# How a near-zero effect can look large in the published record.
# Suppose the true ego-depletion effect is d = 0.05. Many small labs run studies with 20 people per group;
# only studies with a positive, significant result (p < .05, one-tailed direction) reach print.
import math, random
from statistics import NormalDist, mean, stdev
random.seed(4)
TRUE_D, N, STUDIES = 0.05, 20, 4000
z_crit = NormalDist().inv_cdf(0.975)

all_d, published = [], []
for _ in range(STUDIES):
    a = [random.gauss(TRUE_D, 1) for _ in range(N)]
    b = [random.gauss(0, 1) for _ in range(N)]
    sp = math.sqrt((stdev(a) ** 2 + stdev(b) ** 2) / 2)
    d = (mean(a) - mean(b)) / sp
    se = math.sqrt(2 / N + d * d / (4 * N))
    all_d.append(d)
    if d / se > z_crit:
        published.append(d)
print(f"true effect d = {TRUE_D}; {STUDIES} studies with {N} per group")
print(f"mean d of all studies run:      {mean(all_d):5.2f}")
print(f"share reaching significance:    {100 * len(published) / STUDIES:4.1f} %")
print(f"mean d of the published ones:   {mean(published):5.2f}")
print("for comparison: 2010 meta-analysis d = 0.62; 2016 23-lab replication d = 0.04; 2021 36-lab test d = 0.06")
# true effect d = 0.05; 4000 studies with 20 per group
# mean d of all studies run:       0.05
# share reaching significance:     3.9 %
# mean d of the published ones:    0.79
# for comparison: 2010 meta-analysis d = 0.62; 2016 23-lab replication d = 0.04; 2021 36-lab test d = 0.06

# Could half an hour of self-control use up the brain's fuel? Order-of-magnitude arithmetic.
BRAIN_W = 20.0           # W: the adult brain uses roughly 20 % of resting metabolism, about 20 W
TASK_RISE = 0.05         # focused tasks raise whole-brain energy use by a few per cent at most (upper bound)
MINUTES = 30
KJ_PER_G_GLUCOSE = 15.6  # kJ released per gram of glucose fully oxidised
extra_kj = BRAIN_W * TASK_RISE * MINUTES * 60 / 1000
grams = extra_kj / KJ_PER_G_GLUCOSE
BLOOD_GLUCOSE_G = 4.5    # grams of glucose circulating in an adult's blood (about 5 L at 5 mmol/L)
LIVER_GLYCOGEN_G = 80.0  # a typical fed-state liver glycogen store
print(f"extra energy for {MINUTES} min of hard thinking: {extra_kj:.1f} kJ = {extra_kj / 4.184:.2f} kcal")
print(f"glucose needed: {grams:.2f} g, i.e. {100 * grams / BLOOD_GLUCOSE_G:.1f} % of the glucose in the blood "
      f"and {100 * grams / LIVER_GLYCOGEN_G:.2f} % of liver glycogen")
print(f"a 250 mL sugary drink (about 27 g sugar) carries {27 / grams:.0f} times this amount")
# extra energy for 30 min of hard thinking: 1.8 kJ = 0.43 kcal
# glucose needed: 0.12 g, i.e. 2.6 % of the glucose in the blood and 0.14 % of liver glycogen
# a 250 mL sugary drink (about 27 g sugar) carries 234 times this amount