Two-stage Multiple Comparison Research Articles

Sample Size Determination for Two-Stage Multiple Comparisons for Exponential Location Parameters with the Average

In this paper, the design constant is determined based on a criterion of probability of correct detection for a given deviation of k location parameters from the average being at least γ for the two-stage multiple comparisons for location parameters of exponential distributions when scale parameters are unequal. All required values for determining the design constant and then the total sample size for a two-stage procedure are listed in tables for practical use. For illustrative purposes, two examples are given to demonstrate the sample size determination for this two-stage procedure.

A note on the two-stage multiple comparison procedures with the average for exponential location parameters under heteroscedasticity

In this paper, we present new two-stage multiple comparison procedures with the average for location parameters of two-parameter exponential distributions under heteroscedasticity by modifying the existing one proposed by Wu and Wu. Not like one-stage procedures, two-stage multiple comparison procedures are design oriented. A simulation comparison study is done for the new two stage procedures, the old two stage procedures in Wu and Wu and the existing one-stage procedures. The results show that the proposed procedures have shorter confidence length with coverage probabilities closer to the nominal ones than the old two-stage one. At last, an example of four drugs for the treatment for leukemia is studied for illustrative aims.

A new two-stage multiple comparison procedure for comparing several exponential populations with a control under heteroscedasticity

A new two-stage multiple comparison procedure, which maintains power at a pre-specified level, is proposed to construct simultaneous confidence intervals (SCIs) for the distances of location parameters of k treatments from the location of control under heteroscedasticity of scale parameters by taking k+1 members of two parameter exponential distributions. Simulation study reveals that the proposed two-stage procedure performs better than the existing two-stage procedure of Lam and Ng (1990) in terms of coverage probability and average volume of the simultaneous confidence intervals. No additional tables are required to implement the proposed procedure. Implementation of proposed procedure is demonstrated by taking real life data.

One stage multiple comparisons with the average for exponential location parameters under heteroscedasticity

Two-stage multiple comparisons with the average for location parameters of two-parameter exponential distributions under heteroscedasticity are proposed by Wu and Wu [Wu, S.F., Wu, C.C., 2005. Two stage multiple comparisons with the average for exponential location parameters under heteroscedasticity. Journal of Statistical Planning and Inference 134, 392–408]. When the additional sample for the second stage may not be available, one-stage procedures including one-sided and two-sided confidence intervals are proposed in this paper. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and to identify better-than-the-average, worse-than-the-average and not-much-different-from-the-average products in agriculture, the stock market, pharmaceutical industries. Tables of upper limits of critical values are obtained using the technique given in Lam [Lam, K., 1987. Subset selection of normal populations under heteroscedasticity. In: Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection. Sydney, Australia. August 1987. Lam, K., 1988. An improved two-stage selection procedure. Communications in Statistics—Simulation and Computation 17 (3), 995–1006]. An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. The relationship between the one-stage and the two-stage procedures is also elaborated in this paper.

One-stage multiple comparisons with the control for exponential location parameters under heteroscedasticity

Two-stage multiple comparisons with the control for location parameters of two-parameter exponential distributions under heteroscedasticity are proposed by Lam and Ng [Lam, K., Ng, C.K., 1990. Two-stage procedures for comparing several exponential populations with a control when the scale parameters are unknown and unequal. Sequential Analysis 9 (2) 151–164]. When the additional sample for the second stage may not be available, one-stage procedures including one-sided and two-sided confidence intervals are proposed in this paper. These intervals can be used to identify a subset which includes all no-worse-than-the-control treatments in an experimental design and to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, medical research, and automodels. Tables of upper limits of critical values are obtained using the technique given in Lam [Lam, K., 1987. Subset selection of normal populations under heteroscedasticity. In: Proceedings of the Second International Advanced Seminar/Workshop on Inference Procedures Associated with Statistical Ranking and Selection, Sydney, Australia, August 1987; Lam, K., 1988. An improved two-stage selection procedure. Communications in Statistics — Simulation and Computation 17 (3) 995–1006]. An example of comparing four drugs in the treatment of leukemia is given to demonstrate the proposed procedures. The relationship between the one-stage and the two-stage procedure is also discussed in this paper.

Two-stage multiple comparisons with the average for normal distributions under heteroscedasticity

In this article we propose a two-stage procedure for multiple comparisons with the average for normal distributions under heteroscedasity. One-sided and two-sided confidence intervals are proposed. These intervals can be used to identify a subset which includes all no-worse-than-the-average treatments in an experimental design and 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. An upper limit of critical values are obatined using Bonferroni inequality. But the approximate values are shown to be too conservative compared with the simulation critical values in Table 7. Therefore, simulation critical values should be used in our multiple comparison procedures. Statistical tables and software programs are provided for use in practice.

