  Student's $t$ statistic is finding applications today that were never
envisaged when it was introduced more than a century ago. Many of these
applications rely on properties, for example robustness against heavy tailed
sampling distributions, that were not explicitly considered until relatively
recently. In this paper we explore these features of the $t$ statistic in the
context of its application to very high dimensional problems, including feature
selection and ranking, highly multiple hypothesis testing, and sparse, high
dimensional signal detection. Robustness properties of the $t$-ratio are
highlighted, and it is established that those properties are preserved under
applications of the bootstrap. In particular, bootstrap methods correct for
skewness, and therefore lead to second-order accuracy, even in the extreme
tails. Indeed, it is shown that the bootstrap, and also the more popular but
less accurate $t$-distribution and normal approximations, are more effective in
the tails than towards the middle of the distribution. These properties
motivate new methods, for example bootstrap-based techniques for signal
detection, that confine attention to the significant tail of a statistic.
