Sample sizes for constructing confidence intervals and testing hypotheses

1989 ◽  
Vol 8 (7) ◽  
pp. 803-811 ◽  
Author(s):  
David R. Bristol
Keyword(s):  
Confidence Intervals ◽  
Sample Sizes ◽  
Testing Hypotheses

scholarly journals On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Marianne Jonker ◽  
Aad Van der Vaart
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Statistical Models ◽  
Likelihood Ratio Statistic ◽  
External Source ◽  
Nuisance Parameters ◽  
Testing Hypotheses

AbstractIn practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low. In this article, we derive the asymptotic distribution of the likelihood ratio statistic if the nuisance parameters are estimated based on a dataset that is independent of the data used for estimating the parameter of interest. This distribution can be used for correctly testing hypotheses and constructing confidence intervals. Four theoretical and practical examples are given as illustration.

scholarly journals Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

2016 ◽  
Vol 27 (5) ◽  
pp. 1559-1574 ◽  
Author(s):  
Andrew Carkeet ◽  
Yee Teng Goh
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Interval Methods ◽  
Tolerance Interval ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Approximate Methods ◽  
Exact Confidence Intervals ◽  
Tolerance Factors

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes <40 (1999 approximation) and <76 (1986 approximation). For inner confidence limits the approximations are poorer, being permissive for sample sizes of <490 (1986 approximation) and all practical sample sizes (1999 approximation). Exact confidence intervals for 95% limits of agreements, based on two-sided tolerance factors, can be calculated easily based on tables and should be used in preference to the approximate methods, especially for small sample sizes.

scholarly journals Los tamaños de las muestras en encuestas de las ciencias sociales y su repercusión en la generación del conocimiento

2017 ◽  
Vol 11 (22) ◽  
Author(s):  
Juan Rositas Martínez
Keyword(s):  
Factor Analysis ◽  
Sample Size ◽  
Confidence Intervals ◽  
Structural Equation ◽  
Size Factor ◽  
Sample Sizes ◽  
Cronbach’S Alpha ◽  
Cronbach's Alpha ◽  
Alpha Effect ◽  
The Impact

Keywords: confidence intervals, Cronbach's alpha, effect size, factor analysis, hypothesis testing, sample size, structural equation modelingAbstract. The purpose of this paper is to contribute to fulfilling the objectives of social sciences research such as proper estimation, explanation, prediction and control of levels of social reality variables and their interrelationships, especially when dealing with quantitative variables. It was shown that the sample size or the number of observations to be collected and analyzed is transcendental for the adequacy of the method of statistical inference selected and for the impact degree achieved in its results, especially for complying with reports guidelines issued by the American Psychological Association. Methods and formulations were investigated to determine the sample sizes that contribute to have good levels of estimation when establishing confidence intervals, with reasonable wide and relevant and significative magnitudes of the effects. Practical rules suggested by several researchers when determining samples sizes were tested and as a result it was integrated a guide for determining sample sizes for dichotomous, continuous, discrete and Likert variables, correlation and regression methods, factor analysis, Cronbach's alpha, and structural equation models. It is recommended that the reader builds scenarios with this guide and be aware of the implications and relevance in scientific research and decision making of the sample sizes in trying to meet the aforementioned objectives.Palabras clave: análisis factorial, intervalo de confianza, alpha de Cronbach, modelación mediante ecuaciones estructurales, pruebas de hipótesis, tamaño de muestra, tamaño del efectoResumen. El propósito del presente documento es contribuir al cumplimiento de los objetivos de la investigación en las ciencias sociales de estimar, explicar, predecir y controlar niveles de variables de la realidad social y sus interrelaciones, en investigaciones de tipo cuantitativo. Se demostró que el tamaño de la muestra o la cantidad de observaciones que hay que recolectar y analizar es trascendente tanto en la pertinencia del método de inferencia estadístico que se utilice como en el grado de impacto que se logre en sus resultados, sobre todo de cara a cumplir con lineamientos emitidos por la Asociación Americana de Psicología que es la que da la pauta en la mayoría de las publicaciones del área social. Se investigaron métodos y formulaciones para determinar los tamaños de muestra que contribuyan a tener buenos niveles de estimación al momento de establecer los intervalos de confianza, con aperturas razonables y con magnitudes de los efectos que sean de impacto y se pusieron a prueba reglas prácticas sugeridas por varios autores lográndose integrar una guía tanto para variables dicotómicas, continuas, discretas, tipo Likert y para interrelaciones en ellas, ya se trate de análisis factorial, alpha de Cronbach, regresiones o ecuaciones estructurales. Se recomienda que el lector crear escenarios con esta guía y se sensibilice y se convenza de las implicaciones y de trascendencia tanto en la investigación científica como en la toma de decisiones de los tamaños de muestra al tratar de cumplir con los objetivos de la que hemos mencionado.

Bootstrap-based Budget Allocation for Nested Simulation

2021 ◽  
Author(s):  
Kun Zhang ◽  
Guangwu Liu ◽  
Shiyu Wang
Keyword(s):  
Confidence Intervals ◽  
Financial Risk ◽  
Budget Allocation ◽  
Risk Measurement ◽  
Allocation Rule ◽  
Sample Sizes ◽  
Bootstrap Sampling ◽  
Asymptotically Optimal ◽  
Optimal Sample ◽  
Asymptotic Validity

Nested simulation (also referred to as two-level simulation) finds a variety of applications such as financial risk measurement, and a central issue of nested simulation is how to allocate a finite amount of simulation budget to achieve the highest accuracy. In “Bootstrap-based Budget Allocation for Nested Simulation”, Zhang, Liu, and Wang propose a bootstrap-based rule for simulation budget allocation for nested simulation. By utilizing the asymptotically optimal inner- and outer-level sample sizes that are typically unknown, the proposed method employs bootstrap sampling on a small amount of initial samples to estimate the unknown optimal sample sizes, thus providing a reasonably good allocation rule for the main simulation. An allocation rule to ensure the asymptotic validity of confidence intervals is also given.

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