Quantitative Analysis
p-Value: Evidence, Assumptions, and a Common Misread
When I first studied hypothesis testing, I assumed the p-value directly told me whether the null hypothesis was true. That assumption stayed with me longer than I expected, mostly because the language around p-values encourages it.
Only later did it become clear that the p-value is not answering the question people want it to answer.
Where the Confusion Starts
The p-value does not begin with the data.
It begins with an assumption.
You first agree, temporarily, that the null hypothesis is correct. Nothing unusual is happening. Any variation is random.
Only then do you look at the observed result and ask a very narrow question: does this outcome sit comfortably inside that assumption, or does it strain it?
That framing matters more than any definition.
What the Number Is Reacting To
The p-value reacts to extremeness, not truth.
If the result looks ordinary under the null, the p-value stays large.
If the result looks awkward or hard to justify under the null, the p-value shrinks.
That is all that is happening.
It is not judging which hypothesis is right. It is judging whether the null still feels reasonable after seeing the data.
Why This Feels Backward
Most people expect statistics to tell them what is true.
The p-value does not do that. It tells you how uncomfortable the data makes a particular assumption. That reversal is subtle, and it is the source of most misuse.
I used to read small p-values as “strong results.” That interpretation is tempting, but incomplete.
How Decisions Actually Get Made
The p-value never stands alone.
Before seeing the data, a threshold is chosen. That choice reflects how cautious the analyst wants to be about making a false claim. Once that line exists, the p-value simply shows whether the data crossed it.
The decision rule is mechanical. The interpretation still requires judgement.
Why Finance Still Uses It
Markets are noisy. Patterns appear briefly and vanish.
The p-value offers one narrow check: could this pattern plausibly be random if nothing unusual were going on?
It does not measure economic importance. It does not promise repeatability. It only tests compatibility with an assumption.
That limitation is exactly why it is useful.
What It Definitely Does Not Say
A p-value does not tell you the probability that a hypothesis is true.
It does not tell you whether a strategy will work tomorrow.
It does not tell you whether a result matters economically.
Every exam trap around p-values comes from forgetting one of these points.
A More Useful Mental Model
Instead of treating the p-value as a verdict, treat it as pressure.
High pressure means the assumption is struggling.
Low pressure means the assumption is still comfortable.
Nothing more. Nothing less.
Closing Reflection
The p-value is not broken. It is just narrow. It tests one assumption under one framework and reports how tense that relationship is. Once I stopped asking it to answer questions it was never designed to answer, the concept became far easier to work with. For CFA and FRM preparation, that shift in mindset matters far more than memorising formal wording.
