R for MTH107

# R for MTH107

- [Getting Data into R](#RData)
- [Filtering Data in R](#RFilter)
- [Univariate EDA in R](#RUnivEDA)
  - [Quantitative](#RUnivEDAQ)
  - [Categorical](#RUnivEDAC)
  - [Quantitative by Group](#RUnivEDAQC)
- [Bivariate EDA in R](#RBivEDA)
  - [Quantitative](#RBivEDAQ)
  - [Categorical](#RBivEDAC)
- [Linear Regression in R](#RRegression)
- [t-Tests in R](#Rttests)
  - [1-sample t-Test in R](#Rttests1)
  - [2-sample t-Test in R](#Rttests2)
- [Chi-square in R](#RChi)
  - [Chi-square Test in R](#RChiChi)
  - [Goodness-of-Fit Test in R](#RChiGOF)

---

# Load Important Packages

---

## Load Important Packages

- Many calculations in this course require functions in the `NCStats` package.

--
- Nearly all plots in this course require functions in the `ggplot2` package.

&nbsp;

--
- Thus, these packages **MUST** be loaded at the beginning of each session.

```r
#!# Loading important packages ... must do every time
library(NCStats)
library(ggplot2)
```

---

---

# Loading Data into R

---

## Introducing the Data

- Size (bill, flipper, weight) of three Penguin species from three islands in Antarctica.

--
- Collected by [Dr. Kristen Gorman](https://www.uaf.edu/cfos/people/faculty/detail/kristen-gorman.php) and the [Palmer Station, Antarctica LTER](https://pal.lternet.edu/).

---

## Introducing the Data

- Size (bill, flipper, weight) of three Penguin species from three islands in Antarctica.
- Collated by [Allison Horst](https://www.allisonhorst.com/).

---

## Introducing the Data

- Size (bill, flipper, weight) of three Penguin species from three islands in Antarctica.
- Data in [Penguins.csv](https://raw.githubusercontent.com/allisonhorst/penguins/master/data-raw/penguins.csv) on the class' [data webpage](http://derekogle.com/NCMTH107/resources/data_107).

---

## Loading Data into R

1. Download or save data (CSV file) to folder on your computer.
  - Shown in a separate video for both data you must enter and for a data file that is provided to you.

--
1. Start an R script with code for `NCStats` and `ggplot2` packages.

--
1. Save script in **same folder** with the data file.

--
1. Use `Session`, `Set working directory`, `To source file location` to set the working directory (where the data file is located).

--
1. Copy resultant `setwd()` from console and paste into script.

--
1. Use `read.csv()` with filename in quotes to load data into R.
  - Should be assigned to a short object name (what data is called in R).

--
1. Examine data object.
  - Use `str()` to see the structure.
  - Use `peek()` to see a subset of rows/individuals.

---

```r
#!# Set to your OWN working directory ... this is Derek's computer.
*setwd("C:/aaaWork/Web/GitHub/NCMTH107/modules/HO")
```
]
 
.right-panel-loaddata-user[

]

---
count: false
 
## Loading Data into R
.left-panel-loaddata-user[

```r
#!# Set to your OWN working directory ... this is Derek's computer.
setwd("C:/aaaWork/Web/GitHub/NCMTH107/modules/HO")  
*peng <- read.csv("penguins.csv")
```
]
 
.right-panel-loaddata-user[

]

---
count: false
 
## Loading Data into R
.left-panel-loaddata-user[

```r
#!# Set to your OWN working directory ... this is Derek's computer.
setwd("C:/aaaWork/Web/GitHub/NCMTH107/modules/HO")  
peng <- read.csv("penguins.csv")  
*str(peng)
```
]
 
.right-panel-loaddata-user[

```
'data.frame':	344 obs. of  7 variables:
 $ species          : chr  "Adelie" "Adelie" "Adelie" "Adelie" ...
 $ island           : chr  "Torgersen" "Torgersen" "Torgersen" "Torgersen" ...
 $ bill_length_mm   : num  39.1 39.5 40.3 NA 36.7 39.3 38.9 39.2 34.1 42 ...
 $ bill_depth_mm    : num  18.7 17.4 18 NA 19.3 20.6 17.8 19.6 18.1 20.2 ...
 $ flipper_length_mm: int  181 186 195 NA 193 190 181 195 193 190 ...
 $ body_mass_g      : int  3750 3800 3250 NA 3450 3650 3625 4675 3475 4250 ...
 $ sex              : chr  "male" "female" "female" NA ...
```
]

---
count: false
 
## Loading Data into R
.left-panel-loaddata-user[

```r
#!# Set to your OWN working directory ... this is Derek's computer.
setwd("C:/aaaWork/Web/GitHub/NCMTH107/modules/HO")  
peng <- read.csv("penguins.csv")  
str(peng)  
*peek(peng)
```
]
 
.right-panel-loaddata-user[

```
      species    island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1      Adelie Torgersen           39.1          18.7               181        3750   male
18     Adelie Torgersen           42.5          20.7               197        4500   male
36     Adelie     Dream           39.2          21.1               196        4150   male
54     Adelie    Biscoe           42.0          19.5               200        4050   male
72     Adelie Torgersen           39.7          18.4               190        3900   male
91     Adelie     Dream           35.7          18.0               202        3550 female
109    Adelie    Biscoe           38.1          17.0               181        3175 female
127    Adelie Torgersen           38.8          17.6               191        3275 female
145    Adelie     Dream           37.3          16.8               192        3000 female
163    Gentoo    Biscoe           40.9          13.7               214        4650 female
181    Gentoo    Biscoe           48.2          14.3               210        4600 female
199    Gentoo    Biscoe           45.5          13.9               210        4200 female
217    Gentoo    Biscoe           45.8          14.2               219        4700 female
235    Gentoo    Biscoe           47.4          14.6               212        4725 female
253    Gentoo    Biscoe           48.5          15.0               219        4850 female
272    Gentoo    Biscoe             NA            NA                NA          NA   <NA>
290 Chinstrap     Dream           52.0          18.1               201        4050   male
308 Chinstrap     Dream           54.2          20.8               201        4300   male
326 Chinstrap     Dream           49.8          17.3               198        3675 female
344 Chinstrap     Dream           50.2          18.7               198        3775 female
```
]

---

---

# Filtering Data

---

## Isolate Single Variable

- Examine one variable in a data frame.

&nbsp;

--
- use `dataframename$variablename`

---

```r
*headtail(peng)

## Examine just the body mass variable
```
]
 
.right-panel-filterBM-user[

```
      species    island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1      Adelie Torgersen           39.1          18.7               181        3750   male
2      Adelie Torgersen           39.5          17.4               186        3800 female
3      Adelie Torgersen           40.3          18.0               195        3250 female
342 Chinstrap     Dream           49.6          18.2               193        3775   male
343 Chinstrap     Dream           50.8          19.0               210        4100   male
344 Chinstrap     Dream           50.2          18.7               198        3775 female
```
]

---
count: false
 
## Isolate Variable
.left-panel-filterBM-user[

```r
headtail(peng)

## Examine just the body mass variable

*peng$body_mass_g
```
]
 
.right-panel-filterBM-user[

```
  [1] 3750 3800 3250   NA 3450 3650 3625 4675 3475 4250 3300 3700 3200 3800 4400 3700 3450 4500 3325 4200 3400 3600 3800
 [24] 3950 3800 3800 3550 3200 3150 3950 3250 3900 3300 3900 3325 4150 3950 3550 3300 4650 3150 3900 3100 4400 3000 4600
 [47] 3425 2975 3450 4150 3500 4300 3450 4050 2900 3700 3550 3800 2850 3750 3150 4400 3600 4050 2850 3950 3350 4100 3050
 [70] 4450 3600 3900 3550 4150 3700 4250 3700 3900 3550 4000 3200 4700 3800 4200 3350 3550 3800 3500 3950 3600 3550 4300
 [93] 3400 4450 3300 4300 3700 4350 2900 4100 3725 4725 3075 4250 2925 3550 3750 3900 3175 4775 3825 4600 3200 4275 3900
[116] 4075 2900 3775 3350 3325 3150 3500 3450 3875 3050 4000 3275 4300 3050 4000 3325 3500 3500 4475 3425 3900 3175 3975
[139] 3400 4250 3400 3475 3050 3725 3000 3650 4250 3475 3450 3750 3700 4000 4500 5700 4450 5700 5400 4550 4800 5200 4400
[162] 5150 4650 5550 4650 5850 4200 5850 4150 6300 4800 5350 5700 5000 4400 5050 5000 5100 4100 5650 4600 5550 5250 4700
[185] 5050 6050 5150 5400 4950 5250 4350 5350 3950 5700 4300 4750 5550 4900 4200 5400 5100 5300 4850 5300 4400 5000 4900
[208] 5050 4300 5000 4450 5550 4200 5300 4400 5650 4700 5700 4650 5800 4700 5550 4750 5000 5100 5200 4700 5800 4600 6000
[231] 4750 5950 4625 5450 4725 5350 4750 5600 4600 5300 4875 5550 4950 5400 4750 5650 4850 5200 4925 4875 4625 5250 4850
[254] 5600 4975 5500 4725 5500 4700 5500 4575 5500 5000 5950 4650 5500 4375 5850 4875 6000 4925   NA 4850 5750 5200 5400
[277] 3500 3900 3650 3525 3725 3950 3250 3750 4150 3700 3800 3775 3700 4050 3575 4050 3300 3700 3450 4400 3600 3400 2900
[300] 3800 3300 4150 3400 3800 3700 4550 3200 4300 3350 4100 3600 3900 3850 4800 2700 4500 3950 3650 3550 3500 3675 4450
[323] 3400 4300 3250 3675 3325 3950 3600 4050 3350 3450 3250 4050 3800 3525 3950 3650 3650 4000 3400 3775 4100 3775
```
]

---

## Filtering Data

- Create a subset of a larger data.frame based on a condition or conditions.

