need for adjusted estimators or sensitivity analyses.
Mention Bayesian sequential testing or always-valid inference as alternatives that allow continuous monitoring without alpha inflation. Discuss trade-offs in terms of complexity and interpretability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.