Centrality & Variability

.leftcol30[
<center>
<img src="https://raw.githubusercontent.com/emse-eda-gwu/2021-Spring/master/images/eda_hex_sticker.png" width=250>
</center>
]
.rightcol70[
# Week 3: .fancy[Centrality & Variability]

### <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 512 512"><path d="M496 128v16a8 8 0 0 1-8 8h-24v12c0 6.627-5.373 12-12 12H60c-6.627 0-12-5.373-12-12v-12H24a8 8 0 0 1-8-8v-16a8 8 0 0 1 4.941-7.392l232-88a7.996 7.996 0 0 1 6.118 0l232 88A8 8 0 0 1 496 128zm-24 304H40c-13.255 0-24 10.745-24 24v16a8 8 0 0 0 8 8h464a8 8 0 0 0 8-8v-16c0-13.255-10.745-24-24-24zM96 192v192H60c-6.627 0-12 5.373-12 12v20h416v-20c0-6.627-5.373-12-12-12h-36V192h-64v192h-64V192h-64v192h-64V192H96z"/></svg> EMSE 4575: Exploratory Data Analysis
### <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 448 512"><path d="M224 256c70.7 0 128-57.3 128-128S294.7 0 224 0 96 57.3 96 128s57.3 128 128 128zm89.6 32h-16.7c-22.2 10.2-46.9 16-72.9 16s-50.6-5.8-72.9-16h-16.7C60.2 288 0 348.2 0 422.4V464c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48v-41.6c0-74.2-60.2-134.4-134.4-134.4z"/></svg> John Paul Helveston
### <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 448 512"><path d="M0 464c0 26.5 21.5 48 48 48h352c26.5 0 48-21.5 48-48V192H0v272zm320-196c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40zm0 128c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40zM192 268c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40zm0 128c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12h-40c-6.6 0-12-5.4-12-12v-40zM64 268c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12H76c-6.6 0-12-5.4-12-12v-40zm0 128c0-6.6 5.4-12 12-12h40c6.6 0 12 5.4 12 12v40c0 6.6-5.4 12-12 12H76c-6.6 0-12-5.4-12-12v-40zM400 64h-48V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H160V16c0-8.8-7.2-16-16-16h-32c-8.8 0-16 7.2-16 16v48H48C21.5 64 0 85.5 0 112v48h448v-48c0-26.5-21.5-48-48-48z"/></svg> January 27, 2021
]

---
class: center

# Thanks for the heros 😄

|<center><img src="images/heros/helena.png" height="120"></center> Helena | <center><img src="images/heros/katie.gif" height="120"></center> Katie | <center><img src="images/heros/carolyne.jpg" height="120"></center> Carolyne | <center><img src="images/heros/kaveena.png" height="120"></center> Kaveena | <center><img src="images/heros/alejandro.jpg" height="120"></center> Alejandro |
|-|-|-|-|-|
|<center><img src="images/heros/kyara.jpg" height="120"></center> Kyara | <center><img src="images/heros/ebun.gif" height="120"></center> Ebun | <center><img src="images/heros/kareemot.gif" height="120"></center> Kareemot | <center><img src="images/heros/omar1.png" height="120"></center> Omar 1 | <center><img src="images/heros/omar2.jpg" height="120"></center> Omar 2 |
|<center><img src="images/heros/matthew.gif" height="120"></center> Matthew | <center><img src="images/heros/michael.gif" height="120"></center> Michael | <center><img src="images/heros/alexa.jpg" height="120"></center> Alexa | <center><img src="images/heros/kazi.gif" height="120"></center> Kazi| <center><img src="images/heros/eliese.gif" height="120"></center> Eliese |

---

# Updates

## Office hours are set (posted in #links in slack & on BB) :

- 5-7pm Mondays w/Jenny K.
- 4:30-6pm Tuesdays w/Lydia G.
- 7-9pm Tuesdays w/Saurav P.
- 2-4pm Fridays w/Prof. Helveston