&nbsp;

--
- Use `filterD()`
  - First argument is larger data.frame.
  - Following arguments are conditions.

--
  - Assign (save) result to a new object (i.e., name for subsetted data.frame).
  
---

## Filtering Data

Table: Comparison operators used in `filterD()` and their results.

|Comparison Operator          |Rows Returned from Original Data Frame                   |
|:----------------------------|:--------------------------------------------------------|
|`var==value`                 |Rows where `var` **IS equal** to `value`                 |
|`var!=value`                 |Rows where `var` **is NOT equal** to `value`             |
|`var %in% c(value1,value2)`  |Rows where `var` **IS IN** vector of `value`s            |
|`var>value`                  |Rows where `var` is **greater than** `value`             |
|`var>=value`                 |Rows where `var` is **greater than or equal to** `value` |
|`var<value`                  |Rows where `var` is **less than** `value`                |
|`var<=value`                 |Rows where `var` is **less than or equal to** `value`    |
|condition1,condition2        |Rows where **BOTH** conditions are true                  |
|condition1 &#124; condition2 |Rows where **ONE or BOTH** conditions are true           |

---

```r
*headtail(peng)
```
]
 
.right-panel-filter1-auto[

---
count: false
 
## Filtering Data
.left-panel-filter1-auto[

```r
headtail(peng)  
*unique(peng$species)
```
]
 
.right-panel-filter1-auto[

```
[1] "Adelie"    "Gentoo"    "Chinstrap"
```
]

---
count: false
 
## Filtering Data
.left-panel-filter1-auto[

```r
headtail(peng)  
unique(peng$species)

## Isolate just Chinstrap Penguins
*peng_chin <- filterD(peng,species=="Chinstrap")
```
]
 
.right-panel-filter1-auto[

```
[1] "Adelie"    "Gentoo"    "Chinstrap"
```
]

---
count: false
 
## Filtering Data
.left-panel-filter1-auto[

```r
headtail(peng)  
unique(peng$species)

## Isolate just Chinstrap Penguins
peng_chin <- filterD(peng,species=="Chinstrap")  
*peek(peng_chin)
```
]
 
.right-panel-filter1-auto[

```
[1] "Adelie"    "Gentoo"    "Chinstrap"
```

```
     species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1  Chinstrap  Dream           46.5          17.9               192        3500 female
4  Chinstrap  Dream           45.4          18.7               188        3525 female
7  Chinstrap  Dream           46.1          18.2               178        3250 female
11 Chinstrap  Dream           46.6          17.8               193        3800 female
14 Chinstrap  Dream           52.0          18.1               201        4050   male
18 Chinstrap  Dream           58.0          17.8               181        3700 female
21 Chinstrap  Dream           42.4          17.3               181        3600 female
25 Chinstrap  Dream           46.7          17.9               195        3300 female
29 Chinstrap  Dream           46.4          17.8               191        3700 female
32 Chinstrap  Dream           54.2          20.8               201        4300   male
36 Chinstrap  Dream           47.5          16.8               199        3900 female
39 Chinstrap  Dream           46.9          16.6               192        2700 female
43 Chinstrap  Dream           50.9          19.1               196        3550   male
47 Chinstrap  Dream           50.1          17.9               190        3400 female
50 Chinstrap  Dream           49.8          17.3               198        3675 female
54 Chinstrap  Dream           50.7          19.7               203        4050   male
57 Chinstrap  Dream           45.2          16.6               191        3250 female
61 Chinstrap  Dream           51.9          19.5               206        3950   male
64 Chinstrap  Dream           55.8          19.8               207        4000   male
68 Chinstrap  Dream           50.2          18.7               198        3775 female
```
]

---

```r
*headtail(peng)
*unique(peng$species)

## Isolate just Chinstrap and Gentoo Penguins
```
]
 
.right-panel-filter2-user[

```
[1] "Adelie"    "Gentoo"    "Chinstrap"
```
]

---
count: false
 
## Filtering Data
.left-panel-filter2-user[

```r
headtail(peng)  
unique(peng$species)

## Isolate just Chinstrap and Gentoo Penguins

*peng_chingen <- filterD(peng,species %in% c("Chinstrap","Gentoo"))
```
]
 
.right-panel-filter2-user[

```
[1] "Adelie"    "Gentoo"    "Chinstrap"
```
]

---
count: false
 
## Filtering Data
.left-panel-filter2-user[

```r
headtail(peng)  
unique(peng$species)

## Isolate just Chinstrap and Gentoo Penguins

peng_chingen <- filterD(peng,species %in% c("Chinstrap","Gentoo"))  
*peek(peng_chingen)
```
]
 
.right-panel-filter2-user[

```
[1] "Adelie"    "Gentoo"    "Chinstrap"
```

```
      species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1      Gentoo Biscoe           46.1          13.2               211        4500 female
10     Gentoo Biscoe           46.8          15.4               215        5150   male
20     Gentoo Biscoe           48.7          15.1               222        5350   male
30     Gentoo Biscoe           50.0          15.3               220        5550   male
40     Gentoo Biscoe           48.7          15.7               208        5350   male
51     Gentoo Biscoe           46.6          14.2               210        4850 female
61     Gentoo Biscoe           45.3          13.8               208        4200 female
71     Gentoo Biscoe           47.7          15.0               216        4750 female
81     Gentoo Biscoe           49.1          14.5               212        4625 female
91     Gentoo Biscoe           47.5          15.0               218        4950 female
101    Gentoo Biscoe           48.5          15.0               219        4850 female
111    Gentoo Biscoe           50.5          15.2               216        5000 female
121    Gentoo Biscoe           46.8          14.3               215        4850 female
131 Chinstrap  Dream           46.1          18.2               178        3250 female
141 Chinstrap  Dream           50.3          20.0               197        3300   male
152 Chinstrap  Dream           49.5          19.0               200        3800   male
162 Chinstrap  Dream           52.0          20.7               210        4800   male
172 Chinstrap  Dream           49.0          19.6               212        4300   male
182 Chinstrap  Dream           49.3          19.9               203        4050   male
192 Chinstrap  Dream           50.2          18.7               198        3775 female
```
]

---

```r
*headtail(peng)

## Isolate just male Chinstrap Penguins
```
]
 
.right-panel-filter3-user[

---
count: false
 
## Filtering Data
.left-panel-filter3-user[

```r
headtail(peng)

## Isolate just male Chinstrap Penguins

*peng_chinmale <- filterD(peng,species=="Chinstrap",sex=="male")
```
]
 
.right-panel-filter3-user[

---
count: false
 
## Filtering Data
.left-panel-filter3-user[

```r
headtail(peng)

## Isolate just male Chinstrap Penguins

peng_chinmale <- filterD(peng,species=="Chinstrap",sex=="male")  
*peek(peng_chinmale)
```
]
 
.right-panel-filter3-user[

```
     species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g  sex
1  Chinstrap  Dream           50.0          19.5               196        3900 male
2  Chinstrap  Dream           51.3          19.2               193        3650 male
4  Chinstrap  Dream           51.3          18.2               197        3750 male
5  Chinstrap  Dream           51.3          19.9               198        3700 male
7  Chinstrap  Dream           52.0          18.1               201        4050 male
9  Chinstrap  Dream           50.3          20.0               197        3300 male
11 Chinstrap  Dream           48.5          17.5               191        3400 male
13 Chinstrap  Dream           52.0          19.0               197        4150 male
14 Chinstrap  Dream           49.5          19.0               200        3800 male
16 Chinstrap  Dream           54.2          20.8               201        4300 male
18 Chinstrap  Dream           49.7          18.6               195        3600 male
20 Chinstrap  Dream           53.5          19.9               205        4500 male
21 Chinstrap  Dream           49.0          19.5               210        3950 male
23 Chinstrap  Dream           50.8          18.5               201        4450 male
25 Chinstrap  Dream           51.5          18.7               187        3250 male
27 Chinstrap  Dream           50.7          19.7               203        4050 male
29 Chinstrap  Dream           49.3          19.9               203        4050 male
30 Chinstrap  Dream           50.2          18.8               202        3800 male
32 Chinstrap  Dream           55.8          19.8               207        4000 male
34 Chinstrap  Dream           50.8          19.0               210        4100 male
```
]

