#!/usr/bin/env python3 """ Perialetheia - CWIAL Report No. 1 Reproducibility script: regenerates the uncertainty budget and the capability quantities for belief displacement in European GM-food safety discourse. Method: GUM (JCGM 100:2008) uncertainty budget with Type A and Type B components combined in quadrature; capability of detection after Currie (1968) / ISO 11843-1. Terms follow VIM (JCGM 200:2012) and ISO/IEC 17025:2017. No external data files are required: every input below is a declared value drawn from the published Eurobarometer record and the report's Type B assignments. Run: python3 CWIAL-2026-01_reproduce.py Report ID: PERIALETHEIA-CWIAL-2026-01 Status: Amended 2026-09-03. Three changes from the first release: (a) the item base is corrected to the split-ballot base; (b) Type B component names follow the programme taxonomy; (c) the decision against a zero-prevalence null is withdrawn and replaced by capability statements. See the amendment notes at the foot of this file. """ import math # ---------------------------------------------------------------------- # 1. Anchor measurement # Proposition F (FALSE, Tier-1, VFRB id EU-GMFOOD-SAFETY): # "Consuming approved GM food is dangerous to human health." # Anchor wave: Eurobarometer 73.1 (2010), health-safety agreement item. # # BASE. The item was administered on a SPLIT BALLOT. The item base is # 15600, not the wave n. Using the wave n would understate the Type A # component by a factor of sqrt(2) and would misstate a property of the # instrument, whatever its effect on the combined uncertainty. # ---------------------------------------------------------------------- D = 0.59 # measured belief displacement (proportion agreeing with the false claim) n = 15600 # item base, split ballot (NOT the wave n) D_eff = 1.8 # survey design effect, multi-stage face-to-face; # DECLARED, not derived from the design documentation # ---------------------------------------------------------------------- # 2. Type A component (statistical, from observed data) # ---------------------------------------------------------------------- u_A = math.sqrt(D * (1 - D) / n) * math.sqrt(D_eff) # ---------------------------------------------------------------------- # 3. Type B components (evaluated from knowledge; GUM 4.3) # Names follow the programme taxonomy used across the CWIMF reports. # Each is a half-width or bound converted to a standard uncertainty by # the divisor for its assumed distribution. # # u_B4 is not evaluated for this instrument. Eurobarometer 73.1 is a # multi-stage probability sample administered face to face, not an opt-in # panel, so the panel-skew term carries no value here. It is declared as # not applicable rather than assigned a number for symmetry. # # u_B6 is an instrument-specific sixth component. Cross-national # translation has no counterpart in a single-country instrument and is # therefore not part of the five-term core taxonomy. # ---------------------------------------------------------------------- u_B1 = 0.010 # reference classification, Tier-1 bound <= 0.01 u_B2 = 0.050 # instrument bias: question wording and list # context changed between waves and the change # is undocumented in the release # (Normal, half-width 0.10 at k = 2) u_B3 = 0.026 / math.sqrt(3) # temporal mismatch (Rectangular, half-width 0.026) u_B4 = None # panel representativeness: not applicable u_B5 = 0.012 / math.sqrt(6) # adversarial adaptation, residual incl. # coordinated campaign (Triangular, half-width 0.012) u_B6 = 0.017 / math.sqrt(3) # translation and cross-country comparability # (Rectangular, half-width 0.017) components = { "u_A": u_A, "u_B1": u_B1, "u_B2": u_B2, "u_B3": u_B3, "u_B5": u_B5, "u_B6": u_B6, } # ---------------------------------------------------------------------- # 4. Combine (GUM 5.1, independent components -> quadrature) # Input quantities are treated as uncorrelated and the covariance terms # of GUM eq. 13 are dropped explicitly. # ---------------------------------------------------------------------- u_c = math.sqrt(sum(u**2 for u in components.values())) k = 2 U = k * u_c # ---------------------------------------------------------------------- # 5. Capability of the procedure # NOT a decision. For a verified-false proposition the null state is a # population holding the belief at zero prevalence. No such population # has been observed, so u_0 cannot be measured and is approximated by # u_c. That approximation is defensible here: displacement-independent # Type B terms carry over 99 per cent of the combined variance, which is # the condition under which u_0 ~ u_c holds. # ---------------------------------------------------------------------- critical_value = 1.645 * u_c mdd = 3.29 * u_c response_threshold = 3.645 * u_c # ---------------------------------------------------------------------- # 6. Report # ---------------------------------------------------------------------- print(__doc__.strip().splitlines()[1]) print("-" * 64) print(f"{'component':8} {'u_i':>10} {'variance share':>16}") for name, u in components.items(): print(f"{name:8} {u:10.4f} {100*u*u/(u_c*u_c):15.2f}%") print(f"{'u_B4':8} {'n/a':>10} {'not applicable':>16}") print("-" * 64) print(f"Item base (split ballot) n = {n}") print(f"Combined standard uncertainty u_c = {u_c:.4f}") print(f"Coverage factor k = {k}") print(f"Expanded uncertainty U = {U:.4f}") print(f"Belief displacement D = {D:+.2f}") print("-" * 64) print("CAPABILITY OF THE PROCEDURE (properties of the procedure at the null;") print("no decision is issued against a zero-prevalence null):") print(f" critical value 1.645 u_c = {critical_value:.4f}") print(f" min. detectable displ. 3.29 u_c = {mdd:.4f} [Currie convention]") print(f" response threshold 3.645 u_c = {response_threshold:.4f}") print("-" * 64) print("Dominant term: u_B2 (undocumented change of survey instrument),") print(f"contributing {100*u_B2*u_B2/(u_c*u_c):.0f}% of the combined variance.") print(f"Type A carries {100*u_A*u_A/(u_c*u_c):.2f}% of the combined variance.") print() print("Where a response decision is required it must be referred to a") print("difference against a prior measurement of the same instrument on the") print("same population, where a null of no change is attainable, or to an") print("externally declared policy threshold.") # ---------------------------------------------------------------------- # AMENDMENT NOTES (2026-09-03) # # (a) BASE. The first release used n = 31238, the wave n. The health-safety # item was administered on a split ballot and its base is 15600. The # correction raises u_A from 0.0037 to 0.0053 and u_c from 0.0544 to # 0.0545. No reported conclusion changes. # # That the combined uncertainty is insensitive to halving the base is # itself the finding. Type A carries under one per cent of the variance. # Survey precision is not what limits this measurement; the undocumented # instrument change is. # # (b) NAMING. The first release labelled the translation term u_B3 and the # temporal term u_B4, which reverses the programme taxonomy used in the # other reports and in cwial/simulate.py. No value changed. The # translation term is now u_B6 and is declared instrument-specific, # u_B3 is the temporal term, and u_B4 is declared not applicable. # u_B1 is stated as reference classification, its meaning across the # programme, rather than "response classification". # # (c) DECISION. The first release computed |D| / U and printed # "Distinguishable from zero = YES". Both moves are withdrawn. |D| / U # is not the distinguishability criterion, which is the critical value # at 1.645 u_c, and no decision may be issued against a null that cannot # be prepared. Capability quantities are reported in their place. # ----------------------------------------------------------------------