A Simple Conservative and Robust Solution of the Behrens-fisher Problem

Notation. we conform to the convention that random variables shall be denoted by capital letters, whilst constants and observed values of random variables be denoted by lowercase letters. If X is a random variable with a continuous and strictly increasing (cumulative) distribution function over its range, then the unique upper γ point ofX will be denoted byXγ , i.e. Pr{X ≥ Xγ} = γ. The sole exception is that a chi-squared random variable with ν degree of freedom will be denoted by χν , and the upper α point of χ 2 ν by χ 2 ν;α. The symbol ∼ will denote “is distributed as”. The letter Z will denote a standardised normal random variable.