## Meet Lydia

## Jenny has an announcement

---
class: center, middle, inverse

# Tip of the week:

# `theme_set()`

---

# Add "global" settings to all plots

```r
library(knitr)
library(tidyverse)
library(here)
knitr::opts_chunk$set(
    warning = FALSE,
    message = FALSE,
    comment = "#>",
*   fig.path = "figs/", # Plot save path
*   fig.width = 7.252, # Plot dimensions
*   fig.height = 4,
*   fig.retina = 3 # Better plot resolution
)

*theme_set(theme_bw(base_size = 20)) # Set theme for all ggplots
```

---

```r
ggplot(mtcars) + 
  geom_point(aes(x = mpg, y = hp))
```

<img src="figs/unnamed-chunk-3-1.png" width="522.144" />
]
.rightcol[
`theme_bw(base_size = 20)`

<img src="figs/unnamed-chunk-4-1.png" width="522.144" />
]

---

# Week 3: .fancy[Centrality & Variability]

## 1. Data Types
## 2. Measures of Centrality & Variability

## BREAK

## 3. Visualizing Centrality & Variability
## 4. Relationships Between 2 Variables
## 5. Exploratory Data Analysis

---

# Week 3: .fancy[Centrality & Variability]

## 1. .orange[Data Types]
## 2. Measures of Centrality & Variability

## BREAK

## 3. Visualizing Centrality & Variability
## 4. Relationships Between 2 Variables
## 5. Exploratory Data Analysis

---
class: inverse, center, middle

# 24,901

???

If I walked up to you, and said, "The answer is 24,901,"
you would probably be confused.
By itself, a number means nothing.

---
class: inverse, center, middle

# Earth's circumference at the equator:<br>24,901 miles

???

But if I were to tell you that the circumference of the earth at the equator is 24,901 miles, that would mean something.
To be complete and meaningful, quantitative information consists of both quantitative data (the numbers) and categorical data (the labels that tell us what the numbers measure).

---

# Types of Data

Subdivide things into _groups_

- What type?
- Which category?
]

Measure things with numbers

- How many?
- How much?
]

---

## Categorical (discrete) variables

- Order doesn't matter
- Differ in "name" (nominal) only

e.g. `country` in TB case data:

```
#> # A tibble: 6 x 4
#>   country      year  cases population
#>   <chr>       <dbl>  <dbl>      <dbl>
#> 1 Afghanistan  1999    745   19987071
#> 2 Afghanistan  2000   2666   20595360
#> 3 Brazil       1999  37737  172006362
#> 4 Brazil       2000  80488  174504898
#> 5 China        1999 212258 1272915272
#> 6 China        2000 213766 1280428583
```
]]

- Order matters
- Distance between units not equal

e.g.: `Placement` 2017 Boston marathon:

```
#> # A tibble: 6 x 3
#>   Placement `Official Time` Name            
#>       <dbl> <time>          <chr>           
#> 1         1 02:09:37        Kirui, Geoffrey 
#> 2         2 02:09:58        Rupp, Galen     
#> 3         3 02:10:28        Osako, Suguru   
#> 4         4 02:12:08        Biwott, Shadrack
#> 5         5 02:12:35        Chebet, Wilson  
#> 6         6 02:12:45        Abdirahman, Abdi
```
]]

---

## Numerical data

- Numerical scale with<br>arbitrary starting point
- No "0" point
- Can't say "x" is double "y"

e.g.: `temp` in Beaver data

```
#>   day time  temp activ
#> 1 346  840 36.33     0
#> 2 346  850 36.34     0
#> 3 346  900 36.35     0
#> 4 346  910 36.42     0
#> 5 346  920 36.55     0
#> 6 346  930 36.69     0
```
]

- Has a "0" point
- Can be described as percentages
- Can say "x" is double "y"

e.g.: `height` & `speed` in wildlife impacts

```
#> # A tibble: 6 x 3
#>   incident_date       height speed
#>   <dttm>               <dbl> <dbl>
#> 1 2018-12-31 00:00:00    700   200
#> 2 2018-12-27 00:00:00    600   145
#> 3 2018-12-23 00:00:00      0   130
#> 4 2018-12-22 00:00:00    500   160
#> 5 2018-12-21 00:00:00    100   150
#> 6 2018-12-18 00:00:00   4500   250
```
]

