Sample Size Formulas for Normal Theory T Tests

Guenther, William C.

doi:10.2307/2683297

Cited by 35 publications

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“…Note that since k ( ,N) is in part a function of N, k ( ,N) will be updated for each iteration of the sample size procedure, as each iteration is based on a different sample size. This method of planning sample size is consistent with other sample size planning methods so that the expected width is sufficiently narrow (e.g., Guenther, 1981;Hahn & Meeker, 1991;Kelley & Rausch, 2006;Kupper & Hafner, 1989).…”

Section: Estimation and Confidence Interval Formation Formentioning

confidence: 49%

“…9 The method of determining the modified sample size is consistent in theory with other methods of sample size planning in order to attach a probabilistic statement to the confidence interval width being sufficiently narrow (e.g., Guenther, 1981;Hahn & val will be sufficiently narrow (e.g., 99% certain compared with 80% certain) also requires a larger sample size, because increasing the probabilistic component implies that it will be more difficult to achieve the goal satisfactorily. Similarly, as the confidence interval coverage increases (i.e., a decrease in ), for a desired confidence interval width the sample size also increases.…”

Section: Ensuring a Confidence Interval No Wider Than Desired With A mentioning

confidence: 80%

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Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach

Kelley

2007

Behavior Research Methods

113

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The coefficient of variation is a dimensionless number that quantifies the degree of variability relative to the mean. The population coefficient of variation is defined as ,where is the population standard deviation and μ is the population mean. The typical sample estimate of is given aswhere s is the sample standard deviation, the square root of the unbiased estimate of the variance, and M is the sample mean. Equations 1 and 2 are sometimes multiplied by 100 so that the ratio of the standard deviation to the mean is expressed in terms of a percentage. The coefficient of variation has long been a widely used descriptive and inferential quantity in various areas of the biological and medical sciences. Compared with several other effect size measures, the coefficient of variation has not historically been widely used in behavioral, educational, or social sciences. However, some research questions within the behavioral, educational, and social sciences lend themselves to being addressed with the coefficient of variation. At least in part due to the current emphasis in many parts of the literature on the interaction of biological and psychological systems as explanatory factors of behavior (e.g., Frith & Frith, 2001;Kosslyn et al., 2002;Salmon & Hall, 1997; etc.), use of the coefficient of variation will likely continue to increase. 1 An example of where the coefficient of variation is often used is for assays, which are procedures that measure certain designated properties of biological components. The results of repeated trials of such assays are many times reported in terms of the coefficient of variation, because the standard deviations of assays generally increase (or decrease) proportional to the mean increase (or decrease; Reed, Lynn, & Meade, 2002). Coefficients of variation are generally based on a single measurement from different individuals (i.e., an interindividual coefficient of variation). However, intraindividual coefficients of variation, where repeated measures for the same individual are obtained, are also possible. One place where an intraindividual coefficient of variation is of interest is before and after a treatment to evaluate the effectiveness of the treatment (Reed et al., 2002). In a psychiatry setting, Volkow et al. (2002) used the coefficient of variation to compare patterns of homogeneity/heterogeneity in brain metabolism for Alzheimer's disease patients with those in a control group without Alzheimer's. It was shown that the coefficient of variation was larger across the entire cortex, but that there were smaller coefficients of variation in temporal and parietal cortices for Alzheimer's disease patients. As more researchers move to a biology-psychology model of behavior, assays will likely become more prevalent in the behavioral sciences.Of course, the coefficient of variation need not be restricted to biological systems. In a classic experimental psychology setting, Babkoff, Kelly, and Naitoh (2001) 755Copyright 2007 Psychonomic Society, Inc.Sample size planning for the coeffic...

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Section: Estimation and Confidence Interval Formation Formentioning

confidence: 49%

Section: Ensuring a Confidence Interval No Wider Than Desired With A mentioning

confidence: 80%

Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach

Kelley

2007

Behavior Research Methods

113

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“…Literatürde uygun örneklem genişliğinin belirlenmesi ile ilgili yapılmış birçok çalışma bulunmaktadır. [1][2][3][4][5][6] Araştırmacılar, güç analizi yöntemlerini kullanarak örneklem genişliğini belirlerken karmaşık matematiksel ifadeler nedeni ile oldukça zorlanmaktadırlar. Bu nedenle, özellikle son yıllarda, örneklem genişliğinin belirlenmesine yönelik çeşitli hazır yazılımlar (nQuery Advisor, PASS vb.)…”

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Practical Approaches For Determination Of Sample Size In Paired Case-Control Studies

