T-Statistic

A t-statistic is a number that expresses how far an estimate lies from a hypothesized value, measured in units of the estimate's standard error. For a sample mean it is $t = (\bar{x} - \mu_0) / (s / \sqrt{n})$, where $\bar{x}$ is the sample mean, $\mu_0$ the hypothesized mean, $s$ the sample standard deviation and $n$ the number of observations. Under the null hypothesis the statistic follows Student's t-distribution, from which a p-value is obtained. As a rule of thumb, an absolute value above about 2 is significant at the 5 percent level in a large sample.

In finance, t-statistics are reported for average returns, regression coefficients and estimates of alpha. For a strategy tested against a zero mean return, the t-statistic is approximately the annual Sharpe ratio multiplied by the square root of the number of years: a Sharpe ratio of 0.5 over 16 years gives $0.5 \times 4 = 2.0$. When many strategies have been tried, a higher threshold is needed.