# Sample size for the double-blind randomised trial. Listeners hear ONE version of the same
# 90-second business pitch, read by one of four voice actors (2 women, 2 men) and processed so that
# only prosody differs:
#   A: falling final contours + a 0.6-s silent pause before each high-information word
#   B: rising final contours + no added pauses + 15 % faster speech
# Primary outcome: willingness to invest, the share of a hypothetical 10,000-unit budget allocated
# to the venture (0-100 %). Effect in SD units; normal approximation; two-sided alpha 0.05.
import math
from statistics import NormalDist
N = NormalDist()

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

for d in (0.20, 0.25, 0.30, 0.40):
    print(f"standardised effect {d:.2f}: {n_per_arm(d, power=0.8)} per arm for 80 % power, {n_per_arm(d)} for 90 %")
n = n_per_arm(0.25)
# Randomisation is stratified by voice (each voice reads both versions, equally often in each arm),
# and voice enters the analysis as a fixed blocking factor, so it costs no extra sample. The price:
# with only 4 voices the result generalises to other voices only weakly.
print(f"chosen: 0.25 SD, 90 % power -> {n} per arm ({n // 4 + 1} per voice and arm); recruit"
      f" {math.ceil(n / 0.85)} per arm allowing 15 % exclusions, {2 * math.ceil(n / 0.85)} in all")
# standardised effect 0.20: 394 per arm for 80 % power, 527 for 90 %
# standardised effect 0.25: 253 per arm for 80 % power, 338 for 90 %
# standardised effect 0.30: 176 per arm for 80 % power, 235 for 90 %
# standardised effect 0.40: 100 per arm for 80 % power, 133 for 90 %
# chosen: 0.25 SD, 90 % power -> 338 per arm (85 per voice and arm); recruit 398 per arm allowing 15 % exclusions, 796 in all

# Decision rule, fixed before data collection. d = version A (falling + pauses) minus version B
# (rising + no pauses + faster) in willingness to invest, standardised, with its 95 % CI.
SESOI = 0.25

def verdict(d, lo, hi, manip_ok):
    if not manip_ok:
        return f"effect {d:+.2f}: NOT INTERPRETABLE - the stimuli failed the acoustic manipulation check"
    if lo >= SESOI:   v = "version A raises willingness to invest by at least the smallest effect of interest"
    elif lo > 0:      v = "version A raises it; size not shown to reach 0.25 SD"
    elif hi < 0:      v = "version A LOWERS willingness to invest"
    elif lo >= -SESOI and hi <= SESOI: v = "no difference worth acting on"
    else:             v = "unclear"
    return f"effect {d:+.2f} ({lo:+.2f} to {hi:+.2f}): {v}"

# Manipulation check on the stimuli themselves (measured before listeners are recruited): every
# version-A sentence must end with a fall of at least 2 semitones and every version-B declarative
# with a rise of at least 2 semitones; pauses must be 0.6 +/- 0.05 s.
for r in ((0.41, 0.27, 0.55, True), (0.12, -0.03, 0.27, True), (0.05, -0.10, 0.20, True), (0.30, 0.15, 0.45, False)):
    print(verdict(*r))
print("Credibility and persuasiveness ratings are secondary: reported with intervals, never decisive.")
# effect +0.41 (+0.27 to +0.55): version A raises willingness to invest by at least the smallest effect of interest
# effect +0.12 (-0.03 to +0.27): unclear
# effect +0.05 (-0.10 to +0.20): no difference worth acting on
# effect +0.30: NOT INTERPRETABLE - the stimuli failed the acoustic manipulation check
# Credibility and persuasiveness ratings are secondary: reported with intervals, never decisive.