统计代写|生物统计分析代写Biological statistic analysis代考|BIOL6610

Doug I. Jones

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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统计代写|生物统计分析代写Biological statistic analysis代考|Portable Power

The portable power procedure exploits the fact that for the common significance level $\alpha=5 \%$ and a commonly desired power of $1-\beta=80 \%$, the noncentrality parameter $\lambda$ changes comparatively little, allowing us to use a crude approximation for our calculations (Wheeler 1974). Such a procedure is very helpful in the early stages of planning an experiment, when all that is needed are reasonably accurate approximations for sample sizes to gauge the practical implications of an experiment design.
The portable power procedure uses the quantity
$$\phi^2=\lambda / k=n \cdot f^2 .$$
This quantity is reasonably well approximated by $\phi^2=5$ if we expect a few (less than 10 . say) denominator degrees of freedom and by $\phi^2=3$ if we expect many such degrees of freedom. It becomes smaller with an increasing number of treatment groups, but this dependency is often negligible in practice. A reasonable strategy is to calculate the sample size $n=\phi^2 / f^2$ assuming $\phi^2=3$. If the resulting $n$ is small, we should repeat the calculation with $\phi^2=5$ and use the resulting larger sample size.

We illustrate the procedure by revisiting two previous examples. Recall that for $k=4$ and a minimal difference of $\delta_0=1$, we found an effect size of $f^2=0.083$. The exact power analysis for $\alpha=5 \%$ and $1-\beta=80 \%$ indicated a required sample size of 34 . Assuming that the required sample size is sufficiently large, we approximate this analysis using $\phi^2=3$, which yields a sample size of $n=\phi^2 / f^2=3 / 0.083 \approx 36$ and overestimates the exact value by about $7 \%$.

Using again $\alpha=5 \%$ and $1-\beta=80 \%$, a sample size of $n=20$ mice in each of the four treatment groups showed a minimal detectable effect size of $f^2=0.14$ using the exact calculation. Using the approximation $\phi^2=3$, the portable power calculation yields $f^2=\phi^2 / n=0.15$, an error of about $4 \%$.

The portable power approximations are helpful for getting an idea if a necessary minimal effect size is within reach given our resources, and for finding a rough estimate of the minimal effect detectable given a specific experiment size. The approximation error is typically less than $35 \%$ and often considerably lower. Given that the variance estimate is often much less precise, this magnitude of error should be acceptable for a crude calculation in most circumstances. Once a suitable design and margin to determine the final sample size.

统计代写|生物统计分析代写Biological statistic analysis代考|Hasse Diagrams and Linear Model Specification

The analysis of variance has an intimate connection with classical linear regression and both methods are based on describing the observed data by a linear mathematical model (cf. Sect. 4.7). The analysis of more complex designs becomes relatively straightforward when this connection is exploited, and most statistical software will internally run a linear regression procedure for computing an ANOVA. While this relieves the practitioner from much tedious algebra, it still means that the appropriate linear model for an experimental design has to be correctly specified for the software.
The specification has two parts: first, the experimental design has to be translated into the linear model, such that the statistical inferences fully sapture the logical structure of our experiment. And second, the linear model has to be translated into a model specification in the software. We can solve both problems by Hasse diagrams that visualize the logical structure of an experiment, and from which both a linear model formula and a symbolic representation of the model can be derived with relative ease. We already saw some simple examples of these diagrams in Figs. 2.4, $2.7$ and 2.8. We now work out the connection between design, diagram, and model more systematically. Some of the following discussions might seem overly complicated for the relatively simple designs discussed so far, but are necessary for more complex designs in the following chapters.

生物统计分析代考

统计代写|生物统计分析代写生物统计分析代考|便携式电源

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$$\phi^2=\lambda / k=n \cdot f^2 .$$

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MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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