---

```r
*headtail(peng)

## Isolate just Penguins with body mass more than 5900 g ... ~13 lbs
```
]
 
.right-panel-filterHvy-user[

---
count: false
 
## Filtering Data
.left-panel-filterHvy-user[

```r
headtail(peng)

## Isolate just Penguins with body mass more than 5900 g ... ~13 lbs

*peng_heavy <- filterD(peng,body_mass_g>5900)
```
]
 
.right-panel-filterHvy-user[

---
count: false
 
## Filtering Data
.left-panel-filterHvy-user[

```r
headtail(peng)

## Isolate just Penguins with body mass more than 5900 g ... ~13 lbs

peng_heavy <- filterD(peng,body_mass_g>5900)  
*peek(peng_heavy)
```
]
 
.right-panel-filterHvy-user[

```
  species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g  sex
1  Gentoo Biscoe           49.2          15.2               221        6300 male
2  Gentoo Biscoe           59.6          17.0               230        6050 male
3  Gentoo Biscoe           51.1          16.3               220        6000 male
4  Gentoo Biscoe           45.2          16.4               223        5950 male
5  Gentoo Biscoe           49.8          15.9               229        5950 male
6  Gentoo Biscoe           48.8          16.2               222        6000 male
```
]

---

```r
*headtail(peng)

## Isolate Penguins with body masses b/w 4500 and 5000 g
```
]
 
.right-panel-filterWt2-user[

---
count: false
 
## Filtering Data
.left-panel-filterWt2-user[

```r
headtail(peng)

## Isolate Penguins with body masses b/w 4500 and 5000 g

*peng_wt <- filterD(peng,body_mass_g>4500,body_mass_g<5000)
```
]
 
.right-panel-filterWt2-user[

---
count: false
 
## Filtering Data
.left-panel-filterWt2-user[

```r
headtail(peng)

## Isolate Penguins with body masses b/w 4500 and 5000 g

peng_wt <- filterD(peng,body_mass_g>4500,body_mass_g<5000)  
*peek(peng_wt)
```
]
 
.right-panel-filterWt2-user[

```
     species    island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1     Adelie Torgersen           39.2          19.6               195        4675   male
3     Adelie     Dream           39.6          18.8               190        4600   male
5     Adelie    Biscoe           41.0          20.0               203        4725   male
8     Gentoo    Biscoe           46.5          13.5               210        4550 female
10    Gentoo    Biscoe           40.9          13.7               214        4650 female
13    Gentoo    Biscoe           48.2          14.3               210        4600 female
15    Gentoo    Biscoe           42.6          13.7               213        4950 female
18    Gentoo    Biscoe           46.6          14.2               210        4850 female
20    Gentoo    Biscoe           45.8          14.2               219        4700 female
23    Gentoo    Biscoe           47.7          15.0               216        4750 female
25    Gentoo    Biscoe           47.5          14.2               209        4600 female
28    Gentoo    Biscoe           47.4          14.6               212        4725 female
30    Gentoo    Biscoe           43.4          14.4               218        4600 female
33    Gentoo    Biscoe           45.5          14.5               212        4750 female
35    Gentoo    Biscoe           49.4          15.8               216        4925   male
38    Gentoo    Biscoe           48.5          15.0               219        4850 female
40    Gentoo    Biscoe           47.3          13.8               216        4725   <NA>
43    Gentoo    Biscoe           43.5          15.2               213        4650 female
45    Gentoo    Biscoe           47.2          13.7               214        4925 female
48 Chinstrap     Dream           52.0          20.7               210        4800   male
```
]

---

---

# Univariate EDA in R

---

## Univariate EDA - Quantitative
### Summary Statistics

- Computed with `Summarize()`
  - Uses formula of the form `~qvar` as first argument.

--
  - Must include data.frame name in `data=` argument.

--
  - Optionally set number of decimals with `digits=`.

---

```r
*headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins
```
]
 
.right-panel-UnivEDAQsum-user[

```
     species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1  Chinstrap  Dream           46.5          17.9               192        3500 female
2  Chinstrap  Dream           50.0          19.5               196        3900   male
3  Chinstrap  Dream           51.3          19.2               193        3650   male
66 Chinstrap  Dream           49.6          18.2               193        3775   male
67 Chinstrap  Dream           50.8          19.0               210        4100   male
68 Chinstrap  Dream           50.2          18.7               198        3775 female
```
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQsum-user[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

*Summarize(~flipper_length_mm,data=peng_chin,digits=1)
```
]
 
.right-panel-UnivEDAQsum-user[

```
     n   mean     sd    min     Q1 median     Q3    max 
  68.0  195.8    7.1  178.0  191.0  196.0  201.0  212.0 
```
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQsum-user[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

Summarize(~flipper_length_mm,data=peng_chin,digits=1)

## Distribution of bill lengths for Chinstrap Penguins
```
]
 
.right-panel-UnivEDAQsum-user[

```
     n   mean     sd    min     Q1 median     Q3    max 
  68.0  195.8    7.1  178.0  191.0  196.0  201.0  212.0 
```
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQsum-user[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

Summarize(~flipper_length_mm,data=peng_chin,digits=1)

## Distribution of bill lengths for Chinstrap Penguins

*Summarize(~bill_length_mm,data=peng_chin,digits=2)
```
]
 
.right-panel-UnivEDAQsum-user[

```
     n   mean     sd    min     Q1 median     Q3    max 
  68.0  195.8    7.1  178.0  191.0  196.0  201.0  212.0 
```

```
     n   mean     sd    min     Q1 median     Q3    max 
 68.00  48.83   3.34  40.90  46.35  49.55  51.08  58.00 
```
]

---

## Univariate EDA - Quantitative
### Histogram

- Use `ggplot()` to declare data.
  - Must include data.frame name in `data=` argument.

--
  - Set `x=` to variable names in `mapping=aes()`.

--
- "Add on" `geom_histogram()` with
  - `binwidth=` to set bin width.

--
  - `boundary=0` for start of bins.

--
  - `color=` and `fill=` to set bar outline and fill colors.

--
- Clean up with ...
  - `labs()` to label axes,

--
  - `scale_y_continuous(expand=expansion(mult=c(0,0.05)))` to "sit" bars on x-axis, and

--
  - `theme_NCStats()` to make look nice.

---

count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins
```
]
 
.right-panel-UnivEDAQhist-non_seq[

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

*ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm))
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_2_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
* geom_histogram(
* )
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_3_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(  
*   binwidth=5,boundary=0,
  )   
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_4_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(  
    binwidth=5,boundary=0,  
*   color="black",fill="lightgray"
  )   
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_5_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(  
    binwidth=5,boundary=0,  
    color="black",fill="lightgray"  
  ) +  
* labs(x="Flipper Length (mm)",y="Frequency of Penguins")
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_6_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(  
    binwidth=5,boundary=0,  
    color="black",fill="lightgray"  
  ) +  
  labs(x="Flipper Length (mm)",y="Frequency of Penguins") +  
* scale_y_continuous(expand=expansion(mult=c(0,0.05)))
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_7_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist-non_seq[

```r
headtail(peng_chin)

## Distribution of flipper lengths for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(  
    binwidth=5,boundary=0,  
    color="black",fill="lightgray"  
  ) +  
  labs(x="Flipper Length (mm)",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
* theme_NCStats()
```
]
 
.right-panel-UnivEDAQhist-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQhist_non_seq_8_output-1.png" width="100%" />
]

---

count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist2A-rotate[

```r
headtail(peng_chin)

## Distribution of bill lengths for Chinstrap Penguins
ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(binwidth=5,boundary=0,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQhist2A-rotate[

<img src="Penguins_files/figure-html/UnivEDAQhist2A_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist2A-rotate[

```r
headtail(peng_chin)

## Distribution of bill lengths for Chinstrap Penguins
*ggplot(data=peng_chin,mapping=aes(x=bill_length_mm)) +
  geom_histogram(binwidth=5,boundary=0,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQhist2A-rotate[

<img src="Penguins_files/figure-html/UnivEDAQhist2A_rotate_2_output-1.png" width="100%" />
]

---

count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist2B-rotate[

```r
headtail(peng_chin)

## Distribution of bill lengths for Chinstrap Penguins
ggplot(data=peng_chin,mapping=aes(x=bill_length_mm)) +  
  geom_histogram(binwidth=5,boundary=0,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQhist2B-rotate[

<img src="Penguins_files/figure-html/UnivEDAQhist2B_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist2B-rotate[

