How Appropriate Are Popular Sample Size Formulas?

Kupper, Lawrence L.; Hafner, Kerry B.

doi:10.2307/2684511

Cited by 72 publications

(14 citation statements)

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“…According to the numerical assessment, it often requires a larger sample size to meet the necessary precision of tolerance probability than the control of a designated expected half width. The pattern of results between the two precision principles is similar to those reported in Kupper and Hafner (1989) and Shieh and Jan (2012). In the process of sample size calculations, the obtained precision levels associated with the reported sample sizes (N EW1 , N EW2 , N EW3 , N EW4 ) and (N TP1 , N TP2 , N TP3 , N TP4 ) should be less than or greater than the target value of interval half bound and tolerance probability, respectively.…”

Section: Jan and Shiehsupporting

confidence: 60%

“…For most of the situations, prior knowledge or theory alone enables us to determine the appropriate magnitude of interval half width because its scale is the same as that of the linear contrast. On the other hand, the suitable values of tolerance levels are within the range of 0.70 to 0.99 as demonstrated in Kupper and Hafner (1989).…”

Section: Resultsmentioning

confidence: 93%

“…For example, see Kelley, Maxwell, and Rausch (2003); Kupper and Hefner (1989); and Liu (2009) for related discussion in the context of estimating the mean difference between two normal populations with homoscedasticity. Consequently, this investigation updates and expands the current work in sample size determinations of confidence interval estimation for mean comparisons in ANOVA, especially the existing results in Kupper and Hafner (1989), Pan and Kupper (1999), Shieh and Jan (2012), and Wang and Kupper (1997). In addition, the computations of these procedures involve iterative algorithms not currently available in statistical packages, and hence, the computer codes are presented to facilitate the recommended approaches for computing the necessary sample sizes of linear contrast confidence intervals with designated precision in planning research designs.…”

mentioning

confidence: 92%

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Determining Sample Sizes for Precise Contrast Analysis With Heterogeneous Variances

Jan

Shieh

2014

Journal of Educational and Behavioral Statistics

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The analysis of variance (ANOVA) is one of the most frequently used statistical analyses in practical applications. Accordingly, the single and multiple comparison procedures are frequently applied to assess the differences among mean effects. However, the underlying assumption of homogeneous variances may not always be tenable. This study examines the sample size procedures for precise interval estimation of linear contrasts within the context of one-way heteroscedastic ANOVA models. The desired precision of both individual and simultaneous confidence intervals is evaluated with respect to the control of expected half width and to the tolerance probability of interval half width within a designated value. Supplementary computer programs are developed to aid the usefulness and implementation of the proposed techniques. The suggested sample size procedures improve upon the existing approaches and extend the methodology development in the statistical literature. Individual and multiple comparisons of mean effects in homoscedastic analysis of variance (ANOVA) models have received considerable attention in the literature. Accordingly, Bird (2004); Bretz, Hothorn, and Westfall (2010); Cumming (2012); Hahn and Meeker (1991); Hochberg and Tamhane (1987); Hsu (1996);Smithson (2003);Westfall, Tobias, Rom, Wolfinger, and Hochberg (2011); and the references therein provide an excellent and thorough account of the associated properties and explications for constructing confidence intervals in ANOVA and related models. Although the homogeneity of variance formulation provides a convenient and useful setup, it is not unusual for the homoscedasticity assumption to be violated in actual applications. Specifically, Fenstad (1983), Grissom (2000), and Wilcox (1987) emphasized that there are theoretical reasons to expect and empirical results to document the existence of heteroscedasticity is more common than most researchers realize. Therefore, it is prudent to

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Section: Jan and Shiehsupporting

confidence: 60%

Section: Resultsmentioning

confidence: 93%

mentioning

confidence: 92%

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Determining Sample Sizes for Precise Contrast Analysis With Heterogeneous Variances

