外观
Mann–Whitney U检验
在有序测量或不适合常规均值模型时，采用秩信息比较样本。
计算口径
秩检验仍须满足研究设计与独立性等条件。只有额外的分布形状条件满足时，部分检验才可直接解释为中位数差异。
用于两个独立组。U检验针对秩分布，组间分布形状差异也可能造成显著，不能一律解释为中位数不同。
报告各组中位数及四分位数、检验统计量和p值。多组事后比较另列校正结果，不能把每个未经校正的p值独立解释。
同源实现
以下片段来自 core/statistical/comparisons.py 的 nonparametric，由镜像脚本按语法树提取。共享辅助函数和分发逻辑包含在完整下载包中。
py
def nonparametric(data, options, method):
alternative = choice(options, 'alternative', 'two-sided', ('two-sided', 'less', 'greater'))
followup = boolean(options, 'posthoc', False)
correction = choice(options, 'adjustment', 'holm', ('holm', 'bonferroni'))
rows, diagnostics, followups = [], {}, []
if method == 'stat_wilcoxon':
for first, second in paired_columns(data, options):
sample = enough(numeric_frame(data, [first, second]).dropna(), 3)
outcome = _wilcoxon(sample[first].values, sample[second].values, alternative)
rows.append({'variable': first+' − '+second, 'n': len(sample), 'group': _('配对样本'),
'summary': median_iqr(sample[first]-sample[second]), **outcome,
'effect': outcome['rank_biserial']})
diagnostics[first+' − '+second] = outcome
headers = [Column('variable', _('变量对'), 'text'), Column('n', _('配对数'), 'integer'),
Column('summary', _('差值中位数（四分位数）'), 'median_iqr'), Column('statistic', 'W'),
Column('p', 'p', 'p'), Column('effect', _('秩二列相关'))]
elif method == 'stat_friedman':
selected = columns(data, options.get('variables'), 3, 50)
sample = enough(numeric_frame(data, selected).dropna(), 3)
outcome = stats.friedmanchisquare(*[sample[c] for c in selected])
if not np.isfinite(outcome.statistic):
raise ValueError(_('数据缺乏有效的组内秩差异，无法进行Friedman检验'))
kendall = outcome.statistic/(len(sample)*(len(selected)-1))
for i, name in enumerate(selected):
rows.append({'variable': name, 'n': len(sample), 'summary': median_iqr(sample[name]),
'statistic': outcome.statistic if i == 0 else None,
'p': outcome.pvalue if i == 0 else None, 'effect': kendall if i == 0 else None})
if followup:
for i, first in enumerate(selected):
for second in selected[i+1:]:
result = _wilcoxon(sample[first].values, sample[second].values, 'two-sided')
followups.append({'variable': _('相关样本'), 'first': first, 'second': second, **result})
headers = [Column('variable', _('测量变量'), 'text'), Column('n', 'N', 'integer'),
Column('summary', _('中位数（四分位数）'), 'median_iqr'), Column('statistic', 'χ²'),
Column('p', 'p', 'p'), Column('effect', "Kendall's W")]
diagnostics['df'] = len(selected)-1
else:
selected = columns(data, options.get('variables'))
for name in selected:
names, groups = grouped_samples(data, name, options.get('group'))
if method == 'stat_mann_whitney' and len(groups) != 2:
raise ValueError(_('Mann–Whitney U检验需要两个有效组'))
if method == 'stat_mann_whitney':
a, b = groups
outcome = stats.mannwhitneyu(a, b, alternative=alternative, method='auto')
effect = 2*outcome.statistic/(len(a)*len(b))-1
else:
if len(np.unique(np.concatenate(groups))) < 2:
raise ValueError(_('所有观测值相同，无法进行Kruskal–Wallis检验'))
outcome = stats.kruskal(*groups)
effect = max(0., (outcome.statistic-len(groups)+1)/(sum(map(len, groups))-len(groups))) if sum(map(len, groups)) > len(groups) else None
if followup:
for comparison in _dunn(groups):
followups.append({'variable': name, 'first': names[comparison['i']], 'second': names[comparison['j']],
'statistic': comparison['statistic'], 'p': comparison['p']})
for i, (label, group) in enumerate(zip(names, groups)):
rows.append({'variable': name, 'group': label, 'n': len(group), 'summary': median_iqr(group),
'statistic': outcome.statistic if i == 0 else None, 'p': outcome.pvalue if i == 0 else None,
'effect': effect if i == 0 else None})
diagnostics[name] = {'statistic': outcome.statistic, 'p': outcome.pvalue, 'groups': names,
'n': list(map(len, groups)), 'effect': effect}
headers = [Column('variable', _('变量'), 'text', merge=True), Column('group', _('组别'), 'text'),
Column('n', 'N', 'integer'), Column('summary', _('中位数（四分位数）'), 'median_iqr'),
Column('statistic', 'U' if method == 'stat_mann_whitney' else 'H'), Column('p', 'p', 'p'),
Column('effect', _('秩二列相关') if method == 'stat_mann_whitney' else 'ε²')]
tables = [PaperTable(_('非参数检验结果'), headers, rows)]
if followups:
# 每个结局的比较构成一个校正家族，保持不同分析变量相互独立。
for name in dict.fromkeys(row['variable'] for row in followups):
family = [row for row in followups if row['variable'] == name]
adjusted = multipletests([row['p'] for row in family], method=correction)[1]
for row, value in zip(family, adjusted):
row['adjusted_p'] = value
tables.append(PaperTable(_('事后比较'), [Column('variable', _('变量'), 'text'),
Column('first', _('比较组1'), 'text'), Column('second', _('比较组2'), 'text'),
Column('statistic', _('统计量')), Column('adjusted_p', _('校正p值'), 'p')], followups,
_('多重比较采用%(method)s校正。', method=correction)))
diagnostics.update(alternative=alternative, posthoc=followups)
return StatisticalResult(tables, diagnostics)复现本方法
在解压目录安装 requirements.txt 后执行。样例为固定种子的模拟数据，仅供验证；输出不得冒充真实研究结果。
python
import examples._bootstrap
from examples.statistics_cases import build_data, method_cases
from core.statistical.runner import analyze
method = "stat_mann_whitney"
options = dict(method_cases())[method]
result = analyze(build_data(), method, options)
print(result.tables[0].html())