---
class: inverse, center, middle

# Key Questions

## .orange[Does the order matter?]

| Yes | No |
|---|---|
| Ordinal | Nominal |

]

## .orange[Is there a "baseline"?]

| Yes | No |
|---|---|
| Ratio | Interval |
]

---
class: center, middle

# Be careful of how variables are encoded!

---

## .red[When numbers are categories]

- "Dummy coding": e.g., `passedTest` = `1` or `0`)
- "North", "South", "East", "West" = `1`, `2`, `3`, `4`

## .red[When ratio data are discrete (i.e. counts)]

- Number of eggs in a carton, heart beats per minute, etc.
- Continuous variables measured discretely (e.g. age)

## .red[Time]

- As _ordinal_ categories: "Jan.", "Feb.", "Mar.", etc.
- As _interval_ scale: "Jan. 1", "Jan. 2", "Jan. 3", etc.
- As _ratio_ scale: "30 sec", "60 sec", "70 sec", etc.

---

# **Quick practice**: What's the data type?

> Decide [here](https://docs.google.com/presentation/d/1C9-MPyUaHuyYHfz0SxpZb11GDT4xUXvBjhz7wQoEoLE/edit?usp=sharing) (link also in #classroom)

```r
wildlife_impacts %>%
  filter(!is.na(cost_repairs_infl_adj)) %>%
  select(incident_date, time_of_day, species, cost_repairs_infl_adj)
```

```
#> # A tibble: 615 x 4
#>    incident_date       time_of_day species                cost_repairs_infl_adj
#>    <dttm>              <chr>       <chr>                                  <dbl>
#>  1 2018-10-25 00:00:00 Day         Unknown bird - large                    1000
#>  2 2018-09-05 00:00:00 <NA>        Unknown bird - medium                    200
#>  3 2018-08-09 00:00:00 Day         Semipalmated sandpiper                 10000
#>  4 2018-06-24 00:00:00 Day         Unknown bird - large                  100000
#>  5 2018-02-18 00:00:00 Day         Rough-legged hawk                      20000
#>  6 2018-01-05 00:00:00 Night       Brant                                 487000
#>  7 2017-10-31 00:00:00 Day         Unknown bird - small                      51
#>  8 2017-10-12 00:00:00 <NA>        Swainson's thrush                       5120
#>  9 2017-09-17 00:00:00 Day         Cattle egret                          531763
#> 10 2017-09-16 00:00:00 <NA>        Unknown bird - medium                    102
#> # … with 605 more rows
```
]

???

- incident_date:         Interval
- time_of_day:           Ordinal
- species:               Nominal
- cost_repairs_infl_adj: Ratio

---

# Week 3: .fancy[Centrality & Variability]

## 1. Data Types
## 2. .orange[Measures of Centrality & Variability]

## BREAK

## 3. Visualizing Centrality & Variability
## 4. Relationships Between 2 Variables
## 5. Exploratory Data Analysis

---
class: inverse, middle

# .center[.font140[Summary Measures:]]

# This week: .red[Centrality] &  .blue[Variability]

# Next week: .green[Correlation]

---

# .red[Centrality (a.k.a. The "Average" Value)]

### A single number representing the _middle_ of a set of numbers

### **Mean**: `$\frac{\text{Sum of values}}{\text{# of values}}$`

### **Median**: "Middle" value (50% of data above & below)

### **Mode**: Most frequent value (usually for categorical data)

---

# .center[Mean isn't always the "best" choice]

```r
wildlife_impacts %>%
    filter(! is.na(height)) %>%
    summarise(
      mean = mean(height),
      median = median(height))
```

```
#> # A tibble: 1 x 2
#>    mean median
#>   <dbl>  <dbl>
#> 1  984.     50
```
Percent of data below mean:

```
#> [1] "73.9%"
```
]

???

