<p><a href=“fabrizio:”>quote</a></p>
<p>So if Antonovics and Backes show that the estimated change in admissions probability for Asians relative to whites after Proposition 209 all else equal
[/quote]
</p>
<p>That wasn’t the test being performed. The UC Asian discrimination theory predicts that the Before and After effects (on admission probability, of changing a white applicant to Asian) of prop 209 should satify:</p>
<ol>
<li><p>Before < 0 (effect of being Asian was negative; regression coefficient “Asian” < 0)</p></li>
<li><p>After > Before (prop 209 made it better to be Asian; coefficient “Ban*Asian” > 0)</p></li>
<li><p>After is small in absolute magnitude compared to Before (post-209, any effects caused directly by race are minor).</p></li>
</ol>
<p>fabrizio’s postings on this mis-stated what After means in terms of regression coefficients. It is the sum (Asian + Ban<em>Asian), not Ban</em>Asian. The results are then:</p>
<pre><code> UC-B UCLA UCSD UC-D UC-I UCSB UCSC UC-R
</code></pre>
<p>Before -1% +1% +2% -5% -2% +2% -2% -1%
After +1% +4% +4% -1% -4% -3% -2% -2%</p>
<p>change +2% +3% +2% +4% -2% -1% -0% -1%</p>
<p>Only UC Davis is consistent with the standard discrimination theory that would lead to “skyrocketing Asian enrollment after proposition 209”. The signs are somewhat random: the Before and Change coefficients are half positive and half negative (and no pattern in After either, though that is the expected result).</p>
<p>Another test of whether the measured Asian coefficients represent a discrimination effect is to see if the signs of Before and Change are opposite more often than not, so that a pre-existing race effect tends to be mitigated. This does not happen at all. At 4 of 8 schools, a positive or negative Before effect becomes noticeably stronger after prop. 209 and at a fifth, the same or slightly stronger. Only at one school, UC Davis, does the magnitude of the Asian effect (ignoring the sign) become smaller. </p>
<p>
</p>
<p>Here, fabrizio spins and stretches the material into a total dismissal of the overall results of the study as “statistical noise”. The actual comments were more limited and of course were accurate.</p>
<p>The term “small statistical noise” was used for the smaller regression outputs such as the Before/After effects of +1 and -1 at Berkeley which are in reality 1 + X and -1+Y where X and Y represent effects of the choice of model, which data were available, what predictor variables were formed from the data, etc – and where |X| and |Y| can easily be larger than 1: the noise can be larger than the signal. Note also that two of the “effect of 209 ban” Asian coefficients of 1 percent, the ones for UCSB and UCR, are not statistically significant, which is further indication that individual effects of this size, especially when small, are not all that meaningful by themselves (in this regression). </p>
<p>
</p>
<p>Here fabrizio stretches and spins my more specific, limited and accurate comments into a general false “rule” that is easier to attack than the actual comments posted. In addition to the reasons above, 1 percent effects on the estimated admission probability where most of the accepted students have a large admission probability (such as 30 to 70 percent a priori), are small and, given the inaccuracy of the model, likely to be less than model mis-specification error. Effects of 4 percent for UCSD and UCI are more meaningful, but both of them appear as “race” effects after a race ban, which is further evidence that one cannot read the regression coefficients literally without more analysis.</p>
<p>
</p>
<p>And there is a similar reason why people who understand the material do more than E-Z glance at the sign and number of asterisks next to one or two coefficients, before running victory laps and posting denunciations on the Internet.</p>