```r
headtail(peng_chin)

## Distribution of bill lengths for Chinstrap Penguins
ggplot(data=peng_chin,mapping=aes(x=bill_length_mm)) +  
  geom_histogram(binwidth=5,boundary=0,color="black",fill="lightgray") +  
* labs(x="Bill Length (mm)",y="Frequency of Penguins") +
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQhist2B-rotate[

<img src="Penguins_files/figure-html/UnivEDAQhist2B_rotate_2_output-1.png" width="100%" />
]

---

count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist2C-rotate[

```r
headtail(peng_chin)

## Distribution of bill lengths for Chinstrap Penguins
ggplot(data=peng_chin,mapping=aes(x=bill_length_mm)) +  
  geom_histogram(binwidth=5,boundary=0,color="black",fill="lightgray") +  
  labs(x="Bill Length (mm)",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQhist2C-rotate[

<img src="Penguins_files/figure-html/UnivEDAQhist2C_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Quantitative
.left-panel-UnivEDAQhist2C-rotate[

```r
headtail(peng_chin)

## Distribution of bill lengths for Chinstrap Penguins
ggplot(data=peng_chin,mapping=aes(x=bill_length_mm)) +  
* geom_histogram(binwidth=2,boundary=0,color="black",fill="lightgray") +
  labs(x="Bill Length (mm)",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQhist2C-rotate[

<img src="Penguins_files/figure-html/UnivEDAQhist2C_rotate_2_output-1.png" width="100%" />
]

---

## Univariate EDA - Categorical
### Frequency Tables

- Computed with `xtabs()`
  - Uses formula of the form `~cvar` as first argument.

--
  - Must include data.frame name in `data=` argument.

--
  - Assign (save) result to object.

---

```r
*headtail(peng)

## Species composition
```
]
 
.right-panel-UnivEDACsum-user[

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACsum-user[

```r
headtail(peng)

## Species composition

*( freqSpec <- xtabs(~species,data=peng) )

## Samplings by island
```
]
 
.right-panel-UnivEDACsum-user[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACsum-user[

```r
headtail(peng)

## Species composition

( freqSpec <- xtabs(~species,data=peng) )

## Samplings by island

*( freqIsland <- xtabs(~island,data=peng) )

## Sex distribution
```
]
 
.right-panel-UnivEDACsum-user[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACsum-user[

```r
headtail(peng)

## Species composition

( freqSpec <- xtabs(~species,data=peng) )

## Samplings by island

( freqIsland <- xtabs(~island,data=peng) )

## Sex distribution

*( freqSex <- xtabs(~sex,data=peng) )
```
]
 
.right-panel-UnivEDACsum-user[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```

```
sex
female   male 
   165    168 
```
]

---

## Univariate EDA - Categorical
### Percentage Tables

- Computed with `percTable()`
  - Uses saved `xtabs()` object as first argument.

---

```r
*freqSpec
```
]
 
.right-panel-UnivEDACsump-auto[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACsump-auto[

```r
freqSpec  
*percTable(freqSpec)
```
]
 
.right-panel-UnivEDACsump-auto[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```

```
species
   Adelie Chinstrap    Gentoo 
     44.2      19.8      36.0 
```
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACsump-auto[

```r
freqSpec  
percTable(freqSpec)

*freqIsland
```
]
 
.right-panel-UnivEDACsump-auto[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```

```
species
   Adelie Chinstrap    Gentoo 
     44.2      19.8      36.0 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACsump-auto[

```r
freqSpec  
percTable(freqSpec)

freqIsland  
*percTable(freqIsland)
```
]
 
.right-panel-UnivEDACsump-auto[

```
species
   Adelie Chinstrap    Gentoo 
      152        68       124 
```

```
species
   Adelie Chinstrap    Gentoo 
     44.2      19.8      36.0 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```

```
island
   Biscoe     Dream Torgersen 
     48.8      36.0      15.1 
```
]

---

## Univariate EDA - Categorical
### Bar Chart

- Use `ggplot()` to declare data.
  - Must include data.frame name in `data=` argument.
  - Set `x=` to variable names in `mapping=aes()`.

--
- Add on `geom_bar()` with
  - `color=` and `fill=` to set bar outline and fill colors.

--
- Clean up with ...
  - `labs()` to label axes
  - `scale_y_continuous(expand=expansion(mult=c(0,0.05)))` to "sit" bars on x-axis, and
  - `theme_NCStats()` to make look nice.

---

```r
headtail(peng)

## Species composition
```
]
 
.right-panel-UnivEDACbar-non_seq[

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar-non_seq[

```r
headtail(peng)

## Species composition
*ggplot(data=peng,mapping=aes(x=species))
```
]
 
.right-panel-UnivEDACbar-non_seq[

<img src="Penguins_files/figure-html/UnivEDACbar_non_seq_2_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar-non_seq[

```r
headtail(peng)

## Species composition
ggplot(data=peng,mapping=aes(x=species)) +  
* geom_bar(
* )
```
]
 
.right-panel-UnivEDACbar-non_seq[

<img src="Penguins_files/figure-html/UnivEDACbar_non_seq_3_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar-non_seq[

```r
headtail(peng)

## Species composition
ggplot(data=peng,mapping=aes(x=species)) +  
  geom_bar(  
*   color="black",fill="lightgray"
  )   
```
]
 
.right-panel-UnivEDACbar-non_seq[

<img src="Penguins_files/figure-html/UnivEDACbar_non_seq_4_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar-non_seq[

```r
headtail(peng)

## Species composition
ggplot(data=peng,mapping=aes(x=species)) +  
  geom_bar(  
    color="black",fill="lightgray"  
  ) +  
* labs(x="Species",y="Frequency of Penguins")
```
]
 
.right-panel-UnivEDACbar-non_seq[

<img src="Penguins_files/figure-html/UnivEDACbar_non_seq_5_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar-non_seq[

```r
headtail(peng)

## Species composition
ggplot(data=peng,mapping=aes(x=species)) +  
  geom_bar(  
    color="black",fill="lightgray"  
  ) +  
  labs(x="Species",y="Frequency of Penguins") +  
* scale_y_continuous(expand=expansion(mult=c(0,0.05)))
```
]
 
.right-panel-UnivEDACbar-non_seq[

<img src="Penguins_files/figure-html/UnivEDACbar_non_seq_6_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar-non_seq[

```r
headtail(peng)

## Species composition
ggplot(data=peng,mapping=aes(x=species)) +  
  geom_bar(  
    color="black",fill="lightgray"  
  ) +  
  labs(x="Species",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
* theme_NCStats()
```
]
 
.right-panel-UnivEDACbar-non_seq[

<img src="Penguins_files/figure-html/UnivEDACbar_non_seq_7_output-1.png" width="100%" />
]

---

```r
headtail(peng)

## Sampling by Island
ggplot(data=peng,mapping=aes(x=species)) +  
  geom_bar(color="black",fill="lightgray") +  
  labs(x="Species",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDACbar2A-rotate[

<img src="Penguins_files/figure-html/UnivEDACbar2A_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar2A-rotate[

```r
headtail(peng)

## Sampling by Island
*ggplot(data=peng,mapping=aes(x=island)) +
  geom_bar(color="black",fill="lightgray") +  
  labs(x="Species",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDACbar2A-rotate[

<img src="Penguins_files/figure-html/UnivEDACbar2A_rotate_2_output-1.png" width="100%" />
]

---

```r
headtail(peng)

## Sampling by Island
ggplot(data=peng,mapping=aes(x=island)) +  
  geom_bar(color="black",fill="lightgray") +  
  labs(x="Species",y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDACbar2B-rotate[

<img src="Penguins_files/figure-html/UnivEDACbar2B_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Univariate EDA - Categorical
.left-panel-UnivEDACbar2B-rotate[

```r
headtail(peng)

## Sampling by Island
ggplot(data=peng,mapping=aes(x=island)) +  
  geom_bar(color="black",fill="lightgray") +  
* labs(x="Island",y="Frequency of Penguins") +
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDACbar2B-rotate[

<img src="Penguins_files/figure-html/UnivEDACbar2B_rotate_2_output-1.png" width="100%" />
]

---

## Univariate EDA - Quant by Groups
### Summary Statistics

- Computed with `Summarize()`
  - Uses formula of the form `qvar~cvar` as first argument.

--
  - Must include data.frame name in `data=` argument.
  - Optionally set number of decimals with `digits=`.

