<story><title>Simpson&apos;s Paradox</title><url>http://vudlab.com/simpsons/</url></story><parent_chain></parent_chain><comment><author>tlb</author><text>The Omitted Variable Problem is part of my mental framework that causes me to not believe most epidemiological studies, especially ones that confirm a popular belief.&lt;p&gt;The almost universally omitted variable is health-consciousness. Some people are health-conscious and some aren&amp;#x27;t. People who are health-conscious do a whole bunch of things, some of which help (like exercise, sleep well, eat moderately). They also do things that are widely believed to be good for you, like eating broccoli.&lt;p&gt;So if you do a study, you&amp;#x27;ll find that people who eat lots of broccoli are healthier. You&amp;#x27;ll be able to confirm pretty much any widely believed health folk wisdom, unless it&amp;#x27;s something quite harmful, as long as you omit health-consciousness as a variable.</text></comment>
<story><title>Simpson&apos;s Paradox</title><url>http://vudlab.com/simpsons/</url></story><parent_chain></parent_chain><comment><author>tel</author><text>Simpson&amp;#x27;s Paradox is scary if you&amp;#x27;ve not seen it before, but you should not stop here and instead proceed &lt;i&gt;immediately&lt;/i&gt; on to omitted variable bias and the conversation here (&lt;a href=&quot;http://normaldeviate.wordpress.com/2013/06/20/simpsons-paradox-explained/&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;normaldeviate.wordpress.com&amp;#x2F;2013&amp;#x2F;06&amp;#x2F;20&amp;#x2F;simpsons-parad...&lt;/a&gt;).&lt;p&gt;In short, Simpson&amp;#x27;s paradox occurs because probability distributions and causal claims &lt;i&gt;are distinct things&lt;/i&gt; which behave differently. It&amp;#x27;s nothing more than a particular, insidious example of correlation not implying causation. It&amp;#x27;s perfectly possible for a probability distribution to have a &amp;quot;contradictory&amp;quot; shape, but perfectly impossible for logical statements about the world to be contradictory.&lt;p&gt;The resolution is that you shouldn&amp;#x27;t let your probability distributions turn into logical statements without analyzing your causal assumptions. This will lead you to whether or not excluding a variable is omitted variable bias (and whether including an improper one will lead to included variable bias, which is rarely recognized).</text></comment>