On average, where do planes hit birds? 
Saying ~1000 ft is misleading
It's much more likely to be under 100 ft

---
class: inverse

# .center[Beware the "flaw of averages"]

.leftcol[
### What happened to the statistician that crossed a river with an average depth of 3 feet?
]

<img src="images/foa.jpg" width=600>
]

---

# .blue[Variability ("Spread")]

### **Standard deviation**: distribution of values relative to the mean 
### `$s = \sqrt{\frac{\sum_{i=1}^{N}(x_i - \bar{x})^2}{N - 1}}$`

### **Interquartile range (IQR)**: `$Q_3 - Q_1$` (middle 50% of data)

### **Range**: max - min

---

# .center[.fancy[Example:] Days to ship]

.leftcol40[
Complaints are coming in about orders shipped from warehouse B, so you collect some data:

```r
daysToShip
```

```
#>    order warehouseA warehouseB
#> 1      1          3          1
#> 2      2          3          1
#> 3      3          3          1
#> 4      4          4          3
#> 5      5          4          3
#> 6      6          4          4
#> 7      7          5          5
#> 8      8          5          5
#> 9      9          5          5
#> 10    10          5          6
#> 11    11          5          7
#> 12    12          5         10
```
]]

```r
daysToShip %>%
    gather(warehouse, days, warehouseA:warehouseB) %>%
    group_by(warehouse) %>%
    summarise(
*       mean   = mean(days),
*       median = median(days))
```

```
#> # A tibble: 2 x 3
#>   warehouse   mean median
#>   <chr>      <dbl>  <dbl>
#> 1 warehouseA  4.25    4.5
#> 2 warehouseB  4.25    4.5
```
]

---

# .center[.fancy[Example:] Days to ship]

.leftcol40[
Complaints are coming in about orders shipped from warehouse B, so you collect some data:

```r
daysToShip
```

```r
daysToShip %>%
    gather(warehouse, days, warehouseA:warehouseB) %>%
    group_by(warehouse) %>%
    summarise(
        mean   = mean(days),
        median = median(days),
*       range = max(days) - min(days),
*       sd    = sd(days))
```

```
#> # A tibble: 2 x 5
#>   warehouse   mean median range    sd
#>   <chr>      <dbl>  <dbl> <dbl> <dbl>
#> 1 warehouseA  4.25    4.5     2 0.866
#> 2 warehouseB  4.25    4.5     9 2.70
```
]

---

# .center[.fancy[Example:] Days to ship]

---
class: center

# Interpreting the standard deviation

<center>
<img src="figs/days-to-ship-sd-1.png" width=380>
</center>
]

---
class: inverse, center

# Outliers

---

## **Mean** & **Standard Deviation** are sensitive to outliers

**Outliers**: `$Q_1 - 1.5 IQR$` or `$Q_3 + 1.5 IQR$`

**Extreme values**: `$Q_1 - 3 IQR$` or `$Q_3 + 3 IQR$`

```r
data1 <- c(3,3,4,5,5,6,6,7,8,9)
```
- Mean: 5.6
- Standard Deviation: 2.01
- Median: 5.5
- IQR: 2.5
]

```r
data2 <- c(3,3,4,5,5,6,6,7,8,20)
```
- .red[Mean: 6.7]
- .red[Standard Deviation: 4.95]
- .blue[Median: 5.5]
- .blue[IQR: 2.5]
]

---
class: inverse, middle

# .center[Robust statistics for continuous data]
# .center[(less sensitive to outliers)]

## .red[Centrality]: Use _median_ rather than _mean_

## .blue[Variability]: Use _IQR_ rather than _standard deviation_

---
class: inverse

# Practice with summary measurements

### 1) Read in the following data sets:

- `milk_production.csv`
- `lotr_words.csv`

### 2) For each variable in each data set, if possible, summarize its

### 1. .red[Centrality]
### 2. .blue[Variability]

---
class: inverse, center

# Break!

## Stand up, Move around, Stretch!

---

# Week 3: .fancy[Centrality & Variability]

## 1. Data Types
## 2. Measures of Centrality & Variability

## BREAK

## 3. .orange[Visualizing Centrality & Variability]
## 4. Relationships Between 2 Variables
## 5. Exploratory Data Analysis

