A sensitive test will have fewer type II errors, and a specific test will have fewer type I errors.

A type I error is the likelihood of rejecting a null hypothesis when in fact the null hypothesis is true.

A type II error is the likelihood of rejecting an alternative hypothesis when in fact the alternative hypothesis is true.

http://en.wikipedia.org/wiki/Sensitivity_and_specificity

http://en.wikipedia.org/wiki/Type_I_and_type_II_errors

http://www.intuitor.com/statistics/T1T2Errors.html – nice description in terms of convicting an innocent person (type I error) and letting a guilty person go free (type II error)