---

```r
*headtail(peng)

## Distribution of flipper lengths by species
```
]
 
.right-panel-UnivEDAQsum2-user[

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species

*Summarize(flipper_length_mm~species,data=peng,digits=1)
```
]
 
.right-panel-UnivEDAQsum2-user[

```
    species   n nvalid  mean  sd min  Q1 median  Q3 max
1    Adelie 152    151 190.0 6.5 172 186    190 195 210
2 Chinstrap  68     68 195.8 7.1 178 191    196 201 212
3    Gentoo 124    123 217.2 6.5 203 212    216 221 231
```
]

---

## Univariate EDA - Quant by Groups
### Histogram

- Make a histogram exactly as before.

--
- Separate by groups by adding on `facet_wrap()`
  - Must include grouping variable name in `vars()` as first argument.

---

```r
*headtail(peng)

## Distribution of flipper lengths by species
```
]
 
.right-panel-UnivEDAQhist2-user[

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species

*ggplot(data=peng,mapping=aes(x=flipper_length_mm)) +
* geom_histogram(binwidth=5,boundary=0,
*                color="black",fill="lightgray") +
* labs(x="Flipper Length (mm)",
*      y="Frequency of Penguins") +
* scale_y_continuous(expand=expansion(mult=c(0,0.05))) +
* theme_NCStats()
```
]
 
.right-panel-UnivEDAQhist2-user[

<img src="Penguins_files/figure-html/UnivEDAQhist2_user_2_output-1.png" width="100%" />
]

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species

ggplot(data=peng,mapping=aes(x=flipper_length_mm)) +  
  geom_histogram(binwidth=5,boundary=0,  
                 color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",  
       y="Frequency of Penguins") +  
  scale_y_continuous(expand=expansion(mult=c(0,0.05))) +  
  theme_NCStats() +  
* facet_wrap(vars(species))
```
]
 
.right-panel-UnivEDAQhist2-user[

<img src="Penguins_files/figure-html/UnivEDAQhist2_user_3_output-1.png" width="100%" />
]

---

## Univariate EDA - Quant by Groups
### Boxplots

- Use `ggplot()` to declare data.
  - Must include data.frame name in `data=` argument.
  - Set `x=` (group) and `y=` (quantitative) to variable names in `mapping=aes()`.

--
- Add on `geom_boxplot()` with
  - `color=` and `fill=` to set point outline and fill colors.

--
- Clean up with ...
  - `labs()` to label axes
  - `theme_NCStats()` to make look nice.

---

```r
headtail(peng)

## Distribution of flipper lengths by species
```
]
 
.right-panel-UnivEDAQBoxplot-non_seq[

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species
*ggplot(data=peng,mapping=aes(x=species,y=flipper_length_mm))
```
]
 
.right-panel-UnivEDAQBoxplot-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot_non_seq_2_output-1.png" width="100%" />
]

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species
ggplot(data=peng,mapping=aes(x=species,y=flipper_length_mm)) +  
* geom_boxplot(color="black",fill="lightgray")
```
]
 
.right-panel-UnivEDAQBoxplot-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot_non_seq_3_output-1.png" width="100%" />
]

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species
ggplot(data=peng,mapping=aes(x=species,y=flipper_length_mm)) +  
  geom_boxplot(color="black",fill="lightgray") +  
* labs(x="Species",y="Flipper Length (mm)")
```
]
 
.right-panel-UnivEDAQBoxplot-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot_non_seq_4_output-1.png" width="100%" />
]

---
count: false

```r
headtail(peng)

## Distribution of flipper lengths by species
ggplot(data=peng,mapping=aes(x=species,y=flipper_length_mm)) +  
  geom_boxplot(color="black",fill="lightgray") +  
  labs(x="Species",y="Flipper Length (mm)") +  
* theme_NCStats()
```
]
 
.right-panel-UnivEDAQBoxplot-non_seq[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot_non_seq_5_output-1.png" width="100%" />
]

---

```r
headtail(peng)

## Distribution of bill lengths by species
ggplot(data=peng,mapping=aes(x=species,y=flipper_length_mm)) +  
  geom_boxplot(color="black",fill="lightgray") +  
  labs(x="Species",y="Flipper Length (mm)") +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQBoxplot2A-rotate[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot2A_rotate_1_output-1.png" width="100%" />
]

---
count: false

```r
headtail(peng)

## Distribution of bill lengths by species
*ggplot(data=peng,mapping=aes(x=species,y=bill_length_mm)) +
  geom_boxplot(color="black",fill="lightgray") +  
  labs(x="Species",y="Flipper Length (mm)") +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQBoxplot2A-rotate[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot2A_rotate_2_output-1.png" width="100%" />
]

---

```r
headtail(peng)

## Distribution of bill lengths by species
ggplot(data=peng,mapping=aes(x=species,y=bill_length_mm)) +  
  geom_boxplot(color="black",fill="lightgray") +  
  labs(x="Species",y="Flipper Length (mm)") +  
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQBoxplot2B-rotate[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot2B_rotate_1_output-1.png" width="100%" />
]

---
count: false

```r
headtail(peng)

## Distribution of bill lengths by species
ggplot(data=peng,mapping=aes(x=species,y=bill_length_mm)) +  
  geom_boxplot(color="black",fill="lightgray") +  
* labs(x="Species",y="Bill Length (mm)") +
  theme_NCStats()  
```
]
 
.right-panel-UnivEDAQBoxplot2B-rotate[

<img src="Penguins_files/figure-html/UnivEDAQBoxplot2B_rotate_2_output-1.png" width="100%" />
]

---

---

# Bivariate EDA in R

---

## Bivariate EDA - Quantitative
### Correlation Coefficient

- Computed with `corr()`
  - Uses formula of the form `~qvar1+qvar2` as first argument.

--
  - Must include data.frame name in `data=` argument.

--
  - Include `use="pairwise.complete.obs"` to remove any missing values.

---

```r
*headtail(peng_chin)

## Relationship between body mass & flipper length for Chinstrap Penguins
```
]
 
.right-panel-BivEDAQsum-user[

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQsum-user[

```r
headtail(peng_chin)

## Relationship between body mass & flipper length for Chinstrap Penguins

*corr(~body_mass_g+flipper_length_mm,data=peng_chin,
*    use="pairwise.complete.obs")
```
]
 
.right-panel-BivEDAQsum-user[

```
[1] 0.6415594
```
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQsum-user[

```r
headtail(peng_chin)

## Relationship between body mass & flipper length for Chinstrap Penguins

corr(~body_mass_g+flipper_length_mm,data=peng_chin,  
     use="pairwise.complete.obs")

## Relationship between body mass, flipper length, and bill sizes
```
]
 
.right-panel-BivEDAQsum-user[

```
[1] 0.6415594
```
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQsum-user[

```r
headtail(peng_chin)

## Relationship between body mass & flipper length for Chinstrap Penguins

corr(~body_mass_g+flipper_length_mm,data=peng_chin,  
     use="pairwise.complete.obs")

## Relationship between body mass, flipper length, and bill sizes

*corr(~body_mass_g+flipper_length_mm+bill_length_mm+bill_depth_mm,
*    data=peng_chin,use="pairwise.complete.obs",digits=3)
```
]
 
.right-panel-BivEDAQsum-user[

```
[1] 0.6415594
```

```
                  body_mass_g flipper_length_mm bill_length_mm bill_depth_mm
body_mass_g             1.000             0.642          0.514         0.604
flipper_length_mm       0.642             1.000          0.472         0.580
bill_length_mm          0.514             0.472          1.000         0.654
bill_depth_mm           0.604             0.580          0.654         1.000
```
]

---

## Bivariate EDA - Quantitative
### Scatterplot

- Use `ggplot()` to declare data.
  - Must include data.frame name in `data=` argument.
  - Set `x=` and `y=` to variable names in `mapping=aes()`.

--
- Add on `geom_point()` with
  - `pch=21` to make circle with border and fill color options.

--
  - `color=` and `fill=` to set point outline and fill colors.

--
- Clean up with ...
  - `labs()` to label axes
  - `theme_NCStats()` to make look nice.

---

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins
```
]
 
.right-panel-BivEDAQPlot-non_seq[

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot-non_seq[

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins

*ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g))
```
]
 
.right-panel-BivEDAQPlot-non_seq[

<img src="Penguins_files/figure-html/BivEDAQPlot_non_seq_2_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot-non_seq[

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
* geom_point(
* )
```
]
 
.right-panel-BivEDAQPlot-non_seq[

<img src="Penguins_files/figure-html/BivEDAQPlot_non_seq_3_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot-non_seq[

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(  
*   pch=21,
  )   
```
]
 
.right-panel-BivEDAQPlot-non_seq[

<img src="Penguins_files/figure-html/BivEDAQPlot_non_seq_4_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot-non_seq[

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(  
    pch=21,  
*   color="black",fill="lightgray"
  )   
```
]
 
.right-panel-BivEDAQPlot-non_seq[

<img src="Penguins_files/figure-html/BivEDAQPlot_non_seq_5_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot-non_seq[

