# Sample size for the Chapter 8 trial (one parent-child dyad per family).
# Primary outcome: share of 10-second intervals of child dysregulation in a
# frustrating cooperative puzzle task, coded blind from video. ANCOVA on the
# baseline task shrinks the variance by (1 - rho^2). d in SD units of the
# observed score; normal approximation; two-sided alpha .05.
import math
from statistics import NormalDist
N = NormalDist()

def per_arm(d, rho, power=0.90, alpha=0.05):
    z = N.inv_cdf(1 - alpha / 2) + N.inv_cdf(power)
    return math.ceil(2 * z * z * (1 - rho * rho) / (d * d)) + 1

print("dyads per arm for 90 % power")
print(" effect d | baseline-outcome rho = 0.3 | 0.4 | 0.5")
for d in (0.25, 0.30, 0.35, 0.40):
    print(f"   {d:.2f}   | {per_arm(d, 0.3):26d} | {per_arm(d, 0.4):3d} |"
          f" {per_arm(d, 0.5):3d}")
n = per_arm(0.30, 0.4); rec = math.ceil(n / 0.85)
print(f"chosen: d = 0.30, rho = 0.4 -> {n} analysable dyads per arm;")
print(f"  allowing 15 % loss (drop-out, unusable video): recruit {rec} per arm,")
print(f"  {2 * rec} families in all")
print("if the effect were 0.30 SD on the TRUE (error-free) score,")
print("coder unreliability would shrink the observed effect:")
for icc in (0.9, 0.8, 0.7):
    d_obs = 0.30 * math.sqrt(icc)
    print(f"  coder reliability {icc}: observed d = {d_obs:.3f}"
          f" -> {per_arm(d_obs, 0.4)} per arm")
# dyads per arm for 90 % power
#  effect d | baseline-outcome rho = 0.3 | 0.4 | 0.5
#    0.25   |                        307 | 284 | 254
#    0.30   |                        214 | 198 | 177
#    0.35   |                        158 | 146 | 130
#    0.40   |                        121 | 112 | 100
# chosen: d = 0.30, rho = 0.4 -> 198 analysable dyads per arm;
#   allowing 15 % loss (drop-out, unusable video): recruit 233 per arm,
#   466 families in all
# if the effect were 0.30 SD on the TRUE (error-free) score,
# coder unreliability would shrink the observed effect:
#   coder reliability 0.9: observed d = 0.285 -> 219 per arm
#   coder reliability 0.8: observed d = 0.268 -> 247 per arm
#   coder reliability 0.7: observed d = 0.251 -> 282 per arm

# Decision rule, fixed in advance. d = arm A minus arm B (primary outcome,
# pooled-SD units, from the pre-specified ANCOVA); NEGATIVE d = less child
# dysregulation in arm A. SESOI 0.30 SD. Coding gate: ICC(2,1) on the 20 %
# of videos coded twice must be at least 0.75.
SESOI, ICC_MIN = 0.30, 0.75

def verdict(d, lo, hi, icc, fidelity_ok, harms):
    if harms:
        return f"d = {d:+.2f}: PAUSE for safeguarding review - {harms} event(s)"
    if icc < ICC_MIN:
        return f"d = {d:+.2f}: NOT INTERPRETABLE - coder ICC {icc:.2f} < 0.75"
    if not fidelity_ok:
        return f"d = {d:+.2f}: NOT INTERPRETABLE - < 80 % of sessions as planned"
    if hi <= -SESOI: v = "A reduces dysregulation by at least the SESOI"
    elif hi < 0:     v = "A reduces dysregulation; size not shown to reach 0.30"
    elif lo > 0:     v = "A INCREASES dysregulation"
    elif lo >= -SESOI and hi <= SESOI: v = "no difference worth acting on"
    else:            v = "unclear: the interval is too wide to decide"
    return f"d = {d:+.2f} ({lo:+.2f} to {hi:+.2f}): {v}"

for case in ((-0.50, -0.70, -0.30, 0.84, True, 0),
             (-0.22, -0.42, -0.02, 0.84, True, 0),
             (-0.05, -0.25, 0.15, 0.81, True, 0),
             (-0.15, -0.35, 0.05, 0.86, True, 0),
             (-0.45, -0.65, -0.25, 0.68, True, 0),
             (-0.40, -0.60, -0.20, 0.83, False, 0),
             (-0.35, -0.55, -0.15, 0.82, True, 1)):
    print(verdict(*case))
print("secondary outcomes (parent-rated Emotion Regulation Checklist, the")
print("parent's observed pauses) are reported with intervals, never decisive")
# d = -0.50 (-0.70 to -0.30): A reduces dysregulation by at least the SESOI
# d = -0.22 (-0.42 to -0.02): A reduces dysregulation; size not shown to reach 0.30
# d = -0.05 (-0.25 to +0.15): no difference worth acting on
# d = -0.15 (-0.35 to +0.05): unclear: the interval is too wide to decide
# d = -0.45: NOT INTERPRETABLE - coder ICC 0.68 < 0.75
# d = -0.40: NOT INTERPRETABLE - < 80 % of sessions as planned
# d = -0.35: PAUSE for safeguarding review - 1 event(s)
# secondary outcomes (parent-rated Emotion Regulation Checklist, the
# parent's observed pauses) are reported with intervals, never decisive