非参数检验
Python 假设检验
James Chapman
Curriculum Manager, DataCamp
参数检验
- z 检验、t 检验和 ANOVA 均为参数检验
- 假设正态分布
- 需要足够大的样本量
较小的共和党投票数据
print(repub_votes_small)
state county repub_percent_08 repub_percent_12
80 Texas Red River 68.507522 69.944817
84 Texas Walker 60.707197 64.971903
33 Kentucky Powell 57.059533 61.727293
81 Texas Schleicher 74.386503 77.384464
93 West Virginia Morgan 60.857614 64.068711
使用 pingouin.ttest() 的结果
- 5 对观察不足以满足配对 t 检验的样本量条件：
- 两样本合计至少 30 对观察。
alpha = 0.01import pingouin pingouin.ttest(x=repub_votes_potus_08_12_small['repub_percent_08'], y=repub_votes_potus_08_12_small['repub_percent_12'], paired=True, alternative="less")
T dof alternative p-val CI95% cohen-d BF10 power
T-test -5.875753 4 less 0.002096 [-inf, -2.11] 0.500068 26.468 0.239034
非参数检验
- 非参数检验不依赖参数化假设与条件
- 许多非参数检验使用数据的"秩"
x = [1, 15, 3, 10, 6]
from scipy.stats import rankdata
rankdata(x)
array([1., 5., 2., 4., 3.])
非参数检验
- 对于样本量小或数据非正态分布，非参数检验更可靠
非参数检验
- 对于样本量小或数据非正态分布，非参数检验更可靠
Wilcoxon符号秩检验
- 由 Frank Wilcoxon 于 1945 年提出
- 最早的非参数方法之一
Wilcoxon符号秩检验（步骤 1）
- 基于成对数据的绝对差的秩进行检验
repub_votes_small['diff'] = repub_votes_small['repub_percent_08'] -
repub_votes_small['repub_percent_12']
print(repub_votes_small)
state county repub_percent_08 repub_percent_12 diff
80 Texas Red River 68.507522 69.944817 -1.437295
84 Texas Walker 60.707197 64.971903 -4.264705
33 Kentucky Powell 57.059533 61.727293 -4.667760
81 Texas Schleicher 74.386503 77.384464 -2.997961
93 West Virginia Morgan 60.857614 64.068711 -3.211097
Wilcoxon符号秩检验（步骤 2）
- 基于成对数据的绝对差的秩进行检验
repub_votes_small['abs_diff'] = repub_votes_small['diff'].abs()
print(repub_votes_small)
state county repub_percent_08 repub_percent_12 diff abs_diff
80 Texas Red River 68.507522 69.944817 -1.437295 1.437295
84 Texas Walker 60.707197 64.971903 -4.264705 4.264705
33 Kentucky Powell 57.059533 61.727293 -4.667760 4.667760
81 Texas Schleicher 74.386503 77.384464 -2.997961 2.997961
93 West Virginia Morgan 60.857614 64.068711 -3.211097 3.211097
Wilcoxon符号秩检验（步骤 3）
- 基于成对数据的绝对差的秩进行检验
from scipy.stats import rankdata
repub_votes_small['rank_abs_diff'] = rankdata(repub_votes_small['abs_diff'])
print(repub_votes_small)
state county repub_percent_08 repub_percent_12 diff abs_diff rank_abs_diff
80 Texas Red River 68.507522 69.944817 -1.437295 1.437295 1.0
84 Texas Walker 60.707197 64.971903 -4.264705 4.264705 4.0
33 Kentucky Powell 57.059533 61.727293 -4.667760 4.667760 5.0
81 Texas Schleicher 74.386503 77.384464 -2.997961 2.997961 2.0
93 West Virginia Morgan 60.857614 64.068711 -3.211097 3.211097 3.0
Wilcoxon符号秩检验（步骤 4）
state county repub_percent_08 repub_percent_12 diff abs_diff rank_abs_diff
80 Texas Red River 68.507522 69.944817 -1.437295 1.437295 1.0
84 Texas Walker 60.707197 64.971903 -4.264705 4.264705 4.0
33 Kentucky Powell 57.059533 61.727293 -4.667760 4.667760 5.0
81 Texas Schleicher 74.386503 77.384464 -2.997961 2.997961 2.0
93 West Virginia Morgan 60.857614 64.068711 -3.211097 3.211097 3.0
- 合并负差与正差的秩和
T_minus = 1 + 4 + 5 + 2 + 3T_plus = 0W = np.min([T_minus, T_plus])
0
使用 pingouin.wilcoxon() 实现
alpha = 0.01
pingouin.wilcoxon(x=repub_votes_potus_08_12_small['repub_percent_08'],
y=repub_votes_potus_08_12_small['repub_percent_12'],
alternative="less")
W-val alternative p-val RBC CLES
Wilcoxon 0.0 less 0.03125 -1.0 0.72
由于 0.03125 > 0.01，无法拒绝 H0
Passons à la pratique !
Python 假设检验
