非母數檢定
Python 中的假設檢定
James Chapman
Curriculum Manager, DataCamp
母數檢定
- z 檢定、t 檢定與 ANOVA 都是母數檢定
- 假設常態分佈
- 需要足夠大的樣本數
較小的共和黨得票資料
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() 的結果
- 只有 5 對樣本，不足以滿足成對 t 檢定的樣本數條件：
- 各樣本間至少需有 30 對觀測值。
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
非母數檢定
- 非母數檢定可避開母數假設與條件
- 許多非母數檢定使用資料的「名次」
x = [1, 15, 3, 10, 6]
from scipy.stats import rankdata
rankdata(x)
array([1., 5., 2., 4., 3.])
非母數檢定
- 對於小樣本或資料非常態分佈時，非母數檢定比母數檢定更可靠
非母數檢定
- 對於小樣本或資料非常態分佈時，非母數檢定更可靠
Wilcoxon 符號等級檢定
- 由 Frank Wilcoxon 於 1945 年提出
- 最早的非母數方法之一
Wilcoxon 符號等級檢定（步驟 1）
- 以成對資料的「差值絕對值的名次」進行計算
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 符號等級檢定（步驟 2）
- 以成對資料的「差值絕對值的名次」進行計算
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 符號等級檢定（步驟 3）
- 以成對資料的「差值絕對值的名次」進行計算
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 符號等級檢定（步驟 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
- 分別加總負差與正差的名次
T_minus = 1 + 4 + 5 + 2 + 3T_plus = 0W = np.min([T_minus, T_plus])
0
使用 pingouin.wilcoxon() 實作
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
無法拒絕 $H_0$，因為 0.03125 > 0.01
一起來練習吧！
Python 中的假設檢定
