दिन 30: Hypothesis Testing: t-test और Chi-square

import numpy as np
import pandas as pd
t = pd.read_csv("telecom_churn.csv")
t = t[t["tech_support"] != "No internet"]
churn = (t["churn"] == "Yes").to_numpy()
has_ts = (t["tech_support"] == "Yes").to_numpy()
observed = churn[~has_ts].mean() - churn[has_ts].mean()
rng = np.random.default_rng(0)
diffs = []
for _ in range(5000):                       # shuffle labels = world where H0 is true
    lab = rng.permutation(has_ts)
    diffs.append(churn[~lab].mean() - churn[lab].mean())
diffs = np.array(diffs)
print(f"Observed difference: {observed:.3f}")
print(f"Largest shuffled difference: {diffs.max():.3f}")
print(f"p-value ≈ {(np.abs(diffs) >= abs(observed)).mean():.4f}")

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
t = pd.read_csv("telecom_churn.csv"); t = t[t["tech_support"] != "No internet"]
churn = (t["churn"] == "Yes").to_numpy(); ts = (t["tech_support"] == "Yes").to_numpy()
obs = churn[~ts].mean() - churn[ts].mean()
rng = np.random.default_rng(0)
d = [churn[~(l := rng.permutation(ts))].mean() - churn[l].mean() for _ in range(5000)]
plt.figure(figsize=(9, 3.5))
plt.hist(d, bins=40, color="#cbd5e1", label="differences if H₀ were true")
plt.axvline(obs, color="#dc2626", lw=2.5, label=f"observed = {obs:.3f}")
plt.title("The real difference is far outside what chance produces → reject H₀"); plt.legend()
plt.show()

import pandas as pd
from scipy import stats
s = pd.read_csv("sales_data.csv")
r = s["rating"].dropna()
# One-sample: is the average rating different from the target 4.0?
res = stats.ttest_1samp(r, 4.0)
print(f"mean {r.mean():.3f} | t={res.statistic:.2f} p={res.pvalue:.4f}")

import pandas as pd
from scipy import stats
t = pd.read_csv("telecom_churn.csv")
yes = t.loc[t["churn"] == "Yes", "monthly_charges"]
no = t.loc[t["churn"] == "No", "monthly_charges"]
res = stats.ttest_ind(yes, no, equal_var=False)          # Welch’s t-test (safer)
pooled = ((yes.var() + no.var()) / 2) ** 0.5
print(f"churners ₹{yes.mean():.0f} vs stayers ₹{no.mean():.0f}")
print(f"t={res.statistic:.2f}, p={res.pvalue:.2e}, Cohen's d={(yes.mean() - no.mean()) / pooled:.2f}")

import numpy as np
from scipy import stats
rng = np.random.default_rng(4)
before = rng.normal(62, 9, 40).round()                 # mock-test marks before a crash course
after = (before + rng.normal(3, 4, 40)).round()        # same 40 students after
res = stats.ttest_rel(after, before)
print(f"avg gain {np.mean(after - before):.2f} marks | t={res.statistic:.2f} p={res.pvalue:.4f}")

import pandas as pd
from scipy import stats
t = pd.read_csv("telecom_churn.csv")
for col in ["contract", "gender"]:
    table = pd.crosstab(t[col], t["churn"])
    chi2, p, dof, expected = stats.chi2_contingency(table)
    print(f"{col:9s} chi2={chi2:7.1f} dof={dof} p={p:.3g}")
print(pd.crosstab(t["gender"], t["churn"]))

import pandas as pd
from scipy import stats
h = pd.read_csv("house_prices.csv")
h["ppsf"] = h["price_lakh"] * 1e5 / h["area_sqft"]
groups = [g["ppsf"] for _, g in h.groupby("furnishing")]
f, p = stats.f_oneway(*groups)
print(h.groupby("furnishing")["ppsf"].mean().round(0).to_dict())
print(f"ANOVA F={f:.2f}, p={p:.4f}")

import numpy as np
from scipy import stats
rng = np.random.default_rng(0)
false_alarms = sum(stats.ttest_ind(rng.normal(0, 1, 50), rng.normal(0, 1, 50)).pvalue < 0.05 for _ in range(2000))
print(f"No real difference, yet 'significant' in {false_alarms / 2000:.1%} of tests (≈ α)")
for n in [20, 50, 200]:
    power = np.mean([stats.ttest_ind(rng.normal(0, 1, n), rng.normal(0.3, 1, n)).pvalue < 0.05 for _ in range(2000)])
    print(f"real small effect (d=0.3), n={n:3d} per group → detected {power:.0%} of the time")