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index.tex
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pdftitle={Improving Your Statistical Inferences},
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pdfcreator={LaTeX via pandoc}}
\title{Improving Your Statistical Inferences}
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\subtitle{Chinese Translation}
\author{Daniël Lakens}
\date{}
\begin{document}
\maketitle
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\hypertarget{ux524dux8a00}{%
\chapter*{前言}\label{ux524dux8a00}}
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\markboth{前言}{前言}
翻译以及校对人员: Yiwen Zhang, Chuxian Xu, Lan Zhou, Yuanrui Zheng,
Mengmeng Lyu, Yang Xu, Yuhang Zhu, Bowen Wu, Jing Lin, Xinyu Wang,
Xinquan Lu, Jing An, Bolin Cao, Chi Zhang, Weijing Yang, Hang Yu,
Qiushan Liu, Dongyu Liu, Ye Lin, Hao Qin.
我们很高兴能够向各位读者呈现《Improving Your Statistical
Inferences》这本电子书的中文版，Daniël
Lakens教授写这本书的初衷是帮助各位研究者用于设计更好的实验、改进统计推断以及更透明地报告研究信息。我们翻译的初心也是希望更多的中国学者了解到这本书，了解Daniël教授的思想以及理念。
本翻译工作由中国``开放科学中文社区(COSN)''的OpenTransfer小组倾力完成。COSN是一个公益的在线草根社区(https://open-sci.cn/)，以推广基础研究领域的开放、透明和可重复的研究实践为理念。因此，特别感谢OpenTransfer翻译小组及其众多热情的小伙伴，这个项目于2022年初启动，经过了近两年的持续努力，终于在2023年完成。在这个过程中，不断有新的小伙伴加入到群体当中，积极参与翻译和校对工作。这本书的翻译工作是我们通力协作不断打磨的成果，它代表了众多译者的辛勤努力。我们希望，这本书能为您带来有益的信息，启发您思考，并扩展您的视野。
您可以将此资源引用为:
Lakens, D. (2022). Improving Your Statistical Inferences. Retrieved from
https://lakens.github.io/statistical\_inferences\_chinese/.
https://doi.org/10.5281/zenodo.6409077
The full English version is available at:
https://lakens.github.io/statistical\_inferences/. This work and
translation were made possible by VIDI Grant 452-17-013 from the
Netherlands Organisation for Scientific Research.
\begin{figure}
\includegraphics[width=1.5625in,height=\textheight]{images/me.png} \hfill{}
\end{figure}
Daniël Lakens
Eindhoven University of Technology
\begin{figure}
\includegraphics[width=1.5625in,height=\textheight]{images/cos_qr.png} \hfill{}
\end{figure}
Chinese Open Science Network, a network for Transparent, Open, \&
Reproducible Science.
开放科学中文社区，传播透明、开放和可重复的基础研究理念和实践。
\bookmarksetup{startatroot}
\hypertarget{sec-pvalue}{%
\chapter{\texorpdfstring{使用
\emph{p}值进行假设检验}{使用 p值进行假设检验}}\label{sec-pvalue}}
研究者们可以通过收集数据来回答各种研究问题。他们感兴趣的是在不同条件下所收集到的数据结果是否有所差异。对于这个问题的答案是一个
\emph{方向性检验（ordinal claim）},
因为研究者对数据结果进行两两比较时，其平均值可能有大有小也可能没有差异。例如，研究者可能对这样的假设感兴趣：``假设条件A为：学生在进行了充分的学习后进行测试，条件B为学生将花费全部精力用于学习而进行测试，相对条件B来说，条件A的学习成果可能会更优异。在收集数据并得出有测试的学生的平均成绩较高后，研究者可以提出一个有方向性的假设，即与条件B相比，条件A的学生成绩\emph{更好}。方向性假设仅能说明条件之间存在一定差异，但不能量化\textbf{效应大小}。
