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Related Concept Videos

Sample Size Calculation01:19

Sample Size Calculation

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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.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
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One-Way ANOVA: Unequal Sample Sizes01:15

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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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One-Way ANOVA: Equal Sample Sizes01:15

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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
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The equilibrium constant for a reaction is calculated from the equilibrium concentrations (or pressures) of its reactants and products. If these concentrations are known, the calculation simply involves their substitution into the Kc expression.
For example, gaseous nitrogen dioxide forms dinitrogen tetroxide according to this equation:
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Calculating Standard Free Energy Changes02:49

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The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
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Calculating pH Changes in a Buffer Solution02:45

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A buffer can prevent a sudden drop or increase in the pH of a solution after the addition of a strong acid or base up to its buffering capacity; however, such addition of a strong acid or base does result in the slight pH change of the solution. The small pH change can be calculated by determining the resulting change in the concentration of buffer components, i.e., a weak acid and its conjugate base or vice versa. The concentrations obtained using these stoichiometric calculations can be used...
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Determination of Mammalian Cell Counts, Cell Size and Cell Health Using the Moxi Z Mini Automated Cell Counter
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Sample size calculations for comparing two groups of count data.

Lin Wang1, Chunpeng Fan1

  • 1a Department of Biostatistics and Programming , Sanofi US Inc , Bridgewater , NJ , USA .

Journal of Biopharmaceutical Statistics
|July 20, 2018
PubMed
Summary
This summary is machine-generated.

A new sample size formula for count data comparisons is introduced, applicable to any distribution and useful for study planning. This method of moments approach provides an upper bound for sample size calculations, ensuring robust study design.

Keywords:
Method of momentsmixture of negative binomial distributionsrecurrent events

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Area of Science:

  • Biostatistics
  • Statistical Methods

Background:

  • Determining appropriate sample size is crucial for the validity of statistical comparisons.
  • Existing sample size formulas for count data often rely on specific distributional assumptions, such as the negative binomial distribution.
  • Likelihood-based and simulation approaches can be computationally intensive or require strong assumptions.

Purpose of the Study:

  • To derive a novel sample size formula for comparing two groups of count data.
  • To develop a formula that is independent of specific distributional assumptions for count data.
  • To provide a practical tool for sample size estimation in biostatistical research, applicable even when using likelihood-based analyses.

Main Methods:

  • The method of moments was employed to derive the sample size formula.
  • The first and second moments of the count data distribution were matched.
  • The formula was validated for its applicability across various count data distributions.

Main Results:

  • A universally applicable sample size formula for count data was successfully derived.
  • The proposed formula accommodates any count data distribution, including but not limited to the negative binomial distribution.
  • The derived formula can serve as an upper bound for sample sizes calculated using likelihood-based methods.

Conclusions:

  • The developed sample size formula offers a flexible and robust approach for planning studies with count data.
  • This method enhances the reliability of sample size estimations in biostatistics, reducing reliance on restrictive distributional assumptions.
  • The formula's utility is demonstrated through an application in an asthma study design, highlighting its practical relevance.