Demirel¹,

Oruç²,

Gürler³

2016

Turkiye Klinikleri J Biostat

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Neslihan DEMİREL ve ark.EŞLEŞTİRİLMİŞ DURUM-KONTROL ÇALIŞMALARINDA ÖRNEKLEM GENİŞLİĞİNİN BELİRLENMESİ...Turkiye Klinikleri J Biostat 2016;8(1) 36 ORİJİNAL ARAŞTIRMA ORIGINAL RESEARCH linik araştırmalar genellikle yeni bir ilaç veya tıbbi aletin canlılar-da kullanımının etkin ve güvenilir olup olmadığını göstermek için yapılır. Bu nedenle tıp ve veteriner hekimlik alanlarında fazla sayıda deneysel çalışma yapılmaktadır. Maliyetli ve zaman alıcı olan bu ça-lışmalarda sonuçların güvenilir olabilmesi için istatistik yöntemler bakı-mından iyi tasarlanmaları gerekmektedir. Bir bilimsel çalışmanın her aşa-ması dikkatli ve özenli bir şekilde belirlenmelidir. Anahtar Kelimeler: McNemar testi; testin gücü; istatistiksel veri analizi; bağımlı iki örneklem ABSTRACT Objective: Cross-over design or paired case control studies that are using in clinical studies are the methods of design of experiments which requires dependent samples. The problem of sample size determination is generally difficult step of planning the statistical design. The aim of this study is to provide the researchers a practical approach for determining the sample size in paired control studies. Material and Methods: In this study, determination of sample size is mentioned in detail identification for the most common method Mc Nemar Test in paired (dependent) samples. Sample sizes are calculated according to different significance and power level combination. Results: Sample sizes were calculated for McNemar test which is used paired samples studies, for the combination of different power levels (1-β) and significance levels (α). The results are presented in tables. Conclusion: Appropriate sample sizes for the cross-over design or paired-control studies used in clinical studies were calculated and presented in tables. These tables are to provide the researchers a practical approach for determining the sample size in paired control studies.

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“…Excluding (1 Ϫ ␥)100% of the sampling distribution of t values that have the widest confidence limits and then using ␥ in place of in the procedure will ensure that no more than (1 Ϫ ␥)100% of the confidence intervals will be wider than desired, as confidence intervals will be wider than desired if and only if, holding everything else constant, ͉t͉ Ͼ ͉ ␥ ͉, which will occur only (1 Ϫ ␥)100% of the time because of the definition of ␥ . The noncentral nature of d, as explained below, makes the development of a sample size planning procedure more difficult than the development of analogous procedures for effects that follow central distributions (e.g., Guenther, 1981;Hahn & Meeker, 1991;Kupper & Hafner, 1989).…”

mentioning

confidence: 99%

“…The idea of determining sample size so that E[w] ϭ is analogous to other methods of planning sample size when a narrow confidence interval is desired (e.g., Guenther, 1981;Hahn & Meeker, 1991;Kupper & Hafner, 1989 Because the noncentral t distribution is used for confidence intervals for ␦, sample size is solved for computationally. The initial value of the sample size used in the algorithm is based on the standard normal distribution, which guarantees that the initial sample size will not be too large.…”

mentioning

confidence: 99%

Sample size planning for the standardized mean difference: Accuracy in parameter estimation via narrow confidence intervals.

Kelley¹,

Rausch²

2006

Psychological Methods

105

147

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Methods for planning sample size (SS) for the standardized mean difference so that a narrow confidence interval (CI) can be obtained via the accuracy in parameter estimation (AIPE) approach are developed. One method plans SS so that the expected width of the CI is sufficiently narrow. A modification adjusts the SS so that the obtained CI is no wider than desired with some specified degree of certainty (e.g., 99% certain the 95% CI will be no wider than ). The rationale of the AIPE approach to SS planning is given, as is a discussion of the analytic approach to CI formation for the population standardized mean difference. Tables with values of Keywords: sample size planning, standardized mean difference, accuracy in parameter estimation, power analysis, precision analysis One of the simplest measures of effect is the difference between two independent group means. It is this difference that is evaluated with the two-group t test to infer whether the population difference between two group means differs from some specified null value, which is generally set to zero. However, in the behavioral, educational, and social sciences, units of measurement are often arbitrary, different researchers might measure the same phenomenon with different scalings of the same instrument, or different instruments altogether might be used. Because of the lack of standard measurement scales and procedures for most behavioral, educational, and social phenomena, the ability to compare measures of effect across different situations has led many researchers to use standardized measures of effect. Measures of effect, or effect sizes, that are standardized yield scale-free numbers that are not wedded to a specific instrument or scaling metric. Given the measurement issues in behavioral, educational, and social research, such standardized effect sizes provide what is arguably the optimal way to estimate the size of an effect, along with its corresponding confidence interval, for a more communal knowledge base to be developed and so that the results from different studies can be compared more readily.A commonly used and many times intuitively appealing effect size is the standardized mean difference.

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Sample Size Formulas for Normal Theory T Tests

Cited by 35 publications

References 0 publications

Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach

Sample size planning for the coefficient of variation from the accuracy in parameter estimation approach

Practical Approaches For Determination Of Sample Size In Paired Case-Control Studies

Sample size planning for the standardized mean difference: Accuracy in parameter estimation via narrow confidence intervals.

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