The number of subjects doesn&#x27;t really matter all that much.  You can get a statistically significant result with a single subject under the right circumstances.  This doesn&#x27;t happen much in biology and the social sciences, but it happens all the time in physics.  The best example is how the precession of Mercury (one &quot;test subject&quot;) confirmed general relativity.<p>What matters is how likely it was that the result you got simply arose by chance.  This can only be measured relative to some a priori probabilistic model.  If the odds of the result having arisen by chance (the &quot;null hypothesis&quot;) is low, then you can confidently &quot;reject the null hypothesis&quot; and conclude that something else must have happened.  Of course, the statistics can&#x27;t tell you what that &quot;something else&quot; was.  That requires an explanatory theory.<p>The problem is that the probabilistic model is also kind of arbitrary.  For example, suppose you flip a coin ten times and it comes up heads every time.  That odds of that happening by chance are, naively, one in 2^10.  But that is only true if you only do the experiment once.  If you have, say, 2^8 people flipping coins, then the odds of <i>someone</i> seeing 10 heads in a row is one in four.  Parapsychology experiments and stock-trading schemes often fall into this trap.<p>This is a general problem with &quot;big data&quot;.  The more data you have, the more likely you are to see things happen by pure chance that are intuitively unlikely.