The What and the Why of Statistics

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.title[
# The What and the Why of Statistics
]
.subtitle[
## EDP 613
]
.author[
### Week 1
]

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# Basic Ideas

>- **Parameter** - A number describing an entire *population*

>- **Statistic** - A number describing a slice, or a *sample* of a *population*

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# Polar Views of the World

**Frequentist Statisticians** believe that there is one and only one correct parameter that can be found by using multiple samples.

- parameters are fixed and data vary
  - there is a single truth that can be found with enough indicators
  - only objectibity can be used

**Bayesian Statisticians** believe that multiple parameters exist which are all based on varying probabilities.

- parameters vary and the data is fixed
  - there are multiple truths and getting to any one is based on chance
  - subjectivity is a built feature
  
---

# Learning Statistics

- You likely do not know enough about probability so for now assume that the frequentist point-of-view is correct.

- It is easier to begin to learn statistics if you don't have to consider multiple outcomes in superposition.

- We will come back to the Bayesian vs. Frequentist arguement

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# Start

**Descriptive Statistics** - Mathematical techniques for organizing and summarizing a set of numerical data

# Finish

**Inferential Statistics** - Generalizing from a sample to a population

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# Definitions

- Information is collected on *elements* or *individuals*

- The characteristics of the individuals about which we
collect information are called *variables*

- The values of the variables that we obtain are called
*data*

---

# Overarching Types of Data

- *Qualitative variables* (aka *categorical variables*) classify
elements into categories.

- *Quantitative variables* tell how much or how many of
something there is.

---

# Example

Which of the following variables are qualitative and which
are quantitative?

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# Solution

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# Levels of Measurement

<center>
<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;vertical-align: middle !important;background-color: #212121 !important;">  </th>
   <th style="text-align:center;vertical-align: middle !important;background-color: #212121 !important;"> Nominal </th>
   <th style="text-align:center;vertical-align: middle !important;background-color: #212121 !important;"> Ordinal </th>
   <th style="text-align:center;vertical-align: middle !important;background-color: #212121 !important;"> Interval </th>
   <th style="text-align:center;vertical-align: middle !important;background-color: #212121 !important;"> Ratio </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 5em; vertical-align: middle !important;"> Naming, labeling, or classifying observations </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 5em; vertical-align: middle !important;background-color: #212121 !important;"> Ranks categories in order </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;background-color: #212121 !important;">  </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;background-color: #212121 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;background-color: #212121 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;background-color: #212121 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 5em; vertical-align: middle !important;"> Known equal intervals </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;">  </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
   <td style="text-align:center;width: 20em; vertical-align: middle !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 5em; background-color: #212121 !important;"> Includes a natural zero point </td>
   <td style="text-align:center;width: 20em; background-color: #212121 !important;">  </td>
   <td style="text-align:center;width: 20em; background-color: #212121 !important;">  </td>
   <td style="text-align:center;width: 20em; background-color: #212121 !important;">  </td>
   <td style="text-align:center;width: 20em; background-color: #212121 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ffffff;overflow:visible;position:relative;"><path d="M438.6 105.4C451.1 117.9 451.1 138.1 438.6 150.6L182.6 406.6C170.1 419.1 149.9 419.1 137.4 406.6L9.372 278.6C-3.124 266.1-3.124 245.9 9.372 233.4C21.87 220.9 42.13 220.9 54.63 233.4L159.1 338.7L393.4 105.4C405.9 92.88 426.1 92.88 438.6 105.4H438.6z"></path></svg> </td>
  </tr>
</tbody>
</table>
</center>

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# Note

Your textbook pools interval and ratio together as *interval-ratio*.

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# Example

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# Solution

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# Discrete and Continuous

- *Discrete variables* are quantitative variables whose
possible values can be listed
  - possibly infinite
  - obtained by counting

- *Continuous variables* are quantitative variables that can take on any value in some interval.
  - possibly infinite
  - obtained by measuring
  
---

# Example

Which of the following variables are discrete or continuous?

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# Solution

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## That's it. Take a break before our R session!