two-types anchor in "... To Make Predictions"

[Ultimately_Untrue_Thought.git] / notes / deflation.py

diff --git a/notes/deflation.py b/notes/deflation.py
index 77efe23..686ef80 100644 (file)
--- a/notes/deflation.py
+++ b/notes/deflation.py
@@ -9,39 +9,39 @@ seed(1)
 
 def cohens_d(X, Y):
     return (
-        (mean(X) + mean(Y)) /
+        (mean(X) - mean(Y)) /
         sqrt(
             (len(X)*variance(X) + len(Y)*variance(Y)) /
             (len(X) + len(Y))
         )
     )
 
-def population_with_error(μ, σ, n):
+def population_with_error(μ, ε, n):
     def trait():
         return normal(μ, 1)
     def measurement_error():
-        return normal(0, σ)
+        return normal(0, ε)
     return [trait() + measurement_error() for _ in range(n)]
 
 
 # trait differs by 1 standard deviation
-adjusted_f = population_with_error(1, 0, 10000)
-adjusted_m = population_with_error(0, 0, 10000)
+true_f = population_with_error(1, 0, 10000)
+true_m = population_with_error(0, 0, 10000)
 
 # as above, but with 0.5 standard units measurment error
 measured_f = population_with_error(1, 0.5, 10000)
 measured_m = population_with_error(0, 0.5, 10000)
 
-smart_d = cohens_d(adjusted_f, adjusted_m)
-print(smart_d)  # 1.0193773432617055 — d≈1.0, as expected!
+true_d = cohens_d(true_f, true_m)
+print(true_d)  # 1.0193773432617055 — d≈1.0, as expected!
 
 naïve_d = cohens_d(measured_f, measured_m)
-print(naïve_d)  # 0.8953395386313235
+print(naïve_d)  # 0.8953395386313235 — deflated!
 
 
-def performance(g, σ_g, s, n):
+def performance(μ_g, σ_g, s, n):
     def general_ability():
-        return normal(g, σ_g)
+        return normal(μ_g, σ_g)
     def special_ability():
         return normal(s, 1)
     return [general_ability() + special_ability() for _ in range(n)]
@@ -55,7 +55,7 @@ matched_f = performance(0, 0, 1, 10000)
 matched_m = performance(0, 0, 0, 10000)
 
 population_d = cohens_d(population_f, population_m)
-print(population_d)  # 0.7287587808164793
+print(population_d)  # 0.7287587808164793 — deflated!
 
 matched_d = cohens_d(matched_f, matched_m)
-print(matched_d)  # 1.018362581243161
+print(matched_d)  # 1.018362581243161 — as you would expect