---

# "Visualizing data helps us think"

---
class: center

# Anscombe's Quartet

---
class: inverse, center, middle

# The data _type_ determines <br> how to summarize it

---

**Measures**:
- Frequency counts /<br>Proportions
<br>
<br>
<br>
<br>

**Charts**:
- Bars
]

**Measures**:
- Frequency counts /<br>Proportions
- .red[Centrality]:<br>Median, Mode
- .blue[Variability]: IQR
<br>

**Charts**:
- Bars
]

**Measures**:
- .red[Centrality]:<br>Mean, median
- .blue[Variability]: Range, standard deviation, IQR
<br>
<br>

**Charts**:
- Histogram
- Boxplot
]

---

## Summarizing **Nominal** data

```r
wildlife_impacts %>%
*   count(operator, sort = TRUE) %>%
*   mutate(p = n / sum(n))
```

```
#> # A tibble: 4 x 3
#>   operator               n     p
#>   <chr>              <int> <dbl>
#> 1 SOUTHWEST AIRLINES 17970 0.315
#> 2 UNITED AIRLINES    15116 0.265
#> 3 AMERICAN AIRLINES  14887 0.261
#> 4 DELTA AIR LINES     9005 0.158
```
]

```r
wildlife_impacts %>%
    count(operator, sort = TRUE) %>%
*   ggplot() +
*   geom_col(aes(x = n, y = reorder(operator, n)),
*            width = 0.7) +
    labs(x = "Count", y = "Operator")
```

<img src="figs/wildlife-operator-bars-1.png" width="504" />
]]

---

## Summarizing **Ordinal** data

```r
wildlife_impacts %>%
*   count(incident_month, sort = TRUE) %>%
*   mutate(p = n / sum(n))
```

```
#> # A tibble: 12 x 3
#>    incident_month     n      p
#>             <dbl> <int>  <dbl>
#>  1              9  7980 0.140 
#>  2             10  7754 0.136 
#>  3              8  7104 0.125 
#>  4              5  6161 0.108 
#>  5              7  6133 0.108 
#>  6              6  4541 0.0797
#>  7              4  4490 0.0788
#>  8             11  4191 0.0736
#>  9              3  2678 0.0470
#> 10             12  2303 0.0404
#> 11              1  1951 0.0342
#> 12              2  1692 0.0297
```
]]

```r
wildlife_impacts %>%
    count(incident_month, sort = TRUE) %>%
*   ggplot() +
*   geom_col(aes(x = as.factor(incident_month),
*                y = n), width = 0.7) +
    labs(x = "Incident month")
```

<img src="figs/wildlife-months-bar-1.png" width="504" />
]]

---

## Summarizing **continuous** variables

- Skewness
- Number of modes
<br>

**Boxplots**:

- Outliers
- Comparing variables
]
.rightcol70[.border[
<img src = 'images/eda-boxplot.png'>
]]

---

## **Histogram**: Identify Skewness & # of Modes

```r
summary(wildlife_impacts$height)
```

```
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
#>     0.0     0.0    50.0   983.8  1000.0 25000.0   18038
```
]

```r
ggplot(wildlife_impacts) +
* geom_histogram(aes(x = height), bins = 50) +
  labs(x = 'Height (ft)', y = 'Count')
```

<img src="figs/wildlife-height-hist-1.png" width="504" style="display: block; margin: auto;" />
]

---

## **Histogram**: Identify Skewness & # of Modes

```r
ggplot(wildlife_impacts) +
* geom_histogram(aes(x = height), bins = 50) +
  labs(x = 'Height (ft)', y = 'Count')
```

<img src="figs/unnamed-chunk-27-1.png" width="504" style="display: block; margin: auto;" />
]

```r
ggplot(wildlife_impacts) +
* geom_histogram(aes(x = speed), bins = 50) +
  labs(x = 'speed (mph)', y = 'Count')
```

<img src="figs/wildlife-speed-hist-1.png" width="504" style="display: block; margin: auto;" />
]

---

## **Boxplot**: Identify outliers

```r
ggplot(wildlife_impacts) +
*   geom_boxplot(aes(x = height)) +
    labs(x = 'Height (ft)', y = NULL)
```

