import numpy as np
from scipy.stats import rankdata

data = [3.2, 1.5, 4.8, 2.1, 5.0]
ranks = rankdata(data)  # [3, 1, 4, 2, 5]
print(f"数据: {data}")
print(f"秩: {ranks}")
# 秩的好处: 摆脱具体数值, 只看相对大小
# 不受异常值影响

from scipy.stats import binom
import numpy as np
diffs = np.array([3, -2, 5, -1, 4])
n_pos = (diffs > 0).sum()    # 3
n_neg = (diffs < 0).sum()    # 2
# 零假设下, + 和 - 各占一半
n = n_pos + n_neg
p = 2 * binom.cdf(min(n_pos, n_neg), n, 0.5)
print(f"符号检验: + = {n_pos}, - = {n_neg}, p = {p:.4f}")
# p = 1.0 (3 vs 2, 完全无法拒绝 H₀)

from scipy.stats import wilcoxon
import numpy as np

# 配对: 同一批 20 个病人, 用药前后血压
before = np.array([180, 165, 170, 175, 190, 185, 178, 192, 188, 170,
                   182, 168, 175, 195, 178, 188, 172, 165, 180, 175])
after  = np.array([165, 158, 162, 168, 180, 175, 170, 184, 178, 162,
                   170, 160, 168, 188, 172, 180, 165, 158, 172, 168])

w_stat, p_val = wilcoxon(before - after, alternative="greater")
# "greater" 因为我们预期 before > after (血压降)
print(f"Wilcoxon 符号秩: W = {w_stat}, p = {p_val:.4f}")

# 小样本: 直接用精确分布
# 大样本: 上面 z 公式 (Python 自动)

from scipy.stats import mannwhitneyu
import numpy as np

# A 组 (老方法), B 组 (新方法), 各 20 个
np.random.seed(42)
group_a = np.random.exponential(2, 20) + 5
group_b = np.random.exponential(2.5, 20) + 5  # B 组期望更大

u_stat, p_val = mannwhitneyu(group_a, group_b, alternative="less")
print(f"Mann-Whitney U: U = {u_stat}, p = {p_val:.4f}")
# p 小 → A 组显著小于 B 组

from scipy.stats import kruskal
import numpy as np

# 3 种教学方法的效果
np.random.seed(42)
method_1 = np.random.normal(75, 5, 30)
method_2 = np.random.normal(78, 5, 30)
method_3 = np.random.normal(82, 5, 30)

h_stat, p_val = kruskal(method_1, method_2, method_3)
print(f"Kruskal-Wallis: H = {h_stat:.3f}, p = {p_val:.4f}")
# 显著 → 至少两组有差异

from scipy.stats import runs
# 例: 抛硬币 20 次
sequence = "HTHHHTHTTHTHHHTHHTHH"
n_h = sequence.count("H")
n_t = sequence.count("T")
r_stat, p_val = runs(np.array([c == "H" for c in sequence]))
print(f"游程数: {r_stat}, p = {p_val:.4f}")
# p 小 → 不随机 (有趋势)

数据多少组? ─┬─ 1 组 (跟已知值比)
             │     ├─ 正态 → 单样本 t
             │     └─ 偏态 → Wilcoxon 符号秩
             │
             ├─ 2 组 (独立)
             │     ├─ 正态 → 独立 t (Welch)
             │     └─ 偏态 → Mann-Whitney U
             │
             ├─ 2 组 (配对)
             │     ├─ 正态 → 配对 t
             │     └─ 偏态 → Wilcoxon 符号秩
             │
             └─ 3+ 组
                  ├─ 正态 → ANOVA (下章)
                  └─ 偏态 → Kruskal-Wallis

import numpy as np
from scipy import stats

# 模拟 5 个随机种子下, 模型 A 和 B 的 F1
np.random.seed(42)
f1_a = np.random.normal(0.85, 0.03, 5)  # A
f1_b = np.random.normal(0.88, 0.02, 5)  # B 略高

# 1. 配对 t 检验 (正态, 但 n=5 太依赖正态假设)
t_stat, p_t = stats.ttest_rel(f1_b, f1_a)
print(f"配对 t 检验: t = {t_stat:.3f}, p = {p_t:.4f}")

# 2. Wilcoxon 符号秩 (不依赖正态, n=5 更稳)
w_stat, p_w = stats.wilcoxon(f1_b - f1_a)
print(f"Wilcoxon 符号秩: W = {w_stat}, p = {p_w:.4f}")

# 3. 配对 Bootstrap (更稳)
n_boot = 10000
diffs = f1_b - f1_a
boot_means = [np.mean(np.random.choice(diffs, size=len(diffs), replace=True))
              for _ in range(n_boot)]
ci_low, ci_high = np.percentile(boot_means, [2.5, 97.5])
print(f"Bootstrap 95% CI: [{ci_low:.4f}, {ci_high:.4f}]")
# CI 不包含 0 → 显著

import scipy.stats as stats

def auto_test(x, y=None, paired=False, alternative="two-sided"):
    """自动选择参数/非参数检验"""
    if y is None:
        # 单样本
        if len(x) >= 30 and stats.shapiro(x).pvalue > 0.05:
            return stats.ttest_1samp(x, 0, alternative=alternative)
        else:
            return stats.wilcoxon(x - (x.mean() if y is None else 0), alternative=alternative)
    
    # 两样本
    if paired:
        # 配对
        if len(x) >= 30 and stats.shapiro(x - y).pvalue > 0.05:
            return stats.ttest_rel(x, y, alternative=alternative)
        else:
            return stats.wilcoxon(x - y, alternative=alternative)
    else:
        # 独立
        if len(x) >= 30 and stats.shapiro(x).pvalue > 0.05 and stats.shapiro(y).pvalue > 0.05:
            return stats.ttest_ind(x, y, equal_var=False, alternative=alternative)
        else:
            return stats.mannwhitneyu(x, y, alternative=alternative)