Simple explanation of P-value
A P-Value is a measure of how rare a particular outcome is given an assumption. For example, someone tells you they are a 90% Free Throw shooter in Basketball. You doubt their claim and request they step up to the free throw line and shoot 10 shots. They make 5 out of 10. Intuitively without any appeal to mathematics, one would realize this would be a rare outcome and doubt the claim of being a 90% free throw shooter.
The idea of P-Value just makes the notion of rare precise.
It can be shown using something called the binomial probability distribution that if a 90% free throw shooter shot 10 free throws 10,000 times, he/she would only make 5 out of 10 fifteen times!! This means the P-Value = 0.0015 or 0.15%
So smaller P-Values, constitute stronger proof against a challenged assumption. Not once did I have to mention the word sadistics, I mean statistics.
Many readers have probably heard the famous quote that reflects the contempt that many folks have for statistics:
There are three types of falsehoods: 1. Lies 2. Damned Lies 3. Statistics
Hopefully this explanation of P-Values will lessen your anxiety concerning statistics.