P value for Normality test very small despite normal histogram
<p>I've looked over the normality tests in scipy stats for both <a href="http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.mstats.normaltest.html" rel="nofollow noreferrer">scipy.stats.mstats.normaltest</a> as well as <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html" rel="nofollow noreferrer">scipy.stats.shapiro</a> and it looks like they both assume the null hypothesis is that the data they're given is normal.</p>

<p>Ie, a p value less than .05 would indicate that they're not normal.  </p>

<p>I'm doing a regression with LassoCV in SKLearn, and in order to give myself better results I log transformed the answers, which gives a histogram that looks like this:</p>

<p><a href="https://i.stack.imgur.com/poo2E.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/poo2E.png" alt="Histogram of data"></a></p>

<p>Looks normal to me.  </p>

<p>However, when I run the data through either of the two tests mentioned above I get very small p values that would indicate the data is not normal, and in a big way.</p>

<p>This is what I get when I use scipy.stats.shapiro</p>

<pre><code>scipy.stats.shapiro(y)
Out[69]: (0.9919402003288269, 3.8889791653673456e-07)
</code></pre>

<p>And I get this when I run scipy.stats.mstats.normaltest:</p>

<pre><code>scipy.stats.mstats.normaltest(y)
NormaltestResult(statistic=25.755128535282189, pvalue=2.5547293546709236e-06)
</code></pre>

<p>It seems implausible to me that my data would test out as being so far from normality with the histogram it has.</p>

<p>Is there something causing this discrepancy, or am I not interpreting the results correctly?</p>