Pythonで学ぶ統計学 ─ ライブラリ別 早わかり比較 2026年版

import numpy as np
from scipy import stats

# 2標本のt検定(等分散仮定)
rng = np.random.default_rng(42)
group_a = rng.normal(70, 10, 30)
group_b = rng.normal(75, 10, 30)
t, p = stats.ttest_ind(group_a, group_b, equal_var=True)
print(f't = {t:.3f}, p = {p:.4f}')

# 適合度のカイ二乗検定
observed = np.array([18, 22, 20, 14, 16, 10])  # サイコロ目の度数
expected = np.array([16.67] * 6)               # 期待度数
chi2, p = stats.chisquare(observed, expected)
print(f'chi2 = {chi2:.3f}, p = {p:.4f}')

# 正規分布の確率密度・累積分布
from scipy.stats import norm
print(f'P(X < 1.96) = {norm.cdf(1.96):.4f}')
print(f'95%点 = {norm.ppf(0.975):.4f}')

import numpy as np
import pandas as pd
import statsmodels.api as sm

rng = np.random.default_rng(0)
n = 200
df = pd.DataFrame({
    'x1': rng.normal(0, 1, n),
    'x2': rng.normal(0, 1, n),
})
df['y'] = 2.0 * df['x1'] - 1.5 * df['x2'] + rng.normal(0, 0.5, n)

# 切片を追加
X = sm.add_constant(df[['x1', 'x2']])
model = sm.OLS(df['y'], X).fit()
print(model.summary())

# AIC・BIC・決定係数
print(f'R^2 = {model.rsquared:.3f}')
print(f'AIC = {model.aic:.2f}')

import numpy as np
from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.linear_model import LogisticRegression
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
from sklearn.metrics import classification_report, roc_auc_score

X, y = load_breast_cancer(return_X_y=True)
X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.2, random_state=42)

pipe = Pipeline([
    ('scaler', StandardScaler()),
    ('clf', LogisticRegression(max_iter=1000)),
])
pipe.fit(X_tr, y_tr)

y_pred = pipe.predict(X_te)
y_prob = pipe.predict_proba(X_te)[:, 1]
print(classification_report(y_te, y_pred))
print(f'AUC = {roc_auc_score(y_te, y_prob):.3f}')

# 5-fold CV
scores = cross_val_score(pipe, X, y, cv=5, scoring='accuracy')
print(f'CV mean = {scores.mean():.3f} +/- {scores.std():.3f}')

import pandas as pd
import numpy as np

rng = np.random.default_rng(1)
df = pd.DataFrame({
    'group': rng.choice(['A', 'B', 'C'], 1000),
    'score': rng.normal(70, 15, 1000),
    'time': rng.exponential(30, 1000),
})

# グループ別の集計
summary = df.groupby('group').agg(
    n=('score', 'size'),
    mean=('score', 'mean'),
    std=('score', 'std'),
    median=('score', 'median'),
)
print(summary)

# クロス集計
df['score_cat'] = pd.cut(df['score'], bins=[-np.inf, 60, 80, np.inf], labels=['低', '中', '高'])
print(pd.crosstab(df['group'], df['score_cat']))

import numpy as np
from scipy import stats

rng = np.random.default_rng(7)
data = rng.normal(50, 10, 100)

n = len(data)
mean = np.mean(data)
se = np.std(data, ddof=1) / np.sqrt(n)

# 95%信頼区間(t分布)
t_crit = stats.t.ppf(0.975, df=n - 1)
ci_low = mean - t_crit * se
ci_high = mean + t_crit * se
print(f'95% CI: [{ci_low:.2f}, {ci_high:.2f}]')

# numpy だけで標準誤差・分散
print(f'mean = {mean:.3f}, se = {se:.3f}')
print(f'sample variance (ddof=1) = {np.var(data, ddof=1):.3f}')