🔒All inputs are processed locally in your browser. Nothing is transmitted, stored, or logged. Inputs disappear when you close the tab.
SELECTED STUDIES & METHODS · #182

Statistical Reasoning Lab

Five deterministic labs that isolate the statistical-reasoning traps every methods course teaches separately: regression-to-the-mean, survivorship bias, hot-hand run-length, base-rate/Bayes (the prosecutor's fallacy), and a p-hacking spec-curve multiverse. Every lab runs on your inputs plus static, cited built-ins, nothing live, nothing that needs refreshing.

📋 Pure arithmetic + two static historical references (Wald WWII armor problem), no live data, no vintage
Setup · Pre/Post Test Parameters
The "sophomore" score, or the low outlier you're worried about
0 = pure noise, 1 = perfectly stable trait (no regression)
Result
Predicted Post-Test Score
-
Accounts for regression to the mean
Naive (No-Regression) Prediction
-
Assumes the score is a stable trait (r=1)
Expected Regression Amount
-
-
Built-In · Wald's WWII Bomber Armor Problem

Abraham Wald (Statistical Research Group, 1943) was asked where to add armor based on hit locations counted on bombers that RETURNED from missions. The military's instinct was to reinforce the most-hit sections. Wald reasoned the opposite: those sections show heavy damage precisely because planes hit there still made it home. The sections that matter are the ones with few or no hits on returning planes, because planes hit there likely never returned to be counted.

Section% of Returning Planes Hit HereWald's Armor Priority
Your Selection-Rate Math
Survivors, respondents, still-open businesses, funds still reporting, etc.
Result
Survival Rate
-
Non-Survivors (Unobserved)
-
Selection Distortion Index
-
How many "starters" each observed survivor now silently stands in for
Setup · Streak Parameters
Shots, at-bats, coin flips, trading days
e.g., career free-throw %
Result
Expected Longest Run (pure chance)
-
Schilling (1990) closed-form approximation
Std. Deviation of Longest Run
-
Observed vs Expected (z)
-
-
Setup · Prosecutor's-Fallacy Inputs
% of the population who actually has the condition/trait/guilt
P(positive | actually has it)
P(negative | doesn't have it)
Result
True Posterior: P(has it | tested positive)
-
Fallacy Value (Sensitivity, Often Mistaken for the Posterior)
-
Gap
-
How far the intuitive answer is from the correct one
Setup · Seeded Synthetic Dataset

Generates a synthetic two-group dataset (n=20/group) from a seeded pseudo-random generator with a TRUE null effect: there is no real difference between the groups. It then runs all 16 "researcher degree of freedom" analysis paths (exclude/keep an outlier × control/ignore a covariate × full sample/subgroup × one-/two-tailed) and shows how many come back "significant" at p<.05 by chance alone. Same seed always produces the same dataset and the same 16 results, nothing here reads the clock or an unseeded random source.

Re-enter the same seed and re-run to verify: identical multiverse, every time
Spec-Curve · 16 Analysis Paths
Exclude OutlierControl CovariateSubgroup OnlyOne-Tailedp-valueResult