The Toolkit

To detect a standardised effect with 80% power at the 5% level takes about 393 people per group for d = 0.2, 63 for d = 0.5 and 25 for d = 0.8. A study with 30 per group has only 49% power for a medium effect of 0.5 — a coin flip whether it finds an effect that is really there.

• Power calculations need a guess of the effect size; guessing from a small pilot study usually overestimates it.
• Computing “observed power” after a study is uninformative; it is just a restatement of the p-value.
• Low-powered studies that do find effects tend to exaggerate them (Button et al. 2013).

from scipy.stats import norm
z = norm.ppf(0.975) + norm.ppf(0.80)
n_per_group = {d: int(np.ceil(2 * z ** 2 / d ** 2)) for d in (0.2, 0.5, 0.8)}   # normal approximation
power_30 = norm.cdf(0.5 * np.sqrt(30 / 2) - norm.ppf(0.975))                   # d = 0.5 with 30 per group

Assumes import numpy as np and import pandas as pd (and SciPy where imported). Each snippet simulates or makes up its own data, as the comments say.

# Python — power analysis
from statsmodels.stats.power import TTestIndPower

analysis = TTestIndPower()

# How many samples for d=0.5, power=0.8?
n = analysis.solve_power(
    effect_size=0.5, power=0.8, alpha=0.05
)
print(f"Need {n:.0f} per group")

# Power curve
import matplotlib.pyplot as plt
ns = range(10, 200)
powers = [analysis.power(effect_size=0.5, nobs1=n, alpha=0.05) for n in ns]
plt.plot(ns, powers); plt.axhline(0.8, ls='--'); plt.show()