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(  
    pch=21,  
    color="black",fill="lightgray"  
  ) +  
* labs(x="Flipper Length (mm)",y="Body Mass (g)")
```
]
 
.right-panel-BivEDAQPlot-non_seq[

<img src="Penguins_files/figure-html/BivEDAQPlot_non_seq_6_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot-non_seq[

```r
headtail(peng_chin)

## Relationship between body mass and flipper length for Chinstrap Penguins

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(  
    pch=21,  
    color="black",fill="lightgray"  
  ) +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
* theme_NCStats()
```
]
 
.right-panel-BivEDAQPlot-non_seq[

<img src="Penguins_files/figure-html/BivEDAQPlot_non_seq_7_output-1.png" width="100%" />
]

---

```r
headtail(peng)

## Relationship between bill depth and flipper length
ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats()  
```
]
 
.right-panel-BivEDAQPlot2A-rotate[

<img src="Penguins_files/figure-html/BivEDAQPlot2A_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot2A-rotate[

```r
headtail(peng)

## Relationship between bill depth and flipper length
*ggplot(data=peng,mapping=aes(x=flipper_length_mm,y=bill_depth_mm)) +
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats()  
```
]
 
.right-panel-BivEDAQPlot2A-rotate[

<img src="Penguins_files/figure-html/BivEDAQPlot2A_rotate_2_output-1.png" width="100%" />
]

---

```r
headtail(peng)

## Relationship between bill depth and flipper length
ggplot(data=peng,mapping=aes(x=flipper_length_mm,y=bill_depth_mm)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats()  
```
]
 
.right-panel-BivEDAQPlot2B-rotate[

<img src="Penguins_files/figure-html/BivEDAQPlot2B_rotate_1_output-1.png" width="100%" />
]

---
count: false
 
## Bivariate EDA - Quantitative
.left-panel-BivEDAQPlot2B-rotate[

```r
headtail(peng)

## Relationship between bill depth and flipper length
ggplot(data=peng,mapping=aes(x=flipper_length_mm,y=bill_depth_mm)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
* labs(x="Flipper Length (mm)",y="Bill Depth (mm)") +
  theme_NCStats()  
```
]
 
.right-panel-BivEDAQPlot2B-rotate[

<img src="Penguins_files/figure-html/BivEDAQPlot2B_rotate_2_output-1.png" width="100%" />
]

---

## Bivariate EDA - Categorical
### Frequency Tables

- Computed with `xtabs()`
  - Uses formula of the form `~cvarRow+cvarCol` as first argument.

--
  - Must include data.frame name in `data=` argument.
  - Assign (save) result to object.

&nbsp;

--
- Put saved `xtabs()` object in `addmargins()` to show totals.

---

```r
*headtail(peng)

## Species composition by island
```
]
 
.right-panel-BivEDACsum-user[

---
count: false

```r
headtail(peng)

## Species composition by island

*( freqIS <- xtabs(~island+species,data=peng) )
```
]
 
.right-panel-BivEDACsum-user[

```
           species
island      Adelie Chinstrap Gentoo
  Biscoe        44         0    124
  Dream         56        68      0
  Torgersen     52         0      0
```
]

---
count: false

```r
headtail(peng)

## Species composition by island

( freqIS <- xtabs(~island+species,data=peng) )

*addmargins(freqIS)
```
]
 
.right-panel-BivEDACsum-user[

```
           species
island      Adelie Chinstrap Gentoo
  Biscoe        44         0    124
  Dream         56        68      0
  Torgersen     52         0      0
```

```
           species
island      Adelie Chinstrap Gentoo Sum
  Biscoe        44         0    124 168
  Dream         56        68      0 124
  Torgersen     52         0      0  52
  Sum          152        68    124 344
```
]

---
count: false

```r
headtail(peng)

## Species composition by island

( freqIS <- xtabs(~island+species,data=peng) )

addmargins(freqIS)

## Sex distribution by species

*freqSS <- xtabs(~species+sex,data=peng)
*addmargins(freqSS)
```
]
 
.right-panel-BivEDACsum-user[

```
           species
island      Adelie Chinstrap Gentoo
  Biscoe        44         0    124
  Dream         56        68      0
  Torgersen     52         0      0
```

```
           species
island      Adelie Chinstrap Gentoo Sum
  Biscoe        44         0    124 168
  Dream         56        68      0 124
  Torgersen     52         0      0  52
  Sum          152        68    124 344
```

```
           sex
species     female male Sum
  Adelie        73   73 146
  Chinstrap     34   34  68
  Gentoo        58   61 119
  Sum          165  168 333
```
]

---

## Bivariate EDA - Categorical
### Percentage Tables

- Computed with `percTable()`
  - Uses saved `xtabs()` object as first argument.

--
  - Default is to make total percentages.

--
  - Use `margin=1` to make row percentages.
  - Use `margin=2` to make column percentages.

---

```r
## Frequency table
*addmargins(freqIS)
```
]
 
.right-panel-BivEDACsump-user[

---
count: false

```r
## Frequency table
addmargins(freqIS)

## Total percentages table
*percTable(freqIS)
```
]
 
.right-panel-BivEDACsump-user[

```
           species
island      Adelie Chinstrap Gentoo   Sum
  Biscoe      12.8       0.0   36.0  48.8
  Dream       16.3      19.8    0.0  36.1
  Torgersen   15.1       0.0    0.0  15.1
  Sum         44.2      19.8   36.0 100.0
```
]

---
count: false

```r
## Frequency table
addmargins(freqIS)

## Total percentages table
percTable(freqIS)

## Row percentages table
*percTable(freqIS,margin=1)
```
]
 
.right-panel-BivEDACsump-user[

```
           species
island      Adelie Chinstrap Gentoo   Sum
  Biscoe      12.8       0.0   36.0  48.8
  Dream       16.3      19.8    0.0  36.1
  Torgersen   15.1       0.0    0.0  15.1
  Sum         44.2      19.8   36.0 100.0
```

```
           species
island      Adelie Chinstrap Gentoo   Sum
  Biscoe      26.2       0.0   73.8 100.0
  Dream       45.2      54.8    0.0 100.0
  Torgersen  100.0       0.0    0.0 100.0
```
]

---
count: false

```r
## Frequency table
addmargins(freqIS)

## Total percentages table
percTable(freqIS)

## Row percentages table
percTable(freqIS,margin=1)

## Column percentages table
*percTable(freqIS,margin=2)
```
]
 
.right-panel-BivEDACsump-user[

```
           species
island      Adelie Chinstrap Gentoo   Sum
  Biscoe      26.2       0.0   73.8 100.0
  Dream       45.2      54.8    0.0 100.0
  Torgersen  100.0       0.0    0.0 100.0
```

```
           species
island      Adelie Chinstrap Gentoo
  Biscoe      28.9       0.0  100.0
  Dream       36.8     100.0    0.0
  Torgersen   34.2       0.0    0.0
  Sum         99.9     100.0  100.0
```
]

---

---

# Linear Regression in R

---

## Fitting Linear Regression

- Computed with `lm()`
  - Uses formula of the form `qvarResp~qvarExplan` as first argument.

--
  - Must include data.frame name in `data=` argument.
  - Assign (save) result to object.

&nbsp;

--
- Use `rSquared()` to compute r<sup>2</sup> value.

---

```r
*headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps
```
]
 
.right-panel-RegressionSum-user[

---
count: false
 
## Fitting Linear Regression
.left-panel-RegressionSum-user[

```r
headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps

*( slr <- lm(body_mass_g~flipper_length_mm,data=peng_chin) )
```
]
 
.right-panel-RegressionSum-user[

```
Coefficients:
      (Intercept)  flipper_length_mm  
         -3037.20              34.57  
```
]

---
count: false
 
## Fitting Linear Regression
.left-panel-RegressionSum-user[

```r
headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps

( slr <- lm(body_mass_g~flipper_length_mm,data=peng_chin) )  
*rSquared(slr)
```
]
 
.right-panel-RegressionSum-user[

```
Coefficients:
      (Intercept)  flipper_length_mm  
         -3037.20              34.57  
```

```
[1] 0.4115985
```
]

---

## Showing Best-Fit Line

- Make a scatterplot as usual

--
- Add line with `geom_smooth(method="lm",se=FALSE)`

---

```r
headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats()   
```
]
 
.right-panel-RegressionPlot-non_seq[

<img src="Penguins_files/figure-html/RegressionPlot_non_seq_1_output-1.png" width="100%" />
]

---
count: false
 
## Showing Best-Fit Line
.left-panel-RegressionPlot-non_seq[

```r
headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats() +  
* geom_smooth(
* )
```
]
 
.right-panel-RegressionPlot-non_seq[

<img src="Penguins_files/figure-html/RegressionPlot_non_seq_2_output-1.png" width="100%" />
]

---
count: false
 
## Showing Best-Fit Line
.left-panel-RegressionPlot-non_seq[

