Confidence Intervals For Pairwise Comparisons Research Articles

Tests for one and two mean vectors and simultaneous confidence intervals with monotone incomplete data

In this study, we consider the problems of testing for a mean vector and testing the equality of two mean vectors with monotone missing data. We propose new test statistics similar to the simplified Hotelling’s T 2-type test statistic for one-sample and two-sample problems under general-step monotone missing data. Approximate upper percentiles of this new statistics are provided by asymptotic expansion along with transformed test statistics based on Bartlett adjustment. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors are also presented. Furthermore, we investigated the asymptotic behavior of the proposed statistics using a Monte Carlo simulation, and the approximate accuracy of the proposed approximations are provided and discussed. Finally, the numerical power for several statistics is given.

Machining performances of TiN+AlCrN coated WC and Al2O3+TiC inserts for turning of AISI 4140 steel under dry condition

In this work, the machining performances of TiN + AlCrN coated tungsten carbide (WC) and Al2O3+TiC mixed ceramic inserts for turning of AISI 4140 steel were systematically evaluated by multivariate analysis of variance (MANOVA) with varying cutting speeds in the range of 150−220 m/min. MANOVA results showed that the averages surface roughness of workpiece and flank wear width of tool were significantly affected by the cutting speed, the type of inserts and their interaction at the significant level of 0.05. Additionally, the method of Bonferoni 95 % simultaneous confidence intervals for pairwise comparisons indicated that the cutting speed of 220 m/min was suitable for turning of AISI 4140 steel with both types of inserts. Microanalysis based on electron microscopy revealed that the Al2O3+TiC inserts experienced mild abrasion via microploughing, microcutting and microchipping while TiN + AlCrN coated WC ones got severe abrasive wear due to direct cutting and three-body abrasion.

Tests for Normal Mean Vectors with Monotone Incomplete Data

SYNOPTIC ABSTRACTIn this article, we consider the distributions of the Hotelling’s T2-type test statistics for mean vectors when each dataset has a monotone missing data pattern. We give the approximate upper percentiles of the simplified Hotelling’s T2-type statistics in the case of data with k-step monotone missing data patterns. We also consider multivariate multiple comparisons for mean vectors with k-step monotone missing data. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors and comparisons with a control are obtained using Bonferroni’s approximation procedure. Finally, the accuracy and asymptotic behavior of the approximations are investigated by Monte Carlo simulation.

Tests for Equality of Mean Vectors and Simultaneous Confidence Intervals with Two-Step or Three-Step Monotone Missing Data Patterns

SYNOPTIC ABSTRACTIn this article, we consider the problem of testing the equality of two mean vectors when the data have a three-step monotone pattern of missing observations. We propose an approximate upper percentile of the Hotelling’s T2-type statistic in which each dataset has a three-step monotone missing data pattern and the population covariance matrices are equal. Further, we obtain the Hotelling’s T2-type statistics and their approximate upper percentiles in the case of data with unequal two-step monotone missing data patterns. We also consider multivariate multiple comparisons for mean vectors with three-step monotone missing data. Approximate simultaneous confidence intervals for pairwise comparisons among mean vectors and comparisons with a control are obtained using Bonferroni’s approximate upper percentiles of the T2max · p and T2max · c statistics, respectively. Finally, the accuracy of the approximations is investigated via Monte Carlo simulation.

Anesthesia Induction Using Video Glasses as a Distraction Tool for the Management of Preoperative Anxiety in Children

Distraction technology suitable for the perioperative setting is readily available, but there is little evidence to show how it compares with oral midazolam in managing anxiety. Video glasses, which enable children to view and listen to cartoons and movies, may be used through the completion of inhaled induction. We compared the efficacy of oral midazolam and behavioral distraction with video glasses in managing preoperative anxiety in children. In this prospective, randomized study, 96 children aged 4 to 9 years undergoing outpatient surgery were recruited to one of 3 intervention groups receiving midazolam, video glasses, or both. The Modified Yale Preoperative Anxiety Scale was the primary dependent measure used to assess anxiety at baseline before intervention, 20 minutes later at transport to the operating room (OR), and during mask induction. There was no significant increase in anxiety score within any group between baseline and OR transport (P = 0.21, 0.42, and 0.57 for midazolam, video glasses, and combined groups, respectively). An increase in anxiety, though not large enough to be clinically significant, was observed from baseline to induction in the midazolam and combined groups (P = 0.02 and 0.03) but not in the video glasses group (P = 0.38). Confidence intervals for pairwise comparisons in Modified Yale Preoperative Anxiety Scale changes among groups were all within a clinically significant difference of 15 units. The use of video glasses and midazolam alone or in combination maintains baseline levels of anxiety at time of transport to the OR and prevents significantly increased anxiety during induction of anesthesia in children. Video glasses are not inferior to midazolam for preoperative anxiolysis and provide a safe, noninvasive, nonpharmacologic, and pleasant alternative.

