统计分析指南

from scipy import stats

# Shapiro-Wilk检验（样本量<5000）
stat, p_value = stats.shapiro(data)
print(f"Shapiro-Wilk检验: W={stat:.4f}, p={p_value:.4f}")

if p_value > 0.05:
    print("数据符合正态分布假设")
else:
    print("数据不符合正态分布，考虑使用非参数检验")

from scipy import stats

# Levene检验
stat, p_value = stats.levene(group1, group2)
print(f"Levene检验: F={stat:.4f}, p={p_value:.4f}")

if p_value > 0.05:
    print("方差齐性假设满足")
else:
    print("方差不齐，使用Welch's t检验")

import pingouin as pg

# t检验返回Cohen's d
result = pg.ttest(group1, group2)
d = result['cohen-d'].values[0]
print(f"Cohen's d = {d:.2f}")

# ANOVA返回偏η²
aov = pg.anova(dv='score', between='group', data=df)
eta_p2 = aov['np2'].values[0]
print(f"Partial η² = {eta_p2:.3f}")

A组（n = 48, M = 75.2, SD = 8.5）得分显著高于B组
（n = 52, M = 68.3, SD = 9.2），t(98) = 3.82, p < .001, 
d = 0.77, 95% CI [0.36, 1.18]。

单因素方差分析显示处理条件对测试分数有显著主效应，
F(2, 147) = 8.45, p < .001, η²_p = .10。事后比较使用
Tukey HSD表明，条件A（M = 78.2, SD = 7.3）得分显著
高于条件B（M = 71.5, SD = 8.1, p = .002）。

多元线性回归预测考试成绩，整体模型显著，
F(3, 146) = 45.2, p < .001, R² = .48。学习时间
（β = .35, p < .001）和先前GPA（β = .28, p < .001）
是显著预测变量。

import numpy as np
import pingouin as pg
from scipy import stats

# 数据
group_a = np.array([75, 82, 68, 79, 85, 72, 88, 76])
group_b = np.array([65, 70, 62, 68, 75, 60, 72, 66])

# 1. 描述统计
print(f"A组: M={group_a.mean():.2f}, SD={group_a.std():.2f}")
print(f"B组: M={group_b.mean():.2f}, SD={group_b.std():.2f}")

# 2. 正态性检验
_, p_a = stats.shapiro(group_a)
_, p_b = stats.shapiro(group_b)
print(f"正态性: A组 p={p_a:.3f}, B组 p={p_b:.3f}")

# 3. t检验
result = pg.ttest(group_a, group_b)
print(f"t = {result['T'].values[0]:.2f}")
print(f"p = {result['p-val'].values[0]:.4f}")
print(f"Cohen's d = {result['cohen-d'].values[0]:.2f}")