# Sample size for the pre-registered vignette experiment. Two arms (fixed-target contract vs
# state-contingent contract with a written 90-day exploration period and stopping rules), randomised
# within each of five countries. Two co-primary outcomes measured after the same day-90 exit event:
# trust in the foreign partner, and perceived risk of breach. Each tested at two-sided alpha 0.025
# (Bonferroni for two outcomes). Effects in SD units; normal approximation for a t-test.
import math
COUNTRIES = 5  # Malaysia, Indonesia, Thailand, Vietnam, Singapore
from statistics import NormalDist
N = NormalDist()

def n_per_arm(d, alpha=0.025, power=0.90):
    za, zb = N.inv_cdf(1 - alpha / 2), N.inv_cdf(power)
    return math.ceil(2 * (za + zb) ** 2 / d ** 2) + 1

def power(n, d, alpha=0.025):
    return N.cdf(d / math.sqrt(2 / n) - N.inv_cdf(1 - alpha / 2))

for d in (0.20, 0.25, 0.30, 0.40):
    print(f"standardised effect {d:.2f}: {n_per_arm(d, power=0.80):4d} per arm for 80 % power, "
          f"{n_per_arm(d):4d} for 90 %")
n = n_per_arm(0.30)
print(f"chosen: smallest effect of interest 0.30, 90 % power -> {n} analysable per arm")
# Both outcomes must be powered; with correlated outcomes the chance of detecting BOTH true effects
# of 0.30 is at least 1 - 2 * (1 - power) by the union bound:
print(f"power for each outcome {power(n, 0.30):.3f}; for both together at least {1 - 2 * (1 - power(n, 0.30)):.2f}")
recruit = math.ceil(n / 0.80)
print(f"allow 20 % exclusions (failed attention or manipulation checks): recruit {recruit} per arm,"
      f" {2 * recruit} in all, about {math.ceil(2 * recruit / COUNTRIES)} per country")
# standardised effect 0.20:  477 per arm for 80 % power,  622 for 90 %
# standardised effect 0.25:  306 per arm for 80 % power,  399 for 90 %
# standardised effect 0.30:  213 per arm for 80 % power,  277 for 90 %
# standardised effect 0.40:  120 per arm for 80 % power,  157 for 90 %
# chosen: smallest effect of interest 0.30, 90 % power -> 277 analysable per arm
# power for each outcome 0.901; for both together at least 0.80
# allow 20 % exclusions (failed attention or manipulation checks): recruit 347 per arm, 694 in all, about 139 per country

# Decision rule for the vignette experiment, written before any data exist.
# d_trust: state-contingent arm minus fixed-target arm, trust after the day-90 exit (higher = more trust)
# d_risk:  the same for perceived breach risk, sign flipped so that positive = LESS perceived risk.
# Each comes with a 97.5 % confidence interval (two-sided alpha 0.025 per outcome).
SESOI = 0.30

def judge(lo, hi):
    if lo >= SESOI: return "benefit of at least the smallest effect of interest"
    if lo > 0: return "benefit, size not shown to reach 0.30"
    if hi < 0: return "harm"
    if -SESOI <= lo and hi <= SESOI: return "no difference worth acting on"
    return "unclear"

def verdict(trust, risk, pre_trust):
    t, r = judge(*trust[1:]), judge(*risk[1:])
    if t.startswith("benefit") and r.startswith("benefit"):
        overall = "SUPPORTED in this vignette setting"
    elif "harm" in (t, r):
        overall = "CONTRARY: explicit stopping rules made the exit look worse"
    elif t.startswith("benefit") or r.startswith("benefit"):
        overall = "PARTLY supported: one co-primary outcome only"
    else:
        overall = "NOT supported"
    note = ""
    if pre_trust[2] < 0:   # secondary: trust measured before the event, when the clause is first read
        note = "; note: the written exit clause lowered trust before anything happened"
    return f"trust {t}; breach risk {r} -> {overall}{note}"

# Invented results, to show in advance how each pattern will be reported: (estimate, low, high)
examples = (((0.45, 0.31, 0.59), (0.38, 0.24, 0.52), (0.05, -0.08, 0.18)),
            ((0.35, 0.21, 0.49), (0.10, -0.04, 0.24), (-0.20, -0.34, -0.06)),
            ((0.02, -0.12, 0.16), (-0.03, -0.17, 0.11), (0.00, -0.14, 0.14)))
for e in examples:
    print(verdict(*e))
# trust benefit of at least the smallest effect of interest; breach risk benefit, size not shown to reach 0.30 -> SUPPORTED in this vignette setting
# trust benefit, size not shown to reach 0.30; breach risk no difference worth acting on -> PARTLY supported: one co-primary outcome only; note: the written exit clause lowered trust before anything happened
# trust no difference worth acting on; breach risk no difference worth acting on -> NOT supported