The Multivariate Tukey-Kramer Multiple Comparison Procedure Among Four Correlated Mean Vectors

SYNOPTIC ABSTRACTIn this article, conservative simultaneous confidence intervals for pairwise comparisons among mean vectors in multivariate normal distributions are considered. In order to give the simultaneous confidence intervals, we need the value of the upper 100α percentile of the T2max·p statistic. However, it is difficult to find the exact value. So, as an approximation procedure, Seo, Mano and Fujikoshi (1994) proposed the multivariate Tukey-Kramer procedure which is the multivariate version of Tukey-Kramer procedure (Tukey (1953); Kramer (1956, 1957)). Also, the multivariate version of the generalized Tukey conjecture has been affirmatively proved in the case of three correlated mean vectors by Seo, Mano and Fujikoshi (1994). In this article the affirmative proof of the multivariate generalized Tukey conjecture in the case of four mean vectors can be completed. Further, the upper bound for the conservativeness of the multivariate Tukey-Kramer procedure is also given. Finally, numerical results by Monte Carlo simulations and an example to illustrate the procedure are given.

Multiple comparisons of several homoscedastic multivariate populations

The limiting joint distribution of correlated Hotelling’s T 2 statistics associated with multiple comparisons with a control in multivariate one-way layout model is a multivariate central nonsingular chi-square distribution with one-factorial correlation matrix, which has the distribution function expressed in a closed form as an integral of a product of noncentral chi-square distribution functions with respect to a central chi-square density function. For pairwise comparisons, it is a multivariate central singular chi-square distribution whose distribution function is generally intricate. To overcome the complexity of the (exact or asymptotic) distribution theory of $$T^2_{\rm max}$$ -type statistics appeared in simultaneous confidence intervals of mean vectors, improved Bonferroni-type inequalities are applied to construct asymptotically conservative simultaneous confidence intervals for pairwise comparisons as well as comparisons with a control.

Max-min multiple comparison procedure for comparing several dose levels with a zero dose control

The comparison of increasing doses of a compound to a zero dose control is of interest in medical and toxicological studies. Assume that the mean dose effects are non-decreasing among the non-zero doses of the compound. A simple procedure that modifies Dunnett's procedure is proposed to construct simultaneous confidence intervals for pairwise comparisons of each dose group with the zero dose control by utilizing the ordering of the means. The simultaneous lower bounds and upper bounds by the new procedure are monotone, which is not the case with Dunnett's procedure. This is useful to categorize dose levels. The expected gains of the new procedure over Dunnett's procedure are studied. The procedure is shown by real data to compare well with its predecessor.

Max–min multiple comparison procedure for isotonic dose–response curves

Suppose Y ̄ 1, Y ̄ 2,…, Y ̄ k are normal random variables with ordered means μ 1⩽ μ 2⩽⋯⩽ μ k . A simple novel procedure that modifies Tukey's studentized range technique is proposed for constructing simultaneous confidence intervals for pairwise comparisons of means μ i by utilizing the ordering of μ i . The procedure makes substantial improvement over its predecessor.

Trend Tests in Epidemiology: P-Values or Confidence Intervals?

Frequently, p-values are used in reporting epidemiological trend data. Because a p-value is a confounded mixture of effect size and sample size in dichotomous data, Lang, Rothman, and Cann (1998) recommended the slope of a trend line with its standard error and a graphical presentation containing the rate ratios as a function of mid-exposure levels. However, the slope contains the assumption of a dose-response function. This article discusses a proposal based on odds ratios and the corresponding one-sided lower confidence intervals for pair-wise comparisons (‘exposure levels with zero exposure’) as well as comparisons between incremental exposure levels. The proposed method allows both decisions on the global trend, the lowest-observed-adverse-effect-level (LOAEL) and the non-observed-adverse-effect-level (NOAEL), and a simple exploratory analysis.

Intermediate Simultaneous Inference Procedures

Abstract Two well-known simultaneous inference procedures for balanced one-way layout are Tukey's T-method and Scheffe's S-method. The T-method gives short simultaneous confidence intervals for all pair-wise comparisons while paying a high price for high-order comparisons. The S-method is appropriate when one has uniform interest in all contrasts, but gives long confidence intervals for pairwise and other low-order comparisons. In this paper we propose a family of procedures intermediate between the T- and S-methods. The resulting simultaneous intervals are shorter than Scheffe's for low-order comparisons, shorter than Tukey's for high-order comparisons and shorter than both Tukey's and Scheffe's for intermediate comparisons.

Intermediate Simultaneous Inference Procedures

Abstract Two well-known simultaneous inference procedures for balanced one-way layout are Tukey's T-method and Scheffé's S-method. The T-method gives short simultaneous confidence intervals for all pair-wise comparisons while paying a high price for high-order comparisons. The S-method is appropriate when one has uniform interest in all contrasts, but gives long confidence intervals for pairwise and other low-order comparisons. In this paper we propose a family of procedures intermediate between the T- and S-methods. The resulting simultaneous intervals are shorter than Scheffé's for low-order comparisons, shorter than Tukey's for high-order comparisons and shorter than both Tukey's and Scheffé's for intermediate comparisons.