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Victoria Cox - Translating Statistics to Make Decisions: A Guide for the Non-Statistician

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Victoria Cox Translating Statistics to Make Decisions: A Guide for the Non-Statistician
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Translating Statistics to Make Decisions: A Guide for the Non-Statistician: summary, description and annotation

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Examine and solve the common misconceptions and fallacies that non-statisticians bring to their interpretation of statistical results. Explore the many pitfalls that non-statisticiansand also statisticians who present statistical reports to non-statisticiansmust avoid if statistical results are to be correctly used for evidence-based business decision making.

Victoria Cox, senior statistician at the United Kingdoms Defence Science and Technology Laboratory (Dstl), distills the lessons of her long experience presenting the actionable results of complex statistical studies to users of widely varying statistical sophistication across many disciplines: from scientists, engineers, analysts, and information technologists to executives, military personnel, project managers, and officials across UK government departments, industry, academia, and international partners.

The author shows how faulty statistical reasoning often undermines the utility of statistical results even among those with advanced technical training. Translating Statistics teaches statistically naive readers enough about statistical questions, methods, models, assumptions, and statements that they will be able to extract the practical message from statistical reports and better constrain what conclusions cannot be made from the results. To non-statisticians with some statistical training, this book offers brush-ups, reminders, and tips for the proper use of statistics and solutions to common errors. To fellow statisticians, the author demonstrates how to present statistical output to non-statisticians to ensure that the statistical results are correctly understood and properly applied to real-world tasks and decisions. The book avoids algebra and proofs, but it does supply code written in R for those readers who are motivated to work out examples.

Pointing along the way to instructive examples of statistics gone awry, Translating Statistics walks readers through the typical course of a statistical study, progressing from the experimental design stage through the data collection process, exploratory data analysis, descriptive statistics, uncertainty, hypothesis testing, statistical modelling and multivariate methods, to graphs suitable for final presentation. The steady focus throughout the book is on how to turn the mathematical artefacts and specialist jargon that are second nature to statisticians into plain English for corporate customers and stakeholders. The final chapter neatly summarizes the books lessons and insights for accurately communicating statistical reports to the non-statisticians who commission and act on them.

What Youll Learn

  • Recognize and avoid common errors and misconceptions that cause statistical studies to be misinterpreted and misused by non-statisticians in organizational settings

  • Gain a practical understanding of the methods, processes, capabilities, and caveats of statistical studies to improve the application of statistical data to business decisions

  • See how to code statistical solutions in R

Who This Book Is For

Non-statisticiansincluding both those with and without an introductory statistics course under their beltswho consume statistical reports in organizational settings, and statisticians who seek guidance for reporting statistical studies to non-statisticians in ways that will be accurately understood and will inform sound business and technical decisions

