&gt; p values &lt;0.05 indicate that the results are not due to just chance<p>This is not how p values are used. See Gelman:<p>&gt; The p-value does not tell you if the result was due to chance. It tells you whether the results are consistent with being due to chance. That is not the same thing at all.<p><a href="http:&#x2F;&#x2F;andrewgelman.com&#x2F;2013&#x2F;03&#x2F;12&#x2F;misunderstanding-the-p-value&#x2F;" rel="nofollow">http:&#x2F;&#x2F;andrewgelman.com&#x2F;2013&#x2F;03&#x2F;12&#x2F;misunderstanding-the-p-va...</a>