R语言统计分析入门指南

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"《A Introductory statistics with R2.》是由Peter Dalgaard编写的，旨在介绍使用R语言进行统计分析的入门书籍。R语言是一种广泛应用的开源统计计算和图形软件，可在多种操作系统上运行，包括Windows、Unix/Linux平台以及Macintosh。本书不仅关注R语言的基础概念，还通过实例展示了统计分析和图形制作的基本方法，尽管R本身是一个完整的编程语言，但书中主要聚焦于初级概念和实践应用。" 在《A Introductory statistics with R2.》中，读者将学习到： 1. **R语言基础**：R提供了一个友好的环境，用于执行统计计算和创建图形。它拥有丰富的内置函数和包，支持各种统计方法，包括描述性统计、假设检验、回归分析等。 2. **统计分析**：书中涵盖了基本的统计概念，如概率分布（正态分布、二项分布等）、抽样分布、置信区间和假设检验（t检验、卡方检验、F检验等）。此外，还会讨论更复杂的统计方法，如线性模型、广义线性模型和非参数统计。 3. **数据处理**：R提供了强大的数据管理工具，包括数据导入、清洗、转换和排序功能。读者将学会如何有效地操作和预处理数据，为后续分析做好准备。 4. **图形制作**：R的绘图功能强大，可以生成高质量的统计图形，如散点图、直方图、箱线图、生存曲线等。读者将学习如何定制图形的细节，以更好地呈现数据和结果。 5. **编程概念**：虽然不是重点，但书中也会涉及R的编程方面，包括控制流（条件语句、循环）、函数定义和自定义操作。 6. **案例研究**：通过实际的统计问题和案例，读者将看到如何应用所学知识解决实际问题，这有助于巩固理论知识并提高实际操作技能。 7. **参考文献和索引**：书后附有详细的参考文献列表和索引，方便读者进一步探索相关主题和深入研究。这本书适合对统计学有一定了解，并希望通过R语言进行实际分析的初学者。通过阅读和实践，读者不仅可以掌握R语言的基本用法，还能建立起统计分析的坚实基础。同时，由于R是开源的，读者还可以利用其庞大的社区和资源，不断扩展自己的知识和技能。

1.1 First steps 5

we discuss alternative techniques for reading data. For now, we stick to a

single method.

You can do calculations with vectors just like ordinary numbers, as long

as they are of the same length. Suppose that we also have the heights that

correspond to the weights above. The body mass index (BMI) is deﬁned

for each person as the weight in kg divided by the square of the height in

meters. This could be calculated as follows:

> height <- c(1.75, 1.80, 1.65, 1.90, 1.74, 1.91)

> bmi <- weight/height^2

> bmi

[1] 19.59184 22.22222 20.93664 24.93075 31.37799 19.73630

Notice that the operation is carried out elementwise, that is, the ﬁrst value

of bmi is 65

/1.75

and so forth and that the ^ operator is used for raising

a value to a power. (On some keyboards, ^ is a “dead key” and you will

have to press the spacebar afterwards to make it show.)

It is in fact possible to perform arithmetic operations on vectors of differ-

ent length. We already used that when we calculated the height^2 part

above since 2 has length 1. In such cases, the shorter vector is recycled.

This is mostly used with vectors of length 1 (scalars) but sometimes also

in other cases where a repeating pattern is desired. A warning is issued if

the longer vector is not a multiple of the shorter in length.

These conventions for vectorized calculations make it very easy to specify

typical statistical calculations. Consider, for instance, the calculation of the

mean and standard deviation of the weight variable.

First calculate the mean,

∑

/n:

> sum(weight)

[1] 446

> sum(weight)/length(weight)

[1] 74.33333

Then save the mean in a variable xbar and proceed with the calculation

of SD



(

∑

−

)

)/(n − 1). We do this in steps to see the individual

components. The deviations from the mean are

> xbar <- sum(weight)/length(weight)

> weight - xbar

[1] -14.333333 -2.333333 -17.333333 15.666667 20.666667

[6] -2.333333

Notice how xbar, which has length 1, is recycled and subtracted from

each element of weight. The squared deviations will be

> (weight - xbar)^2

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