Not Even Scientists Can Easily Explain P-values
How about:  The p-value is, in a statistical hypothesis test, the probability of Type I error, that is the probability of rejecting the null hypothesis when it is true.<p>Or, suppose we have some data and want to use it to estimate the value of some number b.  It can be that if we can assume something about b, e.g., that b = 0, then we can calculate the probability distribution of our estimate of b.  This assumption about b is the <i>null hypothesis</i>.
Intuitively it is a hypothesis that there is <i>no effect</i>, that what we thought might have happened didn&#x27;t, was a <i>null</i> effect.<p>We can make two mistakes.  We can reject the null hypothesis when it is true -- this is called <i>Type I</i> error.  Or we can accept the null hypothesis when it is false -- this is called <i>Type II</i> error.<p>With our null hypothesis, we get and look at the distribution of our estimate of b and see where our actual estimate is in that distribution.  The p-value is the probability, from the distribution of our estimate, of getting an estimate as far or farther from our null hypothesis value for b as we did.  So, if the p-value is really small, say, 1%, then we can reject the null hypothesis, that is, say that it is false, and be wrong only 1% of the time.<p>E.g., if our null hypothesis is that b = 0 and our estimate of b is 10 and from the distribution of our estimate a value of our estimate being as far as 10 from b = 0 is 1%, then we reject that
b = 0 and conclude that it b is not zero and are wrong only 1% of the time.  If the probability of our estimate being greater than or equal to 10 is 1% and we reject the null hypothesis, then we conclude that b &gt; 0.<p>This is all just hypothesis testing in statistics 101.  Will also want to know about the <i>power</i> of a test, the t-test, the F ratio, the chi-squared test, and <i>resampling</i> and distribution-free tests.<p>There is more detail in<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Type_I_and_type_II_errors" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Type_I_and_type_II_errors</a>