## The Structure of Data

<span style="color: #91204D;"> .large[Kelly McConville | Math 141 | Week 1 | Fall 2020] </span>

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## Announcements

* Complete the [Initial Participation Assignment](https://docs.google.com/document/d/1cAlH0bT6OckIXkxJ4DVAhXeRD_ejJONQwP99pjntMGg/edit?usp=sharing) in your lab's channel of the class Slack Workspace
    + Due before your first lab session.

* We will often do worksheets in-class.  They won't be turned in but are to help us engage with the main ideas of the day.

* We will learn about **Gradescope** for submitting assignments and **RStudio** in Lab this week!
    - For the readings, you don't need to run the R code (yet).

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## Week 1 Topics

* Statistical Thinking

* **Structure of data**

* (Lab) Working in RStudio using RMarkdown documents

* Data Viz

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## Goals for Today

* Recap: Statistical Thinking

* Structure of data

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## Statistical Thinking Worksheet Recap

* Overall, which group was convicted at a higher rate?

* When the victim was white, which group was convicted at a higher rate?

* When the victim was a minority, which group was convicted at a higher rate?

<span style="color: #91204D;"> HOW IS THIS POSSIBLE?</span>

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## Simpson's Paradox

<span style="color: #91204D;"> HOW IS THIS POSSIBLE?</span>

<table>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Minority Defendant Convicted </th>
   <th style="text-align:right;"> Minority Defendant Acquitted </th>
   <th style="text-align:right;"> White Defendant Convicted </th>
   <th style="text-align:right;"> White Defendant Acquitted </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Minority Victim </td>
   <td style="text-align:right;width: 2cm; "> 19 </td>
   <td style="text-align:right;width: 2cm; "> 45 </td>
   <td style="text-align:right;width: 2cm; "> 5 </td>
   <td style="text-align:right;width: 2cm; "> 19 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> White Victim </td>
   <td style="text-align:right;width: 2cm; "> 10 </td>
   <td style="text-align:right;width: 2cm; "> 15 </td>
   <td style="text-align:right;width: 2cm; "> 40 </td>
   <td style="text-align:right;width: 2cm; "> 67 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Total </td>
   <td style="text-align:right;width: 2cm; "> 29 </td>
   <td style="text-align:right;width: 2cm; "> 60 </td>
   <td style="text-align:right;width: 2cm; "> 45 </td>
   <td style="text-align:right;width: 2cm; "> 86 </td>
  </tr>
</tbody>
</table>

**Key factors:**

For what race of the victim, is the conviction rate higher?

&rarr; The conviction rate is 37.9% for white victims and 27.2% for minority victims.

When the defendant is white, what tends to be the race of the victim?

&rarr; White defendants tend to have white victims.  Minority defendants tend to have minority victims.

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## What is "Statistical Thinking?"

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## Statistical Thinking

* Importance of the appropriate measures/metrics.
    + Proportional reasoning

* Utilizing multivariate thinking

* Understanding that context is queen.

* And so much more!

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## What is data?

---

* The dictionary definition:

> "data: factual information (such as measurements or statistics) used as a basis for reasoning, discussion, or calculation" -- Merriam-Webster

* Wikipedia:

> "Data are characteristics or information, usually numerical, that are collected through observation. In a more technical sense, data are a set of values of qualitative or quantitative variables about one or more persons or objects, while a datum (singular of data) is a single value of a single variable."

* Our textbook definition:

> "Data comes to us in a variety of formats, from pictures to text to numbers." -- ModernDive

* Data Feminism:

> "... by the time that information becomes data, it's already been classified in some way. Data after all, is information made *tractable*." -- D'Ignazio and Klein

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### Data Frames

<table class="table table-responsive table-bordered table-striped" style="font-size: 12px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> UserID </th>
   <th style="text-align:right;"> Tree_Height </th>
   <th style="text-align:left;"> Common_Name </th>
   <th style="text-align:left;"> Park </th>
   <th style="text-align:right;"> DBH </th>
   <th style="text-align:left;"> Species_Factoid </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> 1 </td>
   <td style="text-align:right;"> 105 </td>
   <td style="text-align:left;"> Douglas-Fir </td>
   <td style="text-align:left;"> Gammans Park </td>
   <td style="text-align:right;"> 37.4 </td>
   <td style="text-align:left;"> Bracts on cones look like a mouse's feet and tail. </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 2 </td>
   <td style="text-align:right;"> 94 </td>
   <td style="text-align:left;"> Douglas-Fir </td>
   <td style="text-align:left;"> Gammans Park </td>
   <td style="text-align:right;"> 32.5 </td>
   <td style="text-align:left;"> Bracts on cones look like a mouse's feet and tail. </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 3 </td>
   <td style="text-align:right;"> 23 </td>
   <td style="text-align:left;"> Lavalle Hawthorn </td>
   <td style="text-align:left;"> Gammans Park </td>
   <td style="text-align:right;"> 9.7 </td>
   <td style="text-align:left;"> Like most hawthorns, the tree has stout thorns up to 2" long. </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 4 </td>
   <td style="text-align:right;"> 28 </td>
   <td style="text-align:left;"> Northern Red Oak </td>
   <td style="text-align:left;"> Gammans Park </td>
   <td style="text-align:right;"> 10.3 </td>
   <td style="text-align:left;"> Acorns take two years to mature and are an important food source for wildlife. </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 5 </td>
   <td style="text-align:right;"> 102 </td>
   <td style="text-align:left;"> Douglas-Fir </td>
   <td style="text-align:left;"> Gammans Park </td>
   <td style="text-align:right;"> 33.2 </td>
   <td style="text-align:left;"> Bracts on cones look like a mouse's feet and tail. </td>
  </tr>
  <tr>
   <td style="text-align:left;"> 6 </td>
   <td style="text-align:right;"> 95 </td>
   <td style="text-align:left;"> Douglas-Fir </td>
   <td style="text-align:left;"> Gammans Park </td>
   <td style="text-align:right;"> 32.1 </td>
   <td style="text-align:left;"> Bracts on cones look like a mouse's feet and tail. </td>
  </tr>
</tbody>
</table>

Data in spreadsheet-like format where:

* Rows = Observations/cases

* Columns = Variables

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### Data Frames

Rows = Observations/cases

**What are the cases?  What does each row represent?**

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### Data Frames

Columns = Variables

**Variables**: Describe characteristics of the observations

* **Quantitative**: Numerical in nature

* **Categorical**: Values are categories

* **Identification**: Uniquely identify each case

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### Data Frames

**Important to understand what each variable represents and the units of measurement.**

Example questions:

* For categorical variables, what are the categories? Do those categories adequately represent the data represented by that variable?

* For quantitative variables, what values are possible? Were the data rounded or binned?  Are those values actually encoding categories?

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## Lab This Week

* Introduction to R/RStudio
* Introduction to Gradescope