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Related Concept Videos

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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to test a claim regarding the population standard deviation. For example, a 95% confidence interval covers 95% of the area under the curve, and the remaining 5% is equally distributed on either side of the curve. To achieve such confidence intervals, one must determine the critical values. The critical values are simply the values separating the...
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Sample size determination for studies designed to estimate covariate-dependent reference quantile curves.

Christine Jennen-Steinmetz1

  • 1Department of Biostatistics, Central Institute of Mental Health, Medical Faculty Mannheim / Heidelberg University, Mannheim, Germany.

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|December 6, 2013
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Summary

Estimating covariate-dependent quantile curves requires careful consideration of accuracy and sample size. This study proposes a method to determine necessary sample sizes for precise quantile curve estimation, finding large sample sizes are often needed, particularly with quantile regression.

Keywords:
percentilesprecisionquantile curvequantile regressionreference limitssample size

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Accurate estimation of covariate-dependent quantile curves is crucial in various scientific fields.
  • Existing methods may lack sufficient precision or clear sample size guidelines for practical application.

Purpose of the Study:

  • To address accuracy and sample size challenges in estimating covariate-dependent quantile curves.
  • To propose a novel approach for measuring the precision of quantile estimates.
  • To establish a sample size criterion based on desired precision and confidence bounds.

Main Methods:

  • Defined precision of a pth quantile estimate by the probability of its interval.
  • Derived approximate formulae for precision and sample size.
  • Evaluated two methods: normal parametric regression and semiparametric quantile regression.

Main Results:

  • Developed a sample size criterion ensuring a minimum probability for quantile estimates within a specified range.
  • Provided approximate formulas for precision and sample size calculations.
  • Simulation study confirmed the accuracy of the derived approximations.

Conclusions:

  • Significant sample sizes are necessary for constructing accurate covariate-dependent quantile curves.
  • The quantile regression method, while flexible, often requires larger sample sizes for comparable accuracy.
  • The proposed methodology offers a framework for sample size determination in quantile curve estimation.