Testing the mean of an asymmetric population: Johnson's modified t test revisited

Confidence intervals for the mean of an asymmetric distribution can be based on Student's t statistic or on Johnson's modified t statistic; Johnson's statistic has two variants, based on a linear and a quadratic approximation respectively. The quadratic approximation is complicated and is first investigated geometrically, which results in new insight. Next Monte Carlo experiments yield estimates of the coverage and power of several variations on Johnson's test. These experiments show that the quadratic approximation is superior.