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1697Any False Sector Winner After Within-Sector MiningA desk has 12 sectors, each containing 5 genuinely null variants. In each sector it keeps only the smallest p-value, and it flags the sector if that winning p-value is below 1%. Assuming independence, what is the probability at least one sector is falsely flagged?统计简单derivation未尝试免费1698Bonferroni Cutoff After Collapsing to Effective FamiliesA research grid contains 60 model variants, but the desk argues they amount to only 15 effectively distinct families. If it wants family-wise error at most 10% using a Bonferroni family-level rule, what p-value cutoff should it apply to each effective family?统计中等derivation未尝试面试订阅1699Sidak Cutoff for 18 Effective Research ChoicesA desk believes its many correlated parameter tweaks boil down to 18 effectively independent research choices. What Sidak per-choice cutoff controls family-wise error at 5%?统计简单derivation未尝试免费1700BH q Range That Keeps Exactly Three FamiliesFive family-level winners have ordered p-values 0.004, 0.011, 0.018, 0.031, and 0.070. For what range of BH target levels q would Benjamini-Hochberg keep exactly the first three discoveries?统计中等derivation未尝试面试订阅1701Holm Improvement Needed for All Three Themes to PassThree ordered family p-values are 0.012, 0.027, and 0.030. The desk uses Holm at 5% family-wise error. By how much must the middle p-value fall so that all three themes pass?统计中等derivation未尝试面试订阅1703False Positives from Daily Strategy MiningSuppose you test 20 pure-noise trading rules every day for 252 trading days, always at level 5% and without any adjustment. How many false positives do you expect over the full year?统计简单derivation未尝试免费1710Global Error Implied by a Per-Bucket CutoffA desk uses the same per-bucket cutoff 0.0045 across 20 independent event buckets. What family-wise false-positive probability does that imply?统计中等derivation未尝试面试订阅1711Backtest Slide Misreads p = 0.03A PM deck says: ‘The event-study p-value is 0.03, so there is a 97% probability the signal is real.’ What is the statistical mistake?统计简单essay未尝试免费1713No Significance Is Not No EffectA small-cap execution pilot reports p = 0.18 and the note says ‘there is no effect, so we should stop the project.’ Why is that too strong?统计简单essay未尝试免费1716Replication Probability Is Not 1 - pA researcher says: ‘This alpha had p = 0.04, so replication next quarter is 96% likely.’ Why is that interpretation invalid?统计简单essay未尝试免费1717Significant but Commercially UncertainA venue-routing tweak delivers p = 0.01, but the 95% confidence interval for annual savings is [10k, 1.2m]. Why should the team still be cautious?统计简单essay未尝试免费17190.049 vs 0.051 Decision CliffTwo backtests differ only slightly: one reports p = 0.049 and the other p = 0.051. Why is it bad practice to call one ‘real’ and the other ‘not real’ purely because one is below 0.05?统计简单essay未尝试免费1720Low Prior Probability and Positive Predictive ValueSuppose only 1% of tested trading ideas are genuinely predictive. A testing pipeline has 80% power and a 5% false-positive rate. Conditional on obtaining a positive result, what fraction of positives are truly real?统计中等derivation未尝试面试订阅1722Cherry-Picked EndpointA note tests 12 strategy diagnostics but highlights only the one with p = 0.02. What trap should the reviewer flag?统计简单essay未尝试免费1723Underpowered Winner’s CurseA sparse signal library was screened on short samples; the surviving signal is significant but came from a very low-power environment. Why should its in-sample effect size be viewed skeptically?统计中等essay未尝试面试订阅1724Conditioning Direction ErrorA reviewer writes: ‘p = 0.07 means the null hypothesis is true with probability 7%.’ What is wrong with the conditioning direction?统计简单essay未尝试免费1725Fail to Reject vs AcceptAn experiment does not reject the null at 5%. The team writes ‘the null is accepted.’ What is the correct correction?统计简单essay未尝试免费1726Design Effect Under Clustered AssignmentAn experiment randomizes by store rather than by customer. If the average cluster size is m and the intra-cluster correlation is , what is the standard design-effect multiplier on variance?统计中等derivation未尝试面试订阅1727Effective Sample Size After a CUPED-Style Variance ReductionA variance-reduction method shrinks the variance of the treatment-effect estimator by a factor of c where 0<c<1. By what factor does the effective sample size increase?统计中等derivation未尝试面试订阅1728Triggered Analysis Exposure FractionOnly a fraction q of randomized users ever encounter the feature being tested. If the treatment effect exists only on those triggered users, how does the intent-to-treat effect compare with the triggered-user effect?统计中等derivation未尝试面试订阅