title: For Friedman Test, what are the pros and cons of different post hoc comparison method?
body: <p><a href="https://scikit-posthocs.readthedocs.io/en/latest/intro/" rel="nofollow noreferrer">scikit_posthocs</a> lists some post hoc pairwise comparison methods if significant results of the Friedman’s test are obtained. How do I decide which one to use? In my case, the toy dataset <code>df</code> that I have is:</p>
  <p><a href="https://i.stack.imgur.com/JqXQ8.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/JqXQ8.png" alt="enter image description here" /></a></p>
  <pre><code>df = pd.DataFrame(
      data=np.array([[ 581.125,  366.25 ,  144.08 ,  296.575],
         [1743.4  ,  900.85 ,  338.925,  481.6  ],
         [4335.75 , 2000.1  ,  816.75 , 1236.75 ],
         [ 241.925,  540.35 ,  249.9  ,  167.5  ],
         [2822.4  , 1261.35 ,  547.025,  626.05 ],
         [ 568.32 ,  652.55 ,  277.34 ,  265.68 ]]),
      columns=['Both', 'Media Advertisement', 'Neither', 'Store Events'],
      index=['Hardware Accessories', 'Pants', 'Shoes', 'Shorts', 'Sweatshirts',
         'T-Shirts']
  )
  </code></pre>
  <p>I first ran:</p>
  <pre><code>from scipy.stats import friedmanchisquare
  print(friedmanchisquare(*df.T.values))
  </code></pre>
  <p>This gives me
  <code>FriedmanchisquareResult(statistic=12.200000000000003, pvalue=0.006728522930461357)</code></p>
  <p>Now I need to do post hoc analysis, I first ran:</p>
  <pre><code>import scikit_posthocs as sp
  sp.posthoc_conover_friedman(q1_friedman).style.applymap(lambda x: &quot;background-color: yellow&quot; if x &lt; 0.05 else &quot;&quot;)
  </code></pre>
  <p>It gives me this:
  <a href="https://i.stack.imgur.com/BZaXN.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/BZaXN.png" alt="enter image description here" /></a></p>
  <p>I am confused which post hoc analysis approach I should choose to meet my analytic need. In <a href="https://scikit-posthocs.readthedocs.io/en/latest/posthocs_api/" rel="nofollow noreferrer">post hocs API</a>, there are <code>posthoc_nemenyi_friedman</code>, <code>posthoc_conover_friedman</code>, <code>posthoc_siegel_friedman</code> and <code>posthoc_miller_friedman</code> for me to choose from. I tried them all and they returned some conclusions that may slightly differ from one another. Statistically speaking, which approach is appropriate for my case?</p>