We consider pairwise multiple comparison in k normal populations with unequal variances. Games and Howell (1976) proposed a single-step multiple comparison test based on two-sample test statistics of Welch (1949). We propose a closed testing procedure for pairwise multiple comparison. By computational simulations of the power, it is shown that the closed testing procedure is superior to the single-step multiple comparison test procedure of Games and Howell (1976).
In clinical investigator initiated clinical trials, we frequently encounter the situation where it is very difficult to estimate the effect size and the clinically meaningful difference between the treatment and control groups. In this paper we explore various two-phase, three-stage adaptive designs which can be applied to this situation. The first phase determines whether the trial should proceed or not. If the decision is to proceed, then the sample size is re-estimated. The second phase consists of two stages, but the sample size is not re-estimated. We introduce hybrid and alpha-split designs, adding to two existing adaptive designs: Bauer-Köhne design and Lehmacher-Wassmer design. Main findings are: 1) the differences in the overall powers and the average sample number (ASN)s among these designs are small, except for the design which includes O’Brien-Fleming boundaries and the alpha-split design, 2) the two-phase, three-stage design suffers a relative loss of power by 15% but the ASN is less than 50%, as compared to the single stage design under the optimal condition, 3) two-phase, three-stage design compares with the three-stage group sequential design. We conclude that the design can be a candidate when there is no useful information on the effect size.
Few studies have investigated the content of introductory statistics classes for medical school students in Japan. Yet, to assure the quality of university statistics courses and develop a standard curriculum for them, it is necessary to assess the current condition of statistics education. Therefore, we collected data on the type of course (i.e., course title and targeted year for the students), field of specialty of the lecturer, course contents, and which textbooks were pre-specified for the lecture by analyzing the syllabi of statistics courses published on university websites. Next, the result of the survey is summarized. Of the 80 universities surveyed, 45 universities provided the online sylabi for the introductory statistics course. We identified 26 different course titles for statistics classes. Thirty courses (73.3%) were intended for first-year students. Eightteen courses (54.5%) provided two credits. The most common field of specialty for statistics lecturers was mathematics (43.2%). Further, we found that the course contents included various subjects related to mathematics. A total of 35 textbooks were specified. Finally, the conclusion is that mathematical concepts seem to be taught more often than statistical practice in introductory statistics classes. Further, there were large variations in each item of analysis except the target year.