为了做出方向性检验，研究者通常依靠著名的\textbf{假设检验}的方法。
假设检验的一个部分包括计算\textbf{\emph{p}值}，
并检验\emph{p}值是否存在统计学上的\textbf{显著}差异。``显著''意味着某些东西是值得关注的。假设检验用于区分实证数据中的信号（值得关注的）和随机噪音。我们需要区分的是\textbf{统计学显著}以及\textbf{实际效应显著}，前者仅说明观察到的效应是信号还是噪点，而后者取决于效应的大小是否足够大，以便在现实生活中做出有价值的推断。因此，研究者们采用这种方法论的程序来决定是否做出差异性说明，或者作为一种防止验证性偏差的保障。在吉尼斯啤酒厂的内部报告中曾应用过上述统计检验方法，William
Gosset（或称``student''，他开发了\emph{t}检验）在1904年写道 (1904)：
\begin{quote}
一般来说，人们普遍会认为将实验结果的决定权全权交由研究者是相对危险的，因为他们可能带有一定偏见。因此，有人建议采用一个标量作为评判标准，这个标量是在一定数量的数据集中出现重大误差的概率。
\end{quote}
然而根据这种期望，研究者们可能开始倾向于将数据解释为对其假设的支持，即便数据并不是这样。研究者提出差异性说明时，如果假设检验方法使用得当，是可以有效控制研究者自欺欺人的。正如Benjamini（2016）
所提出的，在区分信号和噪点时，\emph{p}值是作为防止被随机因素诱导的第一道防线。有迹象表明，禁止使用\emph{p}值将会使得研究者更容易做出错误结论。针对《基础与应用社会心理学》期刊施行禁止零假设（即无效应）显著之后，人们对后续发表的研究进行了定性分析，其中Fricker（2019）等人认为，相对于使用假设检验，且采用\emph{p}
\textless{}
0.05来说，当研究者仅用描述性统计时，我们发现他们很可能会过度解释和/或夸大他们的结果。研究者提出差异性说明时，如果假设检验方法使用得当，是可以有效控制研究者自欺欺人的。
\hypertarget{ux5173ux4e8epux503cux7684ux4e00ux4e9bux8ff7ux601d}{%
\section{\texorpdfstring{关于\emph{p}值的一些迷思}{关于p值的一些迷思}}\label{ux5173ux4e8epux503cux7684ux4e00ux4e9bux8ff7ux601d}}
在我们厘清\emph{p}值是如何计算之前，更重要是需要弄清在假设检验时，它将如何帮助我们做出合理的差异性说明。\emph{p}值的定义是当零假设为真时，所得到的样本数据或更极端数据的概率。但是这个定义并未告诉我们该如何解释\emph{p}值。
对于p值的解释方式取决于个人的统计思想。从\href{https://en.wikipedia.org/wiki/Ronald_Fisher}{Ronald
Fisher}1925年发表了《研究者统计方法论》一书之后，\emph{p}值的应用开始广泛起来。在Fisherian的理论框架中，\emph{p}值被描述为一个连续测量，这个测量用于描述所得观察数据以及与零假设之间的兼容性
(Greenland et al.,
2016)。兼容性的区间在1（完全兼容）到0（完全不兼容）之间，且每个人都可以以一种统计上的``深思熟虑''来解释\emph{p}值。依据Fisher
(1956)所述，\emph{p}值并不意味着真实世界的某个概率，而是以一种合理且完备的形式，来衡量拒绝他们所期望的假设的程度。Fisher试图将他的理念标化为一种''基础推论''，但这并没有得到其他流派的广泛采纳，如决策理论、似然比检验和贝叶斯推理。事实上，Zabell
(1992)
写道：''基础推论``是Fisher的一个巨大失败''，尽管其他人表示希望它在未来会发展成一个有用的方法
(Schweder \& Hjort,
2016)。Fisherian的\emph{p}值描述了数据与单一假设的不兼容性，因此又被称为\emph{显著性检验}。显著性检验受到限制的主要原因是，研究者只指定了一个零假设（\(H_0\)），而没有指定备择假设（\(H_1\)）。
Neyman和Pearson (1933) 在William Gosset和Ronald
Fisher关于P值的见解的基础上，发展了一种叫做统计假设检验的方法。与Fisher提出的显著性检验相比，其主要区别是，在统计假设检验中，既制定了一个零假设，也规定了一个备选假设。在Neyman-Pearson的理论框架中，统计检验的目标是引导研究者在这两个假设方向上的的决策。根据统计检验的结果，当不知道假设是否为真的情况下，研究者通常暂时将零假设或备则假设为真。在心理学领域，研究者经常使用Fisherian和Neyman-Pearson二者理论框架的不完美结合版，但根据Dienes
(2008) 的说法，Neyman-Pearson的理论方法是
``你在心理学学术期刊中看到的所有数据统计的基础逻辑''。
当进行Neyman-Pearson假设检验时，所得\emph{p}值只是用于对比是否小于所选的
\(\alpha\) 水平，但它小多少并不重要。例如，如果使用0.01的 \(\alpha\)
水平，\emph{p}=0.006和\emph{p}=0.000001都会使研究者迅速做出论断，仿佛世界的真理就是备择假设所描述的。这与Fisherian的p值方法不同，Fisherian的\emph{p}值越低，研究者在心理上更加容易拒绝他们所检验的零假设。Neyman-Pearson的假设检验不认为推论的目标是量化兼容性或依据的一种连续测量。相反，正如Neyman