Two-Stage Multiple Comparisons with the Best for Computer Simulation

We consider the problem of comparing a small number of stochastic systems via computer simulation when the basis for comparison is the expected value of some system performance measure. To solve this problem we develop two-stage sampling procedures that provide confidence intervals for the difference between the expected performance of each system and the best of the others. These confidence intervals are valid under mild conditions, and the procedures allow the experimenter to specify the desired precision in advance. Special cases of our results include standard indifference-zone selection procedures. The paper includes guidelines for experiment design and an illustrative example.

A Robust Two-Stage Multiple Comparison Procedure with Application to a Random Drug Screen

SUMMARY A high-volume random drug screen is used to detect drugs that are effective in reducing atherogenic low density lipoproteins. A two-stage analysis, consisting of an overall F-test along with a multiple comparison procedure to detect differences between treatments and a placebo, seemed appropriate. Due to observations with heavy right tails and more than occasional outliers in the left tail, this analysis based on least squares estimates had insufficient power. As a solution to this problem we present a similar analysis based on the class of robust R-estimates. In general, it was more powerful than the least squares analysis. Furthermore, by a prudent choice of rank score functions, this robust analysis can take advantage of the underlying skewed error structure. Its validity and power are verified in a Monte Carlo study. Atherosclerosis is a leading cause of death in the United States. The search continues for an effective agent to treat this condition. Rather than searching for drugs that reduce serum total cholesterol, the random drug screen discussed in this paper attempts to find agents effective in reducing atherogenic low density lipoproteins. The screen uses the normocholesterolemic male SEA (Susceptible to Experimental Atherosclerosis) Japanese quail as the animal model; see Chapman, Stafford, and Day (1976) for further details on the use of this animal for such studies. Prior to drug testing the birds were randomly allocated to 10-15 groups of 10 quails each. They were housed individually in ten-cage units and fed a commercial diet for 5 days. The drugs to be tested were dissolved or dispersed in ethanol and mixed with the diet. Control groups received a diet mixed with ethanol alone. After 1 week on the diets each bird was bled from the right jugular vein and serum samples were obtained. The response of interest was the amount of beta cholesterol obtained from these birds. From a statistical point of view each application of the screen results in a one-way design. A two-stage procedure seems to be the appropriate analysis. This would include an overall

On Two-Stage Multiple Comparisons with a Control: Handling Unequal Sample Sizes in the First Stage

SYNOPTIC ABSTRACTLet and μ1, …, μJ and σ1, …, σJ be the means and standard deviations of J independent normal random variables. Dudewicz and Dalal (1983) derived a two-stage procedure for obtaining simultaneous confidence intervals for μj-μJ (j=1, …, J-1), with overall probability of coverage exactly 1-α and length of all confidence intervals 2L (where L is a constant chosen in advance by the experimenter). A particularly important feature of their procedure is that the probability coverage is exactly 1-α even when the variances are unequal. Dudewicz and Dalal provided tables of a constant needed to implement their procedure, but their tables are limited to the special case where there are equal first-stage sample sizes. This note proposes a simple yet accurate method for handling unequal first-stage sample sizes.

On Two-Stage Multiple Comparison Procedures When there are Unequal Sample Sizes in the First Stage

A problem of considerable practical importance when applying multiple comparison procedures is that unequal variances can seriously affect power and the probability of a Type I error. A related problem is getting a precise indication of how many observations are required so that the length of the confidence intervals will be reasonably short. Two-stage procedures have been proposed that give an exact solution to these problems, the first stage being a pilot study for the purpose of obtaining sample estimates of the variances. However, the critical values of these procedures are available only when there are equal sample sizes in the first stage. This paper suggests a method of evaluating the experimentwise Type I error probability when the first stage has unequal sample sizes.

On Two-Stage Multiple Comparison Procedures When There Are Unequal Sample Sizes in the First Stage

On Two-Stage Multiple Comparison Procedures When There Are Unequal Sample Sizes in the First Stage

"Type I and Type II errors in simultaneous and two-stage multiple comparison procedures": Correction to Keselman, Games, and Rogan.

"Type I and Type II errors in simultaneous and two-stage multiple comparison procedures": Correction to Keselman, Games, and Rogan.

Type I and Type II errors in simultaneous and two-stage multiple comparison procedures.

Type I and Type II errors in simultaneous and two-stage multiple comparison procedures.

Type I and Type II errors in simultaneous and two-stage multiple comparison procedures.

Responds to T. A. Ryan (see record 1980-29331-001) by emphasizing and demonstrating the usual inferential trade-off between protecting Type I and protecting Type II errors for multiple comparison procedures. Simultaneous test procedures are preferred, but it is felt that there are types of investiga