Lies, Damned Lies, or Statistics- How to Tell the Truth with Statistics, 2017a

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32 1. ONE-VARIABLE STATISTICS: BASICS EXERCISE 1.9. What must be true about a dataset if its range is 0? Give the most interesting example of a dataset with range of 0 and the property you just described that you can think of. What must be true about a dataset if its IQR is 0? Give the most interesting example of a dataset with IQR of 0 and the property you just described that you can think of. What must be true about a dataset if its standard deviation is 0? Give the most interesting example of a dataset with standard deviation of 0 and the property you just described that you can think of. EXERCISE 1.10. Here are some boxplots of test scores, out of 100, on a standardized test given in five different classes – the same test, different classes. For each of these plots, A − E, describe qualitatively (in the sense of §1.3.4) but in as much detail as you can, what must have been the histogram for the data behind this boxplot. Also sketch a possible such histogram, for each case.
CHAPTER 2 Bi-variate Statistics: Basics 2.1. Terminology: Explanatory/Response or Independent/Dependent All of the discussion so far has been for studies which have a single variable. We may collect the values of this variable for a large population, or at least the largest sample we can afford to examine, and we may display the resulting data in a variety of graphical ways, and summarize it in a variety of numerical ways. But in the end all this work can only show a single characteristic of the individuals. If, instead, we want to study a relationship, we need to collect two (at least) variables and develop methods of descriptive statistics which show the relationships between the values of these variables. Relationships in data require at least two variables. While more complex relationships can involve more, in this chapter we will start the project of understanding bivariate data, data where we make two observations for each individual, where we have exactly two variables. If there is a relationship between the two variables we are studying, the most that we could hope for would be that that relationship is due to the fact that one of the variables causes the other. In this situation, we have special names for these variables DEFINITION 2.1.1. In a situation with bivariate data, if one variable can take on any value without (significant) constraint it is called the independent variable, while the second variable, whose value is (at least partially) controlled by the first, is called the dependent variable. Since the value of the dependent variable depends upon the value of the independent variable, we could also say that it is explained by the independent variable. Therefore the independent variable is also called the explanatory variable and the dependent variable is then called the response variable Whenever we have bivariate data and we have made a choice of which variable will be the independent and which the dependent, we write x for the independent and y for the dependent variable. EXAMPLE 2.1.2. Suppose we have a large warehouse of many different boxes of products ready to ship to clients. Perhaps we have packed all the products in boxes which are perfect cubes, because they are stronger and it is easier to stack them efficiently. We could do a study where • the individuals would be the boxes of product; 33
Page 1: Lies, Damned Lies, or Statistics: H
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Page 12 and 13: The first instinct of the scientist
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Part 3 Inferential Statistics
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CHAPTER 6 Basic Inferences The purp
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6.1. THE CENTRAL LIMIT THEOREM 113
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EXERCISES 125 Exercises EXERCISE 6.
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Bibliography [Gal17] Gallup, Presid
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130 INDEX causation, 46 center of a
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Lies, Damned Lies, or Statistics- How to Tell the Truth with Statistics, 2017a

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