Jan

Shieh

2014

Journal of Educational and Behavioral Statistics

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“…The formula assumes that the frequency distribution for the random errors inherent in the process is normal. However, Kupper & Hafner (1989) showed that since this widely used formula is based on a large-sample approximation, it gives sample sizes that are too small; an effect which becomes noticeably worse as the estimated value of n becomes smaller (Fig. 1).…”

Section: How Many Tests?mentioning

confidence: 99%

A statistical study of aggregate testing data with respect to engineering judgement

Howarth

French

1998

EGSP

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Aspects of product-testing and measurement uncertainty are addressed with the intention of providing guidelines to enable engineering judgements to be made which are based on valid scientific criteria. Suggestions are made to enable improved estimates of: (1) the critical range when defining measurement uncertainty; (2) the number of tests required to ensure, with a stated probability, that there is a 95% probability that the estimated mean lies within a stated absolute amount of the underlying population mean; (3) confidence intervals for a single determination; (4) confidence intervals on observed abundance in point-or grain-counts, including an exact upper bound on the proportion of a constituent which could be present (e.g. opal or chert as a contaminant) when no occurrences have been observed; (5) confidence interval on the proportion of sub-standard product present in a source of bulk material, on the basis of routine testing of a continuously delivered product. J-charts for the mean and range are also introduced as an aid to quality assurance. These have excellent performance compared to the better-known Shewhart and cusum charts and are well-suited to manual implementation at a 'shop-floor' level.HOWARTH, R. J. & FRENCH, W. J. 1998. A statistical study of aggregate testing data with respect to engineering judgement.

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“…This formula (1) is one of the most commonly used, although it might underestimate n (Kupper and Hafner 19). However, nowadays the number of replicates can be easily calculated by using any of many statistical packages that are able to estimate the required sample size under different experimental designs, taking into account the effect size, the variance, the degrees of freedom, and other factors (see also the Power analysis described below).…”

Section: Experimental Designmentioning

confidence: 99%

The use of statistical tools in field testing of putative effects of genetically modified plants on nontarget organisms

Semenov

Elsas

Glandorf

et al. 2013

Ecology and Evolution

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To fulfill existing guidelines, applicants that aim to place their genetically modified (GM) insect-resistant crop plants on the market are required to provide data from field experiments that address the potential impacts of the GM plants on nontarget organisms (NTO's). Such data may be based on varied experimental designs. The recent EFSA guidance document for environmental risk assessment (2010) does not provide clear and structured suggestions that address the statistics of field trials on effects on NTO's. This review examines existing practices in GM plant field testing such as the way of randomization, replication, and pseudoreplication. Emphasis is placed on the importance of design features used for the field trials in which effects on NTO's are assessed. The importance of statistical power and the positive and negative aspects of various statistical models are discussed. Equivalence and difference testing are compared, and the importance of checking the distribution of experimental data is stressed to decide on the selection of the proper statistical model. While for continuous data (e.g., pH and temperature) classical statistical approachesfor example, analysis of variance (ANOVA) -are appropriate, for discontinuous data (counts) only generalized linear models (GLM) are shown to be efficient. There is no golden rule as to which statistical test is the most appropriate for any experimental situation. In particular, in experiments in which block designs are used and covariates play a role GLMs should be used. Generic advice is offered that will help in both the setting up of field testing and the interpretation and data analysis of the data obtained in this testing. The combination of decision trees and a checklist for field trials, which are provided, will help in the interpretation of the statistical analyses of field trials and to assess whether such analyses were correctly applied.

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How Appropriate Are Popular Sample Size Formulas?

Cited by 72 publications

References 0 publications

Determining Sample Sizes for Precise Contrast Analysis With Heterogeneous Variances

Determining Sample Sizes for Precise Contrast Analysis With Heterogeneous Variances

A statistical study of aggregate testing data with respect to engineering judgement

The use of statistical tools in field testing of putative effects of genetically modified plants on nontarget organisms

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