Cochran’s Q Test

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cochran Q 测试用于非参数检验，特别是对分，二分

成功或失败

有效或无效

活着或死了

有缺陷的或无缺陷的

python代码

无显著差异，结论一致

# -*- coding: utf-8 -*-
# Import standard packages
import numpy as np
import pandas as pd

# additional packages
from statsmodels.sandbox.stats.runs import cochrans_q

obs = np.array([[1,1,0,1,0,1,1,1,0,0,1,1],
                [1,1,1,1,0,1,1,1,0,1,1,1],
                [1,1,0,0,0,1,1,0,1,0,1,1]])

def cochranQ(obs):
    '''Cochran's Q test: 12 subjects are asked to perform 3 tasks. The outcome of each task is "success" or
    "failure". The results are coded 0 for failure and 1 for success. In the example, subject 1 was successful
    in task 2, but failed tasks 1 and 3.
    Is there a difference between the performance on the three tasks?
    '''

    # I prefer a DataFrame here, as it indicates directly what the values mean
    df = pd.DataFrame(obs.T, columns = ['Diet1', 'Diet2', 'Diet3'])

    # --- >>> START stats <<< ---
    (Q, pVal) = cochrans_q(df)
    # --- >>> STOP stats <<< ---
    print('\nCOCHRAN\'S Q -----------------------------------------------------')
    print('Q = {0:5.3f}, p = {1:5.3f}'.format(Q, pVal))
    if pVal < 0.05:
        print("H1 wins,There is a significant difference between the three tasks.")  

    else:
       print("H0 wins,There was no significant change")

cochranQ(obs)

测试，12个对象参加三种考试，检验三种考试难度是否一样。

H0，三种考试难度相同

H1，三种考试难度不同，至少有一个简单或难

三种考试有显著差异

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