```r
headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats() +  
  geom_smooth(  
*   method="lm",
  )  
```
]
 
.right-panel-RegressionPlot-non_seq[

<img src="Penguins_files/figure-html/RegressionPlot_non_seq_3_output-1.png" width="100%" />
]

---
count: false
 
## Showing Best-Fit Line
.left-panel-RegressionPlot-non_seq[

```r
headtail(peng_chin)

## Can body mass be predicted from flipper length for Chinstraps

ggplot(data=peng_chin,mapping=aes(x=flipper_length_mm,y=body_mass_g)) +  
  geom_point(pch=21,color="black",fill="lightgray") +  
  labs(x="Flipper Length (mm)",y="Body Mass (g)") +  
  theme_NCStats() +  
  geom_smooth(  
    method="lm",  
*   se=FALSE
  )  
```
]
 
.right-panel-RegressionPlot-non_seq[

<img src="Penguins_files/figure-html/RegressionPlot_non_seq_4_output-1.png" width="100%" />
]

---

## Make a Prediction

- Use `predict()`
  - Saved `lm()` object is the first argument

--
  - Second argument is a data frame created with `data.frame()`, including the **EXACT** name of the explanatory variable set equal to the value for which to make the prediction

---

```r
*slr

## Predict body weight if flipper length is 195 mm
```
]
 
.right-panel-RegressionPredict-user[

```
Coefficients:
      (Intercept)  flipper_length_mm  
         -3037.20              34.57  
```
]

---
count: false
 
## Make a Prediction
.left-panel-RegressionPredict-user[

```r
slr

## Predict body weight if flipper length is 195 mm

*predict(slr,data.frame(flipper_length_mm=195))
```
]
 
.right-panel-RegressionPredict-user[

```
Coefficients:
      (Intercept)  flipper_length_mm  
         -3037.20              34.57  
```

```
       1 
3704.616 
```
]

---

---

# t-Tests in R

---

## 1-Sample t-Test

- Computed with `t.test()`

--
  - Use formula of form `~qvar` as first argument.

--
  - Must include data.frame name in `data=` argument.

--
  - Assign value in H<sub>0</sub> to `mu=`.

--
  - Choose H<sub>A</sub> direction in `alt=` with `"two.sided"` for "not equals", `"less"` for "less than", or `"greater"` for "greater than".

--
  - Set confidence level (1-&alpha;) in `conf.level=`

---

```r
headtail(peng_chin)

## Is mean flipper length of Chinstrap Penguins
##  greater than 190 mm.  Use alpha=0.01
```
]
 
.right-panel-ttest1-non_seq[

---
count: false
 
## 1-Sample t-Test
.left-panel-ttest1-non_seq[

```r
headtail(peng_chin)

## Is mean flipper length of Chinstrap Penguins
##  greater than 190 mm.  Use alpha=0.01

*t.test(~flipper_length_mm,data=peng_chin
*      )
```
]
 
.right-panel-ttest1-non_seq[

```
One Sample t-test with flipper_length_mm 
t = 226.4198, df = 67, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0 
95 percent confidence interval:
 194.0972 197.5498 
sample estimates:
mean of x 
 195.8235 
```
]

---
count: false
 
## 1-Sample t-Test
.left-panel-ttest1-non_seq[

```r
headtail(peng_chin)

## Is mean flipper length of Chinstrap Penguins
##  greater than 190 mm.  Use alpha=0.01

t.test(~flipper_length_mm,data=peng_chin  
*      ,mu=190
       )  
```
]
 
.right-panel-ttest1-non_seq[

```
One Sample t-test with flipper_length_mm 
t = 6.7334, df = 67, p-value = 4.531e-09
alternative hypothesis: true mean is not equal to 190 
95 percent confidence interval:
 194.0972 197.5498 
sample estimates:
mean of x 
 195.8235 
```
]

---
count: false
 
## 1-Sample t-Test
.left-panel-ttest1-non_seq[

```r
headtail(peng_chin)

## Is mean flipper length of Chinstrap Penguins
##  greater than 190 mm.  Use alpha=0.01

t.test(~flipper_length_mm,data=peng_chin  
       ,mu=190  
*      ,alt="greater"
       )  
```
]
 
.right-panel-ttest1-non_seq[

```
One Sample t-test with flipper_length_mm 
t = 6.7334, df = 67, p-value = 2.265e-09
alternative hypothesis: true mean is greater than 190 
95 percent confidence interval:
 194.381     Inf 
sample estimates:
mean of x 
 195.8235 
```
]

---
count: false
 
## 1-Sample t-Test
.left-panel-ttest1-non_seq[

```r
headtail(peng_chin)

## Is mean flipper length of Chinstrap Penguins
##  greater than 190 mm.  Use alpha=0.01

t.test(~flipper_length_mm,data=peng_chin  
       ,mu=190  
       ,alt="greater"  
*      ,conf.level=0.99
       )  
```
]
 
.right-panel-ttest1-non_seq[

```
One Sample t-test with flipper_length_mm 
t = 6.7334, df = 67, p-value = 2.265e-09
alternative hypothesis: true mean is greater than 190 
99 percent confidence interval:
 193.7623      Inf 
sample estimates:
mean of x 
 195.8235 
```
]

---

## Levene's Test

- Computed with `levenesTest()`

--
  - Use form of form `qvar~cvar` as first argument.

--
  - Must include data.frame name in `data=` argument.

---

```r
*headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.
```
]
 
.right-panel-LevenesTest-user[

```
      species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g    sex
1      Gentoo Biscoe           46.1          13.2               211        4500 female
2      Gentoo Biscoe           50.0          16.3               230        5700   male
3      Gentoo Biscoe           48.7          14.1               210        4450 female
190 Chinstrap  Dream           49.6          18.2               193        3775   male
191 Chinstrap  Dream           50.8          19.0               210        4100   male
192 Chinstrap  Dream           50.2          18.7               198        3775 female
```
]

---
count: false
 
## Levene's Test
.left-panel-LevenesTest-user[

```r
headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.

*levenesTest(flipper_length_mm~species,data=peng_chingen)
```
]
 
.right-panel-LevenesTest-user[

```
Levene's Test for Homogeneity of Variance (center = median)
       Df F value Pr(>F)
group   1  0.2187 0.6406
      189               
```
]

---

## 2-Sample t-Test

- Computed with `t.test()`

--
  - Use form of form `qvar~cvar` as first argument.
  - Must include data.frame name in `data=` argument.

--
  - Set `var.equal=TRUE` if Levene's Test indicates that variances are equal.
  
--
  - Assign value in H<sub>0</sub> to `mu=` (usually 0, which is the **default**).

--
  - Choose H<sub>A</sub> direction in `alt=` with `"two.sided"` for "not equals", `"less"` for "less than", or `"greater"` for "greater than".

--
  - Set confidence level (1-&alpha;) in `conf.level=`

---

```r
headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.
```
]
 
.right-panel-ttest2-non_seq[

---
count: false
 
## 2-Sample t-Test
.left-panel-ttest2-non_seq[

```r
headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.

*t.test(flipper_length_mm~species,data=peng_chingen
*      )
```
]
 
.right-panel-ttest2-non_seq[

```
Welch Two Sample t-test with flipper_length_mm by species 
t = -20.4633, df = 127.608, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -23.42923 -19.29770 
sample estimates:
mean in group Chinstrap    mean in group Gentoo 
               195.8235                217.1870 
```
]

---
count: false
 
## 2-Sample t-Test
.left-panel-ttest2-non_seq[

```r
headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.

t.test(flipper_length_mm~species,data=peng_chingen  
*      ,var.equal=TRUE
       )  
```
]
 
.right-panel-ttest2-non_seq[

```
 Two Sample t-test with flipper_length_mm by species 
t = -21.0329, df = 189, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -23.36706 -19.35987 
sample estimates:
mean in group Chinstrap    mean in group Gentoo 
               195.8235                217.1870 
```
]

---
count: false
 
## 2-Sample t-Test
.left-panel-ttest2-non_seq[

```r
headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.

t.test(flipper_length_mm~species,data=peng_chingen  
       ,var.equal=TRUE  
*      ,alt="less"
       )  
```
]
 
.right-panel-ttest2-non_seq[

```
 Two Sample t-test with flipper_length_mm by species 
t = -21.0329, df = 189, p-value < 2.2e-16
alternative hypothesis: true difference in means is less than 0 
95 percent confidence interval:
      -Inf -19.68453 
sample estimates:
mean in group Chinstrap    mean in group Gentoo 
               195.8235                217.1870 
```
]

---
count: false
 
## 2-Sample t-Test
.left-panel-ttest2-non_seq[

```r
headtail(peng_chingen)

## Is mean flipper length smaller for Chinstrap
##   than Gentoo Penguins. Use alpha=0.10.

t.test(flipper_length_mm~species,data=peng_chingen  
       ,var.equal=TRUE  
       ,alt="less"  
*      ,conf.level=0.90
       )  
```
]
 
.right-panel-ttest2-non_seq[

