Sample size and the width of the confidence interval for mean difference

Liu, Xiaofeng Steven

doi:10.1348/000711008x276774

Cited by 10 publications

(13 citation statements)

References 14 publications

(29 reference statements)

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“…However, considerable attention has focused on the criterion of tolerance probability of interval half-width within a given value. For example, see Beal (1989), Kelley, Maxwell, and Rausch (2003), Kupper and Hafner (1989), and Liu (2009) for related discussion in the context of estimating the mean difference between two normal populations with homoscedasticity. The empirical illustration in Kupper and Hafner shows that it typically requires a larger sample size to meet the necessary assurance of tolerance probability than the control of a designated expected half-width.…”

Section: Introductionmentioning

confidence: 99%

Optimal sample sizes for precise interval estimation of Welch’s procedure under various allocation and cost considerations

Shieh

Jan²

2011

Behav Res

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Welch's (Biometrika 29: 350-362, 1938) procedure has emerged as a robust alternative to the Student's t test for comparing the means of two normal populations with unknown and possibly unequal variances. To facilitate the advocated statistical practice of confidence intervals and further improve the potential applicability of Welch's procedure, in the present article, we consider exact approaches to optimize sample size determinations for precise interval estimation of the difference between two means under various allocation and cost considerations. The desired precision of a confidence interval is assessed with respect to the control of expected half-width, and to the assurance probability of interval half-width within a designated value. Furthermore, the design schemes in terms of participant allocation and cost constraints include (a) giving the ratio of group sizes, (b) specifying one sample size, (c) attaining maximum precision performance for a fixed cost, and (d) meeting a specified precision level for the least cost. The proposed methods provide useful alternatives to the conventional sample size procedures. Also, the developed programs expand the degree of generality for the existing statistical software packages and can be accessed at brm.psychonomic-journals.org/ content/ supplemental.

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Section: Introductionmentioning

confidence: 99%

Optimal sample sizes for precise interval estimation of Welch’s procedure under various allocation and cost considerations

Shieh

Jan²

2011

Behav Res

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“…However, in practice unequal n j values can happen, for example, if the researcher uses smaller group sizes for more expensive treatments due to a limited budget. The sample size planning methods discussed previously can be extended to situations like this, and the researcher needs to plan the sample size for each group and use the full formula s ANCOVA ( J j=1 c 2 j /n j ) + D to calculate sˆ instead of the simplified one s ANCOVA √ (C /n) + D. One way to achieve this is to define n j as m j ·ñ, where m j is some measure of the cost per participant andñ is a baseline sample size being constant across groups (Hsu, 1994; see also Cochran, 1983;Liu, 2009). The sample size planning process requires m j values as input information and returnsñ, which in turn leads to n j values.…”

Section: Discussionmentioning

confidence: 99%

“…As is indicated by and , w is a random variable based on the random variable s ANCOVA , whereas ω is a constant based on the constant σ ANCOVA . When the sample size is not too small, s ANCOVA is smaller than σ ANCOVA about 50% of the time, making w smaller than ω about 50% of the time (e.g., Liu, 2009). In order to obtain a sufficiently narrow CI in a study with high degree of assurance (e.g., 90% of the time, 99% of the time, etc.…”

Section: Confidence Interval and Sample Size For Unstandardized Comentioning

confidence: 99%

Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals

Lai

Kelley

2011

Brit J Math & Statis

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Contrasts of means are often of interest because they describe the effect size among multiple treatments. High-quality inference of population effect sizes can be achieved through narrow confidence intervals (CIs). Given the close relation between CI width and sample size, we propose two methods to plan the sample size for an ANCOVA or ANOVA study, so that a sufficiently narrow CI for the population (standardized or unstandardized) contrast of interest will be obtained. The standard method plans the sample size so that the expected CI width is sufficiently small. Since CI width is a random variable, the expected width being sufficiently small does not guarantee that the width obtained in a particular study will be sufficiently small. An extended procedure ensures with some specified, high degree of assurance (e.g., 90% of the time) that the CI observed in a particular study will be sufficiently narrow. We also discuss the rationale and usefulness of two different ways to standardize an ANCOVA contrast, and compare three types of standardized contrast in the ANCOVA/ANOVA context. All of the methods we propose have been implemented in the freely available MBESS package in R so that they can be easily applied by researchers.

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“…While other values can be used (eg, 90% and 99% CIs), 95% CIs are most often cited in nursing literature (Cumming, 2007). The upper and lower ends of the interval are confidence limits, and it is within this interval width that the population parameter is likely to lie (Liu, 2009). In other words, if we used the same sampling method to select repeated samples, 95% of them would contain the true population parameter.…”

Section: Confidence Intervalsmentioning

confidence: 99%

Odds Ratios and Confidence Intervals

Laing

Rankin

2011

J Pediatr Oncol Nurs

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Professional registered nurses (RNs) are active participants in seeking and interpreting research evidence. To facilitate knowledge transfer for RNs at the bedside, it behooves researchers to present their findings in a format that facilitates understanding. There is also an expectation that clinicians are capable of interpreting results in a meaningful way. It is important to be able to understand and interpret research reports where statistical methods are used as part of providing the safest and best care for patients. The purpose of this article is to describe the basic concepts of odds ratios and confidence intervals used in research. These statistical measures are used frequently in quantitative research and are often the principle measure of association that is reported. The more comfortable pediatric oncology clinicians are with the interpretation of odds ratios and confidence intervals, the better equipped they will be to bring relevant research results from the "bench" to the bedside.

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Sample size and the width of the confidence interval for mean difference

Cited by 10 publications

References 14 publications

Optimal sample sizes for precise interval estimation of Welch’s procedure under various allocation and cost considerations

Optimal sample sizes for precise interval estimation of Welch’s procedure under various allocation and cost considerations

Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals

Odds Ratios and Confidence Intervals

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