T检验方差分析回归分析

• T检验程序
• 方差分析
• 回归分析

T检验程序

import numpy as np
from scipy import stats

# 准备数据
group_A = [10, 12, 11]
group_B = [15, 16, 14]

# A vs B
t_stat, p_value = stats.ttest_ind(group_A, group_B)
print(f"A vs B: t-statistic = {t_stat}, p-value = {p_value}")

结果

F-Statistic: 24.0
P-Value: 0.008049893100837719
There is a significant difference between the groups.

方差分析

# 使用scipy.stats的f_oneway函数进行单因素方差分析
f_statistic, p_value = stats.f_oneway(group_A, group_B)

# 输出结果
print(f"F-Statistic: {f_statistic}")
print(f"P-Value: {p_value}")

# 判断显著性
alpha = 0.05
if p_value < alpha:
    print("There is a significant difference between the groups.")
else:
    print("There is no significant difference between the groups.")

运行结果

F-Statistic: 24.0
P-Value: 0.008049893100837719
There is a significant difference between the groups.

回归分析

import pandas as pd
import statsmodels.api as sm
import statsmodels.formula.api as smf

# 创建数据
data = {
    'Group': ['A', 'A', 'A', 'B', 'B', 'B'],
    'Value': [10, 12, 11, 15, 16, 14]
}
df = pd.DataFrame(data)

# 添加哑变量
df = pd.get_dummies(df, columns=['Group'], drop_first=True)

# 回归模型
model = smf.ols('Value ~ Group_B', data=df).fit()

# 输出回归结果
print(model.summary())

# 提取方差分析表
anova_table = sm.stats.anova_lm(model, typ=2)
print("\nANOVA Table:")
print(anova_table)

运行结果

OLS Regression Results                            
==============================================================================
Dep. Variable:                  Value   R-squared:                       0.857
Model:                            OLS   Adj. R-squared:                  0.821
Method:                 Least Squares   F-statistic:                     24.00
Date:                Mon, 20 Jan 2025   Prob (F-statistic):            0.00805
Time:                        11:27:46   Log-Likelihood:                -7.2972
No. Observations:                   6   AIC:                             18.59
Df Residuals:                       4   BIC:                             18.18
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
===================================================================================
                      coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------
Intercept          11.0000      0.577     19.053      0.000       9.397      12.603
Group_B[T.True]     4.0000      0.816      4.899      0.008       1.733       6.267
==============================================================================
Omnibus:                          nan   Durbin-Watson:                   2.500
Prob(Omnibus):                    nan   Jarque-Bera (JB):                0.562
Skew:                           0.000   Prob(JB):                        0.755
Kurtosis:                       1.500   Cond. No.                         2.62
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

ANOVA Table:
          sum_sq   df     F   PR(>F)
Group_B     24.0  1.0  24.0  0.00805
Residual     4.0  4.0   NaN      NaN