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The most common misinterpretation of a P value

Many people misunderstand what a P value means. Let's assume that you compared two means and obtained a P value equal to 0.03.

Correct definitions of this P value:

There is a 3% chance of observing a difference as large as you observed even if the two population means are identical (the null hypothesis is true).

or

Random sampling from identical populations would lead to a difference smaller than you observed in 97% of experiments, and larger than you observed in 3% of experiments.

Wrong:

There is a 97% chance that the difference you observed reflects a real difference between populations, and a 3% chance that the difference is due to chance.

This latter statement is a common mistake. If you have a hard time understanding the difference between the correct and incorrect definitions, read this Bayesian perspective.