Confidence Intervals on Nonnegative Linear Combinations of Variances

Graybill, Franklin A.; Wang, Chih–Ming

doi:10.1080/01621459.1980.10477565

Cited by 108 publications

(50 citation statements)

References 8 publications

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“…One of them involves the confidence intervals of ICC for a two-factor nested design in large samples. 26 Another alternative is the modified large-sample (MLS) approach, which was proposed 27 for confidence intervals of nonnegative linear combinations of the variance components. In this approach, the confidence limits under large-sample normal theory are modified so that they become exact for small or moderate sample sizes.…”

Section: Introductionmentioning

confidence: 99%

Confidence intervals for intraclass correlation coefficients in variance components models

Demetrashvili

Wit

Heuvel

2016

Stat Methods Med Res

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Confidence intervals for intraclass correlation coefficients in agreement studies with continuous outcomes are model-specific and no generic approach exists. This paper provides two generic approaches for intraclass correlation coefficients of the form P Q q¼12 p Þ. The first approach uses Satterthwaite's approximation and an F-distribution. The second approach uses the first and second moments of the intraclass correlation coefficient estimate in combination with a Beta distribution. Both approaches are based on the restricted maximum likelihood estimates for the variance components involved. Simulation studies are conducted to examine the coverage probabilities of the confidence intervals for agreement studies with a mix of small sample sizes. Two different three-way variance components models and balanced and unbalanced one-way random effects models are investigated. The proposed approaches are compared with other approaches developed for these specific models. The approach based on the F-distribution provides acceptable coverage probabilities, but the approach based on the Beta distribution results in accurate coverages for most settings in both balanced and unbalanced designs. A real agreement study is provided to illustrate the approaches.

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Section: Introductionmentioning

confidence: 99%

Confidence intervals for intraclass correlation coefficients in variance components models

Demetrashvili

Wit

Heuvel

2016

Stat Methods Med Res

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“…The values of k E and k C depend on the experimental design used for validation and cannot be derived exactly if the design is more complicated than a simple sampling scheme. From 3,7,11,12 it can be shown that, for the general variance-component model, k E and k C can be approximated by…”

Section: Tolerance-interval Rulesmentioning

confidence: 99%

“…This is obtained by multiplyingˆ X by the correction factor C defined by Graybill and Wang 12 , for balanced data, as…”

Section: Tolerance-interval Rulesmentioning

confidence: 99%

Pre‐study analytical method validation: comparison of four alternative approaches based on quality‐level estimation and tolerance intervals

Govaerts

Dewé

Maumy

et al. 2008

Quality & Reliability Eng

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In industry and in laboratories, it is crucial to continuously control the validity of the analytical methods used to follow the products' quality characteristics. Validity must be assessed at two levels. The 'pre-study' validation aims at demonstrating before use that the method will be able to achieve its objectives. The 'in-study' validation is intended to verify, by inserting quality control (QC) samples in routine runs, that the method remains valid over time. At these two levels, the analytical method will be claimed valid if it is possible to prove that a sufficient proportion of analytical results is expected to lie within given acceptance limits [−k,k] around the nominal value. This paper presents and compares four approaches to checking the validity of a measurement method at the pre-study level. They can be classified into two categories. In the first, a lower confidence bound for the estimated probability p of a result lying within the acceptance limits is computed and compared with a given acceptance level. Maximum likelihood and delta methods are used to estimate the quality level p and the corresponding estimator variance.

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“…Graybill and Wang [6] first obtained the above confidence interval for a linear combinations variance components. Zou and co-authors gave a different argument so as to justify the validity of the above confidence interval for any set parameters.…”

Section: Mover Confidence Intervalsmentioning

confidence: 99%

Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

Hasan¹,

Krishnamoorthy²

2017

JSTA

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The problem of estimating the ratio of coefficients of variation of two independent lognormal populations is considered. We propose two closed-form approximate confidence intervals (CIs), one is based on the method of variance estimate recovery (MOVER), and another is based on the fiducial approach. The proposed CIs are compared with another CI available in the literature. Our new confidence intervals are very satisfactory in terms of coverage properties even for small samples, and better than other CIs for small to moderate samples. The methods are illustrated using an example.

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Confidence Intervals on Nonnegative Linear Combinations of Variances

Cited by 108 publications

References 8 publications

Confidence intervals for intraclass correlation coefficients in variance components models

Confidence intervals for intraclass correlation coefficients in variance components models

Pre‐study analytical method validation: comparison of four alternative approaches based on quality‐level estimation and tolerance intervals

Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

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