Spearman相关

量化变量之间关联的方向和强度。

计算口径

检查离群值与关系形状。完整案例让矩阵采用同一批对象；成对删除可能使每个相关系数使用不同样本。

对变量排序后计算关联，适用于单调关系与有序数据；并列值使用平均秩。不以Spearman显著推断原单位下线性关系。

相关系数接近0不代表不存在任何关系。星号只表示对应检验阈值，不代表效应大小；相关不能单独证明因果。原始输出保留每一对的N与p。

同源实现

以下片段来自 core/statistical/association.py 的 correlation，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。

def correlation(data, options, method):
    selected = columns(data, options.get('variables'), 2, 50)
    controls = []
    if method == 'stat_partial_correlation':
        controls = columns(data, options.get('controls'))
        if set(selected).intersection(controls):
            raise ValueError(_('控制变量不能与分析变量重复'))
    policy = choice(options, 'missing', 'complete', ('complete', 'pairwise'))
    if controls and policy != 'complete':
        raise ValueError(_('偏相关使用统一完整样本，请选择完整案例'))
    numeric = numeric_frame(data, selected + controls)
    if policy == 'complete':
        numeric = enough(numeric.dropna(), len(controls)+3)
    residuals = None
    if controls:
        design = np.column_stack([np.ones(len(numeric)), numeric[controls].values])
        if np.linalg.matrix_rank(design) < design.shape[1]:
            raise ValueError(_('控制变量存在完全共线性，请减少重复信息的变量'))
        residuals = numeric[selected].values - design @ np.linalg.lstsq(design, numeric[selected].values, rcond=None)[0]
    rows, pairs = [], []
    for i, name in enumerate(selected):
        row = {'variable': name, 'n': int(numeric[name].notna().sum()),
               'mean': numeric[name].mean(), 'sd': numeric[name].std(ddof=1)}
        for j, other in enumerate(selected):
            if j > i:
                row['r'+str(j)] = None
                continue
            sample = enough(numeric[[name, other]].dropna() if i != j else numeric[[name]].dropna(), 3)
            if i == j:
                varying(sample[name].values, name)
                row['r'+str(j)] = (1.0, None)
                continue
            if residuals is not None:
                x, y = residuals[:, i], residuals[:, j]
            else:
                x, y = sample[name].values, sample[other].values
            varying(x, name)
            varying(y, other)
            if method == 'stat_spearman':
                r, p = stats.spearmanr(x, y)
            else:
                r, p = stats.pearsonr(x, y)
            degrees = len(x)-len(controls)-2
            if controls:
                p = 0.0 if abs(r) >= 1 else 2*stats.t.sf(abs(r)*np.sqrt(degrees/(1-r*r)), degrees)
            row['r'+str(j)] = (float(r), float(p))
            pairs.append({'left': name, 'right': other, 'n': len(x), 'r': r, 'p': p, 'df': degrees})
        rows.append(row)
    headers = [Column('variable', _('变量'), 'text')]
    if boolean(options, 'include_descriptives', True):
        headers += [Column('n', 'N', 'integer'), Column('mean', _('均值')), Column('sd', _('标准差'))]
    headers += [Column('r'+str(i), str(i+1), 'correlation') for i in range(len(selected))]
    for i, row in enumerate(rows):
        row['variable'] = str(i+1)+'. '+row['variable']
    return StatisticalResult([PaperTable(_('相关分析'), headers, rows, _('* p<0.05，** p<0.01，*** p<0.001。'))],
                             {'pairs': pairs, 'controls': controls, 'missing': policy,
                              'n_by_variable': {name: int(numeric[name].notna().sum()) for name in selected}})

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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。

import examples._bootstrap
from examples.statistics_cases import build_data, method_cases
from core.statistical.runner import analyze

method = "stat_spearman"
options = dict(method_cases())[method]
result = analyze(build_data(), method, options)
print(result.tables[0].html())

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