<img src="figs/wildlife-height-boxplot-1.png" width="504" style="display: block; margin: auto;" />
]

```r
ggplot(wildlife_impacts) +
*   geom_boxplot(aes(x = speed)) +
    labs(x = 'Speed (mph)', y = NULL)
```

<img src="figs/wildlife-speed-boxplot-1.png" width="504" style="display: block; margin: auto;" />
]

---

- Skewness
- Modes

]
.rightcol[
## Boxplot

- Outliers
<br><br>

<img src="figs/unnamed-chunk-29-1.png" width="504" style="display: block; margin: auto;" />
]

---
class: inverse

# Practicing visual summaries

- `faithful.csv`
- `marathon.csv`

2) Summarize the following variables using an appropriate chart (bar chart, histogram, and / or boxplot):

- faithful: `eruptions`
- faithful: `waiting`
- marathon: `Age`
- marathon: `State`
- marathon: `Country`
- marathon: `` `Official Time` ``
]

---

# Week 3: .fancy[Centrality & Variability]

## 1. Data Types
## 2. Measures of Centrality & Variability

## BREAK

## 3. Visualizing Centrality & Variability
## 4. .orange[Relationships Between 2 Variables]
## 5. Exploratory Data Analysis

---

## Two **Categorical** Variables

Summarize with a table of counts

```r
wildlife_impacts %>%
*   count(operator, time_of_day)
```

```
#> # A tibble: 20 x 3
#>    operator           time_of_day     n
#>    <chr>              <chr>       <int>
#>  1 AMERICAN AIRLINES  Dawn          458
#>  2 AMERICAN AIRLINES  Day          7809
#>  3 AMERICAN AIRLINES  Dusk          584
#>  4 AMERICAN AIRLINES  Night        3710
#>  5 AMERICAN AIRLINES  <NA>         2326
#>  6 DELTA AIR LINES    Dawn          267
#>  7 DELTA AIR LINES    Day          4846
#>  8 DELTA AIR LINES    Dusk          353
#>  9 DELTA AIR LINES    Night        2090
#> 10 DELTA AIR LINES    <NA>         1449
#> 11 SOUTHWEST AIRLINES Dawn          394
#> 12 SOUTHWEST AIRLINES Day          9109
#> 13 SOUTHWEST AIRLINES Dusk          599
#> 14 SOUTHWEST AIRLINES Night        5425
#> 15 SOUTHWEST AIRLINES <NA>         2443
#> 16 UNITED AIRLINES    Dawn          151
#> 17 UNITED AIRLINES    Day          3359
#> 18 UNITED AIRLINES    Dusk          181
#> 19 UNITED AIRLINES    Night        1510
#> 20 UNITED AIRLINES    <NA>         9915
```
]

---

## Two **Categorical** Variables

Convert to "wide" format with `spread()` to make it easier to compare values

```r
wildlife_impacts %>%
    count(operator, time_of_day) %>%
*   spread(key = time_of_day, value = n)
```

```
#> # A tibble: 4 x 6
#>   operator            Dawn   Day  Dusk Night `<NA>`
#>   <chr>              <int> <int> <int> <int>  <int>
#> 1 AMERICAN AIRLINES    458  7809   584  3710   2326
#> 2 DELTA AIR LINES      267  4846   353  2090   1449
#> 3 SOUTHWEST AIRLINES   394  9109   599  5425   2443
#> 4 UNITED AIRLINES      151  3359   181  1510   9915
```
]

---

## Two **Categorical** Variables

Visualize with bars:<br>map **fill** to denote 2nd categorical var

```r
wildlife_impacts %>%
  count(operator, time_of_day) %>%
  ggplot() +
  geom_col(aes(x = n,
               y = reorder(operator, n),
*              fill = reorder(time_of_day, n)),
           width = 0.7,
*          position = 'dodge') +
  theme(legend.position = "bottom") +
  labs(fill = "Time of day", y = NULL)
```
]
.rightcol55[
<img src="figs/unnamed-chunk-33-1.png" width="648" style="display: block; margin: auto;" />
]

