Simpson’s Paradox (2016)
So, this is the data that the wikipedia page on Simpson&#x27;s Paradox cites for the Berkeley study, and that the author of the article has quoted:<p><pre><code>                     Men              Women
    Department Applied  Admitted Applied  Admitted
    A          [825]    62%      108      [82%]
    B          [560]    63%      25       [68%]
    C          325      [37%]    [593]    34%
    D          [417]    33%      375      [35%]
    E          191      [28%]    [393]    24%
    F          [373]    6%       341      [7%]

</code></pre>
Above, I&#x27;ve bracketed in each pair of columns a) the sex with the most applicants and b) the sex with the most admissions, in a department. If that data is really the Berkeley data, then it&#x27;s clear that the bias is against the sex with the most applicants, rather than either men or women.<p>I can propose a mechanism for this kind of (with some abuse of terminology) selection bias. A department accepts some applications, then realises they&#x27;ve admitted too many applicants of one sex and start rejecting applicants from the dominant sex in an attempt to redress the balance. They make a mess of it and end up biased too far in the opposite direction than they originally started.<p>Also note that in 4 out of 6 departments, more men applied than women, explaining why more departments appear biased against men (provided my observation holds).<p>However, I can&#x27;t be sure whether this is actually the original data because it&#x27;s nowhere to be found on my pdf copy of the study (Sex bias in graduate admission) which I believe I got from here: <a href="https:&#x2F;&#x2F;homepage.stat.uiowa.edu&#x2F;~mbognar&#x2F;1030&#x2F;Bickel-Berkeley.pdf" rel="nofollow">https:&#x2F;&#x2F;homepage.stat.uiowa.edu&#x2F;~mbognar&#x2F;1030&#x2F;Bickel-Berkele...</a>. If anyone knows where this data actually comes from, I&#x27;d welcome a pointer.