Two-sample two-stage and purely sequential methodologies for tests of hypotheses with applications: comparing normal means when the two variances are unknown and unequal. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Mukhopadhyay, Nitis; Zhuang, Yan
• Is Part Of: Sequential analysis. Volume 38:Issue 1(2019)
• Page Start: 69
• Page End: 114
• Publication Date: 2019-01-02
• Subjects: Compare two means -- hypothesis tests -- normal populations -- purely sequential sampling -- two-stage sampling -- type-I error probability -- type-II error probability; 62A01 -- 62D05 -- 62F03 -- 62F05 -- 62L12 -- 62L10 -- 62L05 -- 62P10; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2019.1574445
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: In this paper, we develop appropriate sampling methodologies for testing hypotheses regarding the difference of mean values from two independent (or dependent) normal populations when their variances are unknown and unequal. We design two-stage and purely sequential testing methodologies of hypotheses for comparing the unknown means by determining the appropriate sample sizes while controlling both type-I and type-II error probabilities at or below preassigned levels α, β respectively. Such methodologies are constructed under both unequal and equal sample size designs. We prove that both two-stage and purely sequential testing strategies enjoy a number of practically appealing properties. Extensive sets of computer simulations and real data analyses empirically validate our theoretical findings.