---

## Two **Continuous** Variables

Visualize with scatterplot - looking for _clustering_ and/or _correlational_ relationship

```r
ggplot(wildlife_impacts) +
* geom_point(aes(x = speed, y = height),
*            size = 0.5) +
  labs(x = 'Speed (mph)',
       y = 'Height (f)')
```
]

.rightcol55[
<img src="figs/unnamed-chunk-34-1.png" width="504" style="display: block; margin: auto;" />
]

---

## One **Continuous**, One **Categorical**

Visualize with **boxplot**

```r
ggplot(wildlife_impacts) +
* geom_boxplot(aes(x = speed,
*                  y = operator)) +
  labs(x = 'Speed (mph)',
       y = 'Airline')
```
]

.rightcol55[
<img src="figs/unnamed-chunk-35-1.png" width="504" style="display: block; margin: auto;" />
]

---
class: inverse

# Practice with visualizing _relationships_

1) Read in the following data sets:

- `marathon.csv`
- `wildlife_impacts.csv`

2) Visualize the _relationships_ between the following variables using an appropriate chart (bar plots, scatterplots, and / or box plots):

- marathon: `Age` & `Official Time`
- marathon: Country & `Official Time`
- wildlife_impacts: `state` & `operator`

---

# Week 3: .fancy[Centrality & Variability]

## 1. Data Types
## 2. Measures of Centrality & Variability

## BREAK

## 3. Visualizing Centrality & Variability
## 4. Relationships Between 2 Variables
## 5. .orange[Exploratory Data Analysis]

---

### Goal: **Form** hypotheses.
### Improves quality of **questions**.
### (do this in THIS class)
]

### Goal: **Test** hypotheses.
### Improves quality of **answers**.
### (do this in your stats classes)
]

---
class: center, inverse

# Don't be Icarus

---
class: inverse, middle

## "Far better an approximate answer to the _right_ question, which is often vague, than an exact answer to the _wrong_ question, which can always be made precise."
## — John Tukey

---
class: center
background-color: #FFFFFF

**EDA is an iterative process to help you<br>_understand_ your data and ask better questions**

---

## Visualizing variation

- What type of **variation** occurs within my variables?
- What type of **covariation** occurs between my variables?

Check out [these guides](https://eda.seas.gwu.edu/2021-Spring/ref-visualizing-data.html#choosing-the-right-chart)
]
.rightcol70[
<center>
<img src = "images/plots-table.png" width = "800">
</center>
]

---
class: inverse

# Practice doing EDA

1) Read in the candy_rankings.csv data sets

2) Preview the data, note the data types and what each variable is.

3) Visualize (at least) three _relationships_ between two variables (guided by a question) using an appropriate chart:

- Bar chart
- Scatterplot
- Boxplot

---
class: center, middle, inverse

# Start thinking about research questions

---

# Writing a research question

Follow [these guidelines](https://writingcenter.gmu.edu/guides/how-to-write-a-research-question) - your question should be:

- **Clear**: your audience can easily understand its purpose without additional explanation.

- **Focused**: it is narrow enough that it can be addressed thoroughly with the data available and within the limits of the final project report.

- **Concise**: it is expressed in the fewest possible words.

- **Complex**: it is not answerable with a simple "yes" or "no," but rather requires synthesis and analysis of data.

- **Arguable**: its potential answers are open to debate rather than accepted facts (do others care about it?)

---

# Writing a research question

**Bad question: Why are social networking sites harmful?**

- Unclear: it does not specify _which_ social networking sites or state what harm is being caused; assumes that "harm" exists.

**Improved question: How are online users experiencing or addressing privacy issues on such social networking sites as Facebook and Twitter?**

- Specifies the sites (Facebook and Twitter), type of harm (privacy issues), and who is harmed (online users).

**Other good examples**: See the [Example Projects Page](https://eda.seas.gwu.edu/2021-Spring/ref-example-analyses.html) page

---

# Start self-organizing for projects

> Find your topic / teammate(s) [here](https://docs.google.com/presentation/d/15ohFg5a9y6ZMk5tGGm4ho7Rj97eVTgcBwgVac5W-Yzc/edit?usp=sharing) (link also in #classroom)