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Victoria Cox 2017
Victoria Cox Translating Statistics to Make Decisions 10.1007/978-1-4842-2256-0_1
1. Design of Experiments
What Do I Need to Do to Get the Data?
Victoria Cox 1
(1)
Dstl, Salisbury, UK
To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of .
R. A. Fisher
As Sir Ronald Fisher so eloquently put it, if an experiment isnt designed well then any conclusions made from the resulting data may not be useable or may have to be reported with too many accompanying caveats.
The point of an experimental design is to systematically investigate the problem space to a required minimized risk level, basically so you get the most out of your relevant collected data. However the main thing to note here is that it doesnt take long to design a good experiment, you just need to think about in the right order.
Figure shows the suggested process to follow when thinking about designing any experiment with the following sections delving into more detail for each part of the process.
Figure 1-1 Design of experiments thought process Straight away you can see - photo 1
Figure 1-1.
Design of experiments thought process
Straight away you can see that experimental design is more than just a question of how many do I need to do? That is a common misconception. With that in mind, lets go through the steps in the process.
Forming the Study Question
The first item that needs to be done is to actually define the question . Generally the customer will give you a task such as how good are these new detectors? Then the initial stage of the process is to establish what they really want to know and why.
You need to gain as much (sensible) information as possible so that the experiment doesnt go down the wrong route and the resulting data will be able to adequately answer the customers question. Knowing the key questions to ask can facilitate the discussion and help the customer understand why this information is important. It also ensures that you are both on the same page about what is required, and how the project will progress.
Forming Hypotheses
The reason for delving into the exact study question is due to the fact that it helps form the hypothesis to be tested in the analysis, an in depth description can be found in Chapter . Briefly, you have a null hypothesis, which is your no action case and your alternative hypothesis, which is your take action case. Therefore with a customer question of is the new method better than our own, the null hypothesis would be there is no difference between the current and new methods and the alternative would be that the new method is better than the current with the latter requiring things to be changed to use the new method, hence action case.
Hypotheses also can be either one-sided or two-sided. This just means that for a one-sided hypothesis you are interested in your sample being either larger or smaller than a value or another sample but not both. Two-sided means you are interested in a general difference between samples or between the sample and a threshold value regardless of direction.
This information about sidedness is important as it has an effect not only on the analysis but also on the power and sample size calculations as the risk calculated for each is split differently, more in Chapter . Generally, if the interest is only one-sided then a smaller sample size will be required as there will be no information about the other side of the data. However, it is important to note that this needs to be decided before the experiment and not changed afterward, otherwise the design of experiments may not be suitable.
Information Required
A lot of the time the design of experiments process needs to be iterative due to resource constraints, such as having limited funds or time, but here are some key points to discuss up front:
  • What is the question you want answered? This can help lead you to form a hypothesis and also to define the other questions.
  • Why does it need answering? By getting more detail it can actually change the emphasis of the question they want answered and should focus the design and testing that will be required (e.g., are the new detectors better than our current detector and which ones are best?). It also can help highlight any subquestions.
  • What do you want investigated? Asking this question will enable the customer to think about the variables that will be used in the design along with the numerical ranges of interest. It also could uncover any variables that may have been overlooked, see the Experimental Design section.
  • How are the results going to be applied? This can lead to thoughts about applicability to other areas as well as highlighting the assumptions that need to be mademore in the Defining the Scope of the Study section.
  • What level of risk is acceptable? You want to know about the confidence and power levels. Translating this information into risk, however, can be much more accessible for non-statisticians, see more detail in the Power and Sample Size section.
  • Can you explain some of the subject matter to me? This bullet may be optional dependent on your background - if the subject matter is new to you. By getting more details about the practical side allows you to comprehend what is realistically doable in terms of conducting the experiment (e.g., applying complete randomization to an experiment that requires 30 min. to set up each iteration is not practical).
You need to start with the broad questions then lead into the more precise questions, such as those about risk levels, to get the answers you need to continue. Once you have all the information required and have moved to the process of using any existing data, it can soon highlight issues about achieving the required risk levels due to possible constraints or large variation. This would necessitate further discussions about the scope of the study and the variables themselveshence the process being an iterative one.
Power and Sample Size
Before looking at the information needed as well as how to actually run the calculations there are some misconceptions that need to be addressed.
Contrary to popular belief bigger is not always better, at some point the relative gain will plateau off, therefore doing more repeats would be a waste of resources. The sample size will vary depending on the type of data you are looking at, the variation of the data, and what risk levels you need to achieve.
On the other hand, it is wrong to use a sample size of 3 just because you could get published. Many non-statistical journals are now improving their review process by demanding a power calculation be included in the paper, which is good practice. In terms of animal studies, although we all must adhere to using as small a number of animals as possible, there is no point running an experiment if the power is weak as that means the results will be worthless and therefore a waste of those lives. It would be better not to run the experiment rather than gain inconclusive results just from trying to look as if you are using fewer animals. The ethical review process requires power calculations to be included, as under-powered proposals will be rejected due to that last point.
Another common misconception is about significance; generating a larger sample size will not guarantee significant results. If there are significant effects to be found then an adequate sample size will be efficient for finding them. However, there always will be your defined level of risk that they arent found, which is one minus the power levelsee the Risk section. There is also the fact that there may not be any significant differences to find in the first place.
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