(1957) 所写的：
\begin{quote}
当我们对行为做出总结归纳时，应当承认每个正经研究的目的，都是在几个可选方案中为某一个方案提供依据。The
content of the
\end{quote}
简洁了当点说，人们可能会觉得在做某一行为的决策时，不应该拘泥于单一的统计测试结果，这一点经常被提出来作为对Neyman-Pearson统计推断方法的批评。然而，这种批评与Neyman所说的
``行为''的定义不径相同。诚然，实施一项新政策的决策不应基于单一的研究结果。然而，Neyman认为提出科学主张也是一种
``行为''，他曾写道（1957年，第10页），一项研究的结论阶段包括：
\begin{quote}
一种行为意愿或对某一行动的决策，也许就是对各种假设采取特定的态度。
\end{quote}
Cox (1958) 写道:
\begin{quote}
可以这么说：当进行推论时，我们就是''决定''对总体进行某种类型的陈述，因此，只要不对决定一词进行过于狭义的解释，那么研究的统计决策就包含了推论的过程。其实重点是，统计推断的主要问题在于决定哪些类型的声明是有意义的，以及它们到底意味着什么。
\end{quote}
因此，在Neyman-Pearson的方法中，\emph{p}值就是意味着需要对哪类声明进行决策的基础。在科研中，类似的声明通常是以\textbf{辅助假设}的形式支撑着大多数新兴实验，或者说，为了使实验按计划进行，一些基础假设的提出必须是准确的
(Hempel,
1966)。例如，如果设计的实验中，被试能看到颜色是很重要的，我们的基础假设就是\href{https://en.wikipedia.org/wiki/Ishihara_test}{Ishihara
test}（一种色盲测试）能够成功识别哪些被试是色盲，且这个假设为真。
\hypertarget{ux5efaux7acbux4e00ux4e2aux96f6ux6a21ux578b}{%
\section{建立一个零模型}\label{ux5efaux7acbux4e00ux4e2aux96f6ux6a21ux578b}}
假设每组10人，一共有两组，我问他们有多喜欢《指环王》（LOTR）三部曲的加长版。这意味着我们的\textbf{总样本量}是20，每组的样本量为10。第一组的被试包括了我的朋友，而第二组的被试包括了我妻子的朋友。我们的朋友对问题进行了1\textasciitilde10的评分。因此，我的朋友们那组是8.7，我妻子朋友的那组均值是7.7。我们可以通过查阅原始数据以及绘制相关图表对两组数据进行比较。
\begin{table}
\caption{两组朋友对指环王加长版的评分}
\begin{tabular}[t]{lcc}
\toprule
& Daniel的朋友 & Kyra的朋友\\
\midrule
friend\_1 & 9 & 9\\
friend\_2 & 7 & 6\\
friend\_3 & 8 & 7\\
friend\_4 & 9 & 8\\
friend\_5 & 8 & 7\\
\addlinespace
friend\_6 & 9 & 9\\
friend\_7 & 9 & 8\\
friend\_8 & 10 & 8\\
friend\_9 & 9 & 8\\
friend\_10 & 9 & 7\\
\bottomrule
\end{tabular}
\end{table}
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\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e6>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e6>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e6>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Kyra的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e6>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e6>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e6>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9c>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e5>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8f>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <8b>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <e7>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <9a>
\end{verbatim}
\begin{verbatim}
Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
conversion failure on 'Daniel的朋友' in 'mbcsToSbcs': dot substituted for <84>
\end{verbatim}