I started with the composite metric part and that went okay.
Start by defining a combined quality metric that appropriately weights the three binary tests, then model the probability of passing all tests using logistic regression or a similar framework. Use Bayesian inference or bootstrapping to quantify uncertainty and apply multiple comparison corrections to identify the best group rigorously.
Pro tip: Emphasize that the choice of metric should align with business impact—e.g., if one test is more critical, weight it higher—and always validate assumptions with sensitivity analyses.
Decide on a metric that aggregates the three binary tests, such as the probability of passing all tests (intersection) or a weighted sum of passes. Consider using a latent variable model (e.g., item response theory) to account for test difficulty and correlation.
Use logistic regression with group as a categorical predictor to estimate each group's probability of passing each test, or model the combined metric directly. For unequal group sizes, ensure the model accounts for varying sample sizes via weighting or Bayesian methods.
Obtain confidence intervals or posterior distributions for each group's metric using bootstrapping or Bayesian credible intervals. This provides a range of plausible values and accounts for sampling variability.
Apply a correction like Bonferroni, Holm-Bonferroni, or false discovery rate (FDR) to control the family-wise error rate when comparing all groups. Alternatively, use a Bayesian approach with informative priors or model-based comparisons.
Rank groups by their estimated metric and determine if the top group is statistically significantly better than the others after adjustment. Consider practical significance and effect sizes, not just p-values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.