Multiple comparisons with the average for normal distributions

In this article we propose some multiple comparison procedures with the average. Simultaneous confidence intervals are considered for normal distributions with common known or unknown variances. These procedures can be used to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, stock market, medical research, and auto models. The percentage points for singular multivariate normal and multivariate t distributions are investigated. Furthermore, the case of normal distributions under heteroscedasticity is also developed. An example is given.