第四十四篇 Know What Statistical Tools You Have and How to Use Them

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Know　What Statistical Tools You Have and How to Use Them
知道你掌握了什么统计工具并怎样使用吗？
by Christine M. Anderson-Cook
克丽斯蒂恩.M.亚当森-库克 著


Recently, there has been exciting discussion about statistical engineering and its potential to redefine the role of statisticians and increase our influence in business and industry through expanded participation in decision making for high-impact problems.
近来一直在激烈进行着关于以下内容的讨论：统计工程及其重新定义统计专家的角色的潜力，以及通过在有重大影响力问题的决断中扩大参与度来，在商业与工业领域增加我们的影响度的潜力。

For those of you new to the discussion, statistical thinking is the strategic-level thinking that helps us appreciate that statistics is relevant for decision making in the presence of uncertainty, and statistical methods are the operational tools that help us to solve problems.
对于那些你新近讨论的内容而言，统计思想是一种战略层级的思维方法，这种思维方法帮助我们对在不确定性存在的情况下做出决断时统计资料的恰当性做出正确评价。而且那些统计方法是帮助我们解决问题的可操作工具。

Think of statistical engineering as the tactical glue that joins these concepts to form a cohesive plan of action that includes identifying important problems in which understanding and characterizing the patterns we see are important, and then developing a sequence of steps to move from problem definition through a complete solution using a combination of relevant tools.
统计工程的思维作为战略粘合剂将那些概念联合起来形成一个有凝聚力的行动计划，计划包括：确定重要问题——在这些问题中，我们看到的理解和描述模式是重要的；然后运用合适的工具组合开发出一系列步骤以完成从问题识别到彻底解决的进展。

To make a positive impact using statistical engineering, we must be able to use our set of tools in a systematic, sequential way to define, understand, improve and maintain our products and processes. But just like with any home improvement problem, before you can start fixing things, you need to make sure you have the right tools and have them organized in your toolbox so you can find and use them at the right moment.
为利用统计工程来产生积极的影响，我们必须能够运用我们的整套工具，以系统的、次序的方式来定义、理解、改进和维护我们的产品与过程。然而正如任何家装问题一样，在开始固定部件之前，你需要确保自己有合适的工具，并且已在工具箱中安排好以便你可以适时找到工具来使用。

Toolbox inventory
It should be apparent that we all have a slightly different collection of tools in our toolboxes, based on our work experiences and formal training. It is helpful, too, to have friendly, generous neighbors with bigger sets of tools who are willing to share.
工具箱清单
很明显，我们所有的人在自己的工具箱中存放工具的方式都有所不同，这基于我们的工作经验和日常训练。当然也都希望能有一个拥有多套工具并且愿意共享的友好而且大方的邻居。

But a big part of successful do-it-yourself projects is knowing what tool you need and when you need it, and being able to get a new, specialized tool when needed. It’s fine to say, "I need a thingamajig," as long as you can describe what you need it to do.
但成功的自己动手（DIY）项目的一大部分是知道你需要什么工具以及什么时候需要，并且能够在需要的时候得到新的、专门的工具。只要你能够描述你需要用来做什么，说出“我需要某某东西”是件好事情。

Is your statistical toolbox well organized and complete? Do you have a mental organizational structure to help you determine if you need a hammer, a screwdriver or a pair of pliers to tackle a particular problem?
你的统计工具箱完全准备好了吗？你有一个内心的组织结构来帮助你决定是否需要一个锤子还是一把螺丝刀或者是一把钳子来处理异常问题？

When I first started work as a statistical consultant many years ago, I discovered the most difficult problems did not begin with questions from a scientist or engineer, such as, "How do I do a two-sample t-test for this set of data?" Rather, questions were more along the lines of "I’m having problems understanding why I am getting this unintuitive result."
多年以前当我作为统计顾问开始工作时，我发现最困难的问题并不是以科学家或者工程师的诸如“对这组数据我如何做样本t-检验？”之类的疑问开始。更确切地说，疑问大多沿于“我理解不了为什么我能得到这个用直觉得不到的结果？”之类。

Often, I was overwhelmed by how to get started, and it did not feel like I would be able to solve the problem at hand with a single tool. For me, the big breakthrough came when a wise colleague encouraged me to take stock of my statistics toolbox.
我经常被如何开始弄得不知所措，而且并不是看起来的那样，我凭掌握的一个简单工具就应该能解决问题。对于我来说，当一位聪明的同事鼓励我对我的统计工具箱做出判断时，一个大的突破点出现了。

One summer as a graduate student, I literally did that: I started by identifying categories of problems, types of data and types of answers that might be sought, and then I proceeded to populate a multi-dimensional table with methods I had learned in various undergraduate and graduate classes.
作研究生的一个夏天，我毫不夸张地做到了：开始确定问题的种类、数据的类型以及可能找到的答案的类型，然后继续用我在本科课程和研究生课程中学到的方法填充一张多维表。

To help make this more concrete, here are a few of the dimensions of my organizational structure. One set of categories focuses on the category of the problem to be solved:
为有助于使其更具体，列出了我的组织结构中的几张表。一种分类形式集中于需要解决问题的种类。

