The Market

A stock in your portfolio jumped 3% today. Your colleague calls it a signal — surely something happened. A new product launch, a leaked earnings report, insider activity. The move feels meaningful. Your finger hovers over the buy button.

But before you act on what looks like information, you need to ask the question that separates disciplined investors from everyone else: how often would noise alone produce a move this large?

Volatility Is the Denominator

Drag the Annual Volatility slider up to 60%. Watch the z-score collapse. That 3% move that looked significant is now well within the noise band — a daily occurrence for a volatile stock. The distribution widens, and today's move becomes unremarkable.

Now drag it back down to 10%. The curve tightens. The same 3% move is now nearly five standard deviations from zero — an event so rare that noise almost certainly didn't cause it. Same move, different context, completely different conclusion.

The Noise Band

The shaded region shows where most daily moves fall by pure chance. At 20% annual volatility, a typical day moves about 1.3% — that's the daily standard deviation, derived by dividing the annual figure by the square root of 252 trading days.

Drag the Trading Days slider to 252. Now you're asking a different question: across an entire year of trading, how many days would you expect to see a move this extreme by chance alone? Even a p-value of 0.02 means five days a year. What looked like a once-in-a-lifetime event happens every other month.

The Equation

Toggle the equation overlay above. The z-score tells you how many standard deviations today's move sits from zero. The p-value tells you how often noise alone would produce a move this extreme or more — in either direction.

Drag each slider and watch its term light up. The daily move is in the numerator — it's your observed data. The volatility is in the denominator — it's your noise floor. A large move divided by large noise is nothing. A moderate move divided by small noise is everything. Context is the denominator.

The Pattern

Five chapters, and the pattern is unmistakable. Every time you see a result that looks surprising — a positive test, a faint signal, a poll lead, an updated belief, a price spike — the question is never “is this big?” The question is always “is this big relative to the noise?”

But what about evidence that isn't independent? In the next chapter, you'll enter a courtroom where every piece of evidence is tangled with every other — and separating signal from noise becomes a matter of life and freedom.