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

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6 1. ONE-VARIABLE STATISTICS: BASICS would essentially be the collection of all the names on all class rosters of courses in the last five years at all US 4-year colleges and universities. When doing an actual scientific study, we are usually not interested so much in the individuals themselves, but rather in DEFINITION 1.1.5. A variable in a statistical study is the answer of a question the researcher is asking about each individual. There are two types: • A categorical variable is one whose values have a finite number of possibilities. • A quantitative variable is one whose values are numbers (so, potentially an infinite number of possibilities). The variable is something which (as the name says) varies, in the sense that it can have a different value for each individual in the population (although that is not necessary). EXAMPLE 1.1.6. In Example 1.1.2, the variable most likely would be who they voted for, a categorical variable with only possible values “Mickey Mouse” or “Daffy Duck” (or whoever the names on the ballot were). EXAMPLE 1.1.7. In Example 1.1.3, the variable most likely would be what face of the coin was facing up after the flip, a categorical variable with values “heads” and “tails.” EXAMPLE 1.1.8. There are several variables we might use in Example 1.1.4. One might be how many homework problems did the student do in that course. Another could be how many hours total did the student spend doing homework over that whole semester, for that course. Both of those would be quantitative variables. A categorical variable for the same population would be what letter grade did the student get in the course, which has possible values A, A-, B+,...,D-, F. In many [most?] interesting studies, the population is too large for it to be practical to go observe the values of some interesting variable. Sometimes it is not just impractical, but actually impossible – think of the example we gave of all the flips of the coin, even in the ones in the future. So instead, we often work with DEFINITION 1.1.9. A sample is a subset of a population under study. OftenweusethevariableN to indicate the size of a whole population and the variable n for the size of a sample; as we have said, usually n
1.2. VISUAL REPRESENTATION OF DATA, I 7 1.2. Visual Representation of Data, I: Categorical Variables Suppose we have a population and variable in which we are interested. We get a sample, which could be large or small, and look at the values of the our variable for the individuals in that sample. We shall informally refer to this collection of values as a dataset. In this section, we suppose also that the variable we are looking at is categorical. Then we can summarize the dataset by telling which categorical values did we see for the individuals in the sample, and how often we saw those values. There are two ways we can make pictures of this information: bar charts and pie charts. 1.2.1. Bar Charts I: Frequency Charts. We can take the values which we saw for individuals in the sample along the x-axis of a graph, and over each such label make a box whose height indicates how many individuals had that value – the frequency of occurrence of that value. This is called a bar chart. As with all graphs, you should always label all axes. The x-axis will be labeled with some description of the variable in question, the y-axis label will always be “frequency” (or some synonym like “count” or “number of times”). EXAMPLE 1.2.1. In Example 1.1.7, suppose we took a sample of consisting of the next 10 flips of our coin. Suppose further that 4 of the flips came up heads – write it as “H” – and 6 came up tails, T. Then the corresponding bar chart would look like 1.2.2. Bar Charts II: Relative Frequency Charts. There is a variant of the above kind of bar chart which actually looks nearly the same but changes the labels on the y-axis. That is, instead of making the height of each bar be how many times each categorical value occurred, we could make it be what fraction of the sample had that categorical value –the relative frequency. This fraction is often displayed as a percentage.
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Page 12 and 13: The first instinct of the scientist
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Page 43 and 44: CHAPTER 2 Bi-variate Statistics: Ba
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56 4. PROBABILITY THEORY There is o
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58 4. PROBABILITY THEORY Sometimes,
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76 4. PROBABILITY THEORY FACT 4.3.1
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84 4. PROBABILITY THEORY In order t
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86 4. PROBABILITY THEORY What we kn
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88 4. PROBABILITY THEORY EXERCISE 4
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92 5. BRINGING HOME THE DATA guidel
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94 5. BRINGING HOME THE DATA Simila
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102 5. BRINGING HOME THE DATA 5.2.5
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104 5. BRINGING HOME THE DATA 5.3.
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106 5. BRINGING HOME THE DATA In th
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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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6.2. BASIC CONFIDENCE INTERVALS 115
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6.3. BASIC HYPOTHESIS TESTING 117 6
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6.3. BASIC HYPOTHESIS TESTING 119 N
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6.3. BASIC HYPOTHESIS TESTING 121 M
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The two hypotheses then are 6.3. BA
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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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