130 lines
2.8 KiB
Markdown
130 lines
2.8 KiB
Markdown
# 统计分析和假设检验
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## 描述性统计
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```python
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def describe_column(series):
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return {
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'count': len(series),
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'mean': series.mean(),
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'std': series.std(),
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'min': series.min(),
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'q25': series.quantile(0.25),
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'median': series.median(),
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'q75': series.quantile(0.75),
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'max': series.max(),
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'skew': series.skew(),
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'kurtosis': series.kurtosis()
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}
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```
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## T检验
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```python
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from scipy import stats
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# 独立样本T检验（两组均值比较）
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stat, p = stats.ttest_ind(group1, group2)
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# 配对T检验
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stat, p = stats.ttest_rel(before, after)
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# 单样本T检验
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stat, p = stats.ttest_1samp(sample, popmean=100)
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# 结果解读
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print(f"p={p:.4f}, {'显著' if p < 0.05 else '不显著'}")
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```
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## 卡方检验
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```python
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# 分类变量独立性检验
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contingency = pd.crosstab(df['col1'], df['col2'])
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chi2, p, dof, expected = stats.chi2_contingency(contingency)
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```
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## A/B测试
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```python
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from statsmodels.stats.proportion import proportions_ztest
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def ab_test(ctrl_conv, ctrl_n, treat_conv, treat_n, alpha=0.05):
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count = np.array([treat_conv, ctrl_conv])
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nobs = np.array([treat_n, ctrl_n])
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stat, p = proportions_ztest(count, nobs)
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ctrl_rate = ctrl_conv / ctrl_n
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treat_rate = treat_conv / treat_n
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lift = (treat_rate - ctrl_rate) / ctrl_rate * 100
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return {
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'ctrl_rate': f"{ctrl_rate:.2%}",
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'treat_rate': f"{treat_rate:.2%}",
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'lift': f"{lift:.1f}%",
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'p_value': p,
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'significant': p < alpha
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}
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```
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## ANOVA
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```python
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# 单因素方差分析
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f_stat, p = stats.f_oneway(g1, g2, g3)
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# 事后检验
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from statsmodels.stats.multicomp import pairwise_tukeyhsd
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tukey = pairwise_tukeyhsd(df['value'], df['group'])
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print(tukey.summary())
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```
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## 相关性分析
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```python
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# Pearson/Spearman相关
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corr = df.select_dtypes(include=[np.number]).corr(method='pearson')
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# 找高相关对
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high_corr = []
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for i in range(len(corr.columns)):
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for j in range(i+1, len(corr.columns)):
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if abs(corr.iloc[i,j]) > 0.7:
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high_corr.append((corr.columns[i], corr.columns[j], corr.iloc[i,j]))
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```
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## 回归分析
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```python
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import statsmodels.api as sm
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X = df[features]
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y = df[target]
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X = sm.add_constant(X)
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model = sm.OLS(y, X).fit()
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print(model.summary())
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print(f"R² = {model.rsquared:.4f}")
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```
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## 效应量
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```python
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# Cohen's d
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def cohens_d(g1, g2):
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n1, n2 = len(g1), len(g2)
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pooled_std = np.sqrt(((n1-1)*g1.var() + (n2-1)*g2.var()) / (n1+n2-2))
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return (g1.mean() - g2.mean()) / pooled_std
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# |d| < 0.2 小, 0.2-0.8 中, > 0.8 大
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```
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## 样本量计算
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```python
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from statsmodels.stats.power import TTestIndPower
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analysis = TTestIndPower()
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n = analysis.solve_power(effect_size=0.5, alpha=0.05, power=0.8)
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print(f"每组需要 {int(np.ceil(n))} 样本")
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```
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