Every number on a research screen is an estimate built from a finite sample, and every estimate carries an error bar around it. The t-statistic is the ratio of the estimate to that error bar.
t = (mean - 0) / (sd / sqrt(n))
The denominator is the standard error: the sample standard deviation divided by the square root of the number of observations. A t of 2.0 says the estimate sits two standard errors above zero. A t of 0.4 says the effect is smaller than the noise surrounding it, no matter how attractive the headline number looks.
Illustrative arithmetic. Suppose a momentum sort over the Nifty 500 produces a mean monthly long-short spread of 0.62% with a monthly standard deviation of 4.1%, measured across 180 months:
t = 0.62 / (4.1 / sqrt(180)) = 2.03
Run the identical test on 36 months instead of 180 and the t falls to 0.91 on exactly the same average return. Nothing about the strategy changed. You simply have less evidence.
How to read the number
| Absolute t | Reading |
|---|---|
| Under 1.0 | Indistinguishable from zero |
| 1.0 to 2.0 | Suggestive, not evidence |
| Around 2.0 | Clears the conventional bar for a single test you specified in advance |
| 2.0 to 3.0 | Reasonable for one test, thin if you searched to find it |
| Above 3.0 | Survives a moderate penalty for having searched |
What the number does not tell you
The 2.0 bar is a convention. It comes from the roughly 5% two-sided tail of a normal distribution, a line someone drew because it was a round number, not a property of markets. There is nothing that changes at 1.99.
The n in the formula has to be independent observations. If you sample 12-month forward returns monthly, each observation shares eleven months of data with its neighbour, and sqrt(n) overstates your evidence by a wide margin. The same happens when many stocks respond to one macro shock on the same day. The honest denominator is closer to the number of non-overlapping periods than to the number of rows.
The largest problem is search. A t of 2.4 on the first idea you tested means something. The same 2.4 on the best of 200 scans means close to nothing, because the expected largest t from pure noise across 200 tries is already near 3.0. Read any t-statistic alongside the count of things you tested before you found it.