```
 Two Sample t-test with flipper_length_mm by species 
t = -21.0329, df = 189, p-value < 2.2e-16
alternative hypothesis: true difference in means is less than 0 
90 percent confidence interval:
      -Inf -20.05721 
sample estimates:
mean in group Chinstrap    mean in group Gentoo 
               195.8235                217.1870 
```
]

---

---

# Chi-square Tests in R

---

## Chi-square Test

- Must have a two-way observed frequency table
  - Grouping variable should be in rows.
  - Response variable should be in columns.

--
  - **Raw data** ... use `xtabs()` (*described in reading and here*).

--
  - **Summarized data** ... use `matrix()` (*described in reading*).

&nbsp;

--
- Compute chi-square results with `chisq.test()`.
  - Object with observed frequency table as first argument.

--
  - Use `correct=FALSE` to "turn-off" continuity correction.

--
  - Assign (save) result to an object.

--
  - Obtain expected table by appending `$expected` to object name.

--
  - Construct a row-percentages table to examine differences.

---

```r
*headtail(peng)

## Does sex ratio differ among species of Penguins.
##  Use alpha=0.01
```
]
 
.right-panel-chi-user[

---
count: false
 
## Chi-square Test
.left-panel-chi-user[

```r
headtail(peng)

## Does sex ratio differ among species of Penguins.
##  Use alpha=0.01

*( peng_sex <- xtabs(~species+sex,data=peng) )
```
]
 
.right-panel-chi-user[

```
           sex
species     female male
  Adelie        73   73
  Chinstrap     34   34
  Gentoo        58   61
```
]

---
count: false
 
## Chi-square Test
.left-panel-chi-user[

```r
headtail(peng)

## Does sex ratio differ among species of Penguins.
##  Use alpha=0.01

( peng_sex <- xtabs(~species+sex,data=peng) )

*( chi_ps <- chisq.test(peng_sex,correct=FALSE) )
```
]
 
.right-panel-chi-user[

```
           sex
species     female male
  Adelie        73   73
  Chinstrap     34   34
  Gentoo        58   61
```

```
Pearson's Chi-squared test with peng_sex 
X-squared = 0.0486, df = 2, p-value = 0.976
```
]

---
count: false
 
## Chi-square Test
.left-panel-chi-user[

```r
headtail(peng)

## Does sex ratio differ among species of Penguins.
##  Use alpha=0.01

( peng_sex <- xtabs(~species+sex,data=peng) )

( chi_ps <- chisq.test(peng_sex,correct=FALSE) )

*chi_ps$expected
```
]
 
.right-panel-chi-user[

```
           sex
species     female male
  Adelie        73   73
  Chinstrap     34   34
  Gentoo        58   61
```

```
Pearson's Chi-squared test with peng_sex 
X-squared = 0.0486, df = 2, p-value = 0.976
```

```
           sex
species       female     male
  Adelie    72.34234 73.65766
  Chinstrap 33.69369 34.30631
  Gentoo    58.96396 60.03604
```
]

---
count: false
 
## Chi-square Test
.left-panel-chi-user[

```r
headtail(peng)

## Does sex ratio differ among species of Penguins.
##  Use alpha=0.01

( peng_sex <- xtabs(~species+sex,data=peng) )

( chi_ps <- chisq.test(peng_sex,correct=FALSE) )

chi_ps$expected

*percTable(peng_sex,margin=1)
```
]
 
.right-panel-chi-user[

```
           sex
species     female male
  Adelie        73   73
  Chinstrap     34   34
  Gentoo        58   61
```

```
Pearson's Chi-squared test with peng_sex 
X-squared = 0.0486, df = 2, p-value = 0.976
```

```
           sex
species       female     male
  Adelie    72.34234 73.65766
  Chinstrap 33.69369 34.30631
  Gentoo    58.96396 60.03604
```

```
           sex
species     female  male   Sum
  Adelie      50.0  50.0 100.0
  Chinstrap   50.0  50.0 100.0
  Gentoo      48.7  51.3 100.0
```
]

---

## Goodness-of-Fit Test

- Make an expected table with `c()` with names.
  - Any values that are proportional to the expected proportions.

--
- Create an observed frequency table.
  - **Raw Data** ... use `xtabs()` (*demonstrated here and in reading*).
  - **Summmarized Data ** ... use `c()` with names (*demonstrated in reading*).

&nbsp;

--
- Compute GOF results with `chisq.test()`
  - Observed table is first argument.

--
  - Expected table object in `p=` argument.

--
  - Use `rescale.p=TRUE` to assure proper expected values.

--
  - Use `correct=FALSE` to "turn-off" continuity correction.

--
  - Assign (save) result to an object.

--
  - Obtain expected table by appending `$expected` to object name.

--
  - Use `gofCI()` to see how expected and observed proportions compare.

---

```r
*headtail(peng)

## Do samples from islands follow a 3:2:1 ratio
## for Biscoe, Dream, and Torgerson. Use alpha=0.01.
```
]
 
.right-panel-gof-user[

---
count: false
 
## Goodness-of-Fit Test
.left-panel-gof-user[

```r
headtail(peng)

## Do samples from islands follow a 3:2:1 ratio
## for Biscoe, Dream, and Torgerson. Use alpha=0.01.

*( exp <- c("Biscoe"=3,"Dream"=2,"Torgerson"=1) )
```
]
 
.right-panel-gof-user[

```
   Biscoe     Dream Torgerson 
        3         2         1 
```
]

---
count: false
 
## Goodness-of-Fit Test
.left-panel-gof-user[

```r
headtail(peng)

## Do samples from islands follow a 3:2:1 ratio
## for Biscoe, Dream, and Torgerson. Use alpha=0.01.

( exp <- c("Biscoe"=3,"Dream"=2,"Torgerson"=1) )

*( peng_isle <- xtabs(~island,data=peng) )
```
]
 
.right-panel-gof-user[

```
   Biscoe     Dream Torgerson 
        3         2         1 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```
]

---
count: false
 
## Goodness-of-Fit Test
.left-panel-gof-user[

```r
headtail(peng)

## Do samples from islands follow a 3:2:1 ratio
## for Biscoe, Dream, and Torgerson. Use alpha=0.01.

( exp <- c("Biscoe"=3,"Dream"=2,"Torgerson"=1) )

( peng_isle <- xtabs(~island,data=peng) )

*( gof_pi <- chisq.test(peng_isle,p=exp,rescale.p=TRUE,correct=FALSE) )
```
]
 
.right-panel-gof-user[

```
   Biscoe     Dream Torgerson 
        3         2         1 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```

```
Chi-squared test for given probabilities with peng_isle 
X-squared = 1.3488, df = 2, p-value = 0.5095
```
]

---
count: false
 
## Goodness-of-Fit Test
.left-panel-gof-user[

```r
headtail(peng)

## Do samples from islands follow a 3:2:1 ratio
## for Biscoe, Dream, and Torgerson. Use alpha=0.01.

( exp <- c("Biscoe"=3,"Dream"=2,"Torgerson"=1) )

( peng_isle <- xtabs(~island,data=peng) )

( gof_pi <- chisq.test(peng_isle,p=exp,rescale.p=TRUE,correct=FALSE) )

*gof_pi$expected
```
]
 
.right-panel-gof-user[

```
   Biscoe     Dream Torgerson 
        3         2         1 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```

```
Chi-squared test for given probabilities with peng_isle 
X-squared = 1.3488, df = 2, p-value = 0.5095
```

```
   Biscoe     Dream Torgersen 
172.00000 114.66667  57.33333 
```
]

---
count: false
 
## Goodness-of-Fit Test
.left-panel-gof-user[

```r
headtail(peng)

## Do samples from islands follow a 3:2:1 ratio
## for Biscoe, Dream, and Torgerson. Use alpha=0.01.

( exp <- c("Biscoe"=3,"Dream"=2,"Torgerson"=1) )

( peng_isle <- xtabs(~island,data=peng) )

( gof_pi <- chisq.test(peng_isle,p=exp,rescale.p=TRUE,correct=FALSE) )

gof_pi$expected

*gofCI(gof_pi,digits=3)
```
]
 
.right-panel-gof-user[

```
   Biscoe     Dream Torgerson 
        3         2         1 
```

```
island
   Biscoe     Dream Torgersen 
      168       124        52 
```

```
Chi-squared test for given probabilities with peng_isle 
X-squared = 1.3488, df = 2, p-value = 0.5095
```

```
   Biscoe     Dream Torgersen 
172.00000 114.66667  57.33333 
```

```
          p.obs p.LCI p.UCI p.exp
Biscoe    0.488 0.436 0.541 0.500
Dream     0.360 0.312 0.412 0.333
Torgersen 0.151 0.117 0.193 0.167
```
]

---