1. Data collection: design of experiments and sampling.

1、数据收集：试验设计和取样

1. Exploratory methods: checking for patterns in data, basic summaries or characteristics.

2、探索方法：在数据、基本概貌或者特性方面检查样本

1. Formal analysis: hypothesis testing, estimating characteristics or model parameters.

3、规范分析：假设检验，评价特征或者模型参数

A separate dimension considers the type of data involved: continuous, ordinal or nominal. Yet another dimension considers if there is a natural response or responses you wish to describe as a function of one or more explanatory variables, or if all the data are on equal footing with no natural response.
一张独立的表所考虑的数据类型包括：连续型的，顺序型的或者额定的。而另外一个表所考虑的是是否有一个自然响应或者你希望描述成一个或更多解析变量的函数的响应，又或者是否所有数据与无任何自然响应均在平等基础上。

Of course, for the response (y)/explanatory variable (x) case, you can have all combinations of continuous, ordinal or nominal for each category of x and y. Figure 1 shows a sample of the crossed categories.
当然，以响应（y）/解析变量（x）为例，对于每一个x和y的类型来说，你可以有连续型的、顺序型的或者额定的所有组合。图1表示了一个交叉分类的例子。

http://www.asq.org/img/qp/105348-figure1.gif


Within each cell, there are also other subcategories to consider, including parametric or nonparametric methods, as well as graphical, numerical or both. It should be quite obvious there would be many potential labels or dimensions on which to structure your framework. I hazard a guess that if it were easy to peer into the minds of other statisticians, you would see the organization looks quite different for different people.
在每个单元格内，也有别的子类需要考虑，包括有参数的或者无参数的方法，同样地包括图形化的、数字化的或者两者均有方法。这应是很明显的：或许有很多潜在的标签或者表，基于这些可以构成你的框架。我大胆假设：如果很容易与其他统计专家的思维同步的话，你会明白对不同的人来说组织看起来非常不一样。

What is important, however, is there is a structure that feels natural and rich enough to you for the statistical tools you have.
然而，重要的是对于你所拥有的统计工具而言有一个你感觉自然而丰富的结构。

Dealing with gaps
处理差距

After I completed this exercise, I found some interesting by products also emerged. Not only did I have several sheets of paper that reminded me of all the things I knew, but I also had created a framework to help me organize all future additions to my toolbox.
在完成这些练习后，我发现了也出现了一些有趣的事情。我不仅有几页纸能使我想起我所知道的所有事情，而且创作了一个框架以帮我组织所有将来我工具箱增加的东西

It also helped highlight the blank cells in my array, which sometimes led me to think of a scenario in which this configuration of choices might occur and how I might tackle finding a solution. Perhaps most importantly, when I was confronted with a new problem, I had a starting point for sorting out how to begin finding a solution.
有时我想起一个场景：这种配置的选择可能发生，我又怎样才能找到解决问题的办法，这帮助点亮我的数组中的空白单元格。或许最重要的，当面临一个新问题的时候，我有一个起点以整理出如何开始求解决方案。

As a professor at Virginia Tech in Blacksburg, I taught a statistical consulting class several times. One of the assignments for students was to first identify categories (which they found surprisingly difficult), and then populate their own array with what they knew. After a first pass, we had a group discussion, and the students were encouraged to add more methods they knew but forgot to include.
作为位于Blacksburg的弗吉尼亚工学院的一位教授，我讲授过几次统计咨询课程。其中一个学生任务就是先确定类别（他们发现令人惊讶的困难），然后用他们所知道的填充自己的阵列。经过第一阶段后，我们举行一次小组讨论，并且鼓励学生加入他们知道的却忘记了包括进取的更多方法。

I must confess: As much as I thought this was a good exercise for them to work through, I was quite interested to see how differently the results would turn out. A couple of things became clear to me:
我必须承认：虽然我认为对他们来说这是一个锻炼工作的机会，但还是很有兴趣看看最后的到的结果有何不同。

1. There are many sensible frameworks on which to organize our tools.

1、有许多可以用来组织我们的工具的合适框架。

1. The students often did not remember a substantial number of the tools they had, which might limit their options when trying to solve real-world problems.

2、学生经常想不起来他们所拥有的相当数量的工具，这样在试着解决实际问题的时候就限制了他们的观点。

1. The completeness and accuracy of the assignment was extremely highly correlated with how well the students did in their studies.

3、任务的完整性和精确性是与学生在研究中如何做好高度相关。

1. There is a bit of a chicken-and-egg problem with the third point: Were the students capable because they had a good framework, or did a good framework help them do well Regardless of which is true, or if there is some truth to both, we can all improve our problem solving and statistical engineering skills if we have a good handle on what tools are in our statistical toolbox.

4、紧随第三点，有一些先有鸡还是先有蛋的问题：学生有能力是因为他们有一个好的框架，还是一个好的框架帮助他们做的更好？无论哪一个答案正确，又或者是两个都有一点正确，如果对我们的统计工具箱里有些什么工具有一个很好的把握，我们所有人都能改善我们解决问题的能力和统计工程技能。