Multiple-Comparisons with a Control when Variances are Unknown and Unequal

SYNOPTIC ABSTRACT

Suppose given k independent populations π₁,…,π_k, where observations from π_i are normally distributed N(μ_i,σ²_i) (l≤i<k) with μ₁,…,μ_k unknown, and suppose that joint (simultaneous) confidence intervals on the k-1 paired differences of means with a control μ₁-μ_i. (2≤i≤k) (say) are desired. Previous work on this problem, with various assumptions about σ²₁,…,σ_2k, is reviewed (Section 1). We develop a procedure which solves the general problem with σ²₁,…,σ²_k unknown (Section 2). Tables needed to apply the procedure of Section 2 are given (Section 3). An example of application to a data set is given (Section 4). This paper is a sequel to a previous paper by the same authors which considered problems of ranking and selection with unknown and unequal variances.

Key Words and Phrases:

• multiple comparisons
• control
• heteroscedasticity
• simultaneous intervals
• comparisons with a standard
• multivariate nonexistence