Multiple Sampling

---

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# Packages needed and a Note about Icons

Please load up the following packages. Remember to first install the ones you don't have.

```r
library(tidyverse)
library(mosaic)
library(ggplot2movies)
library(viridis)
library(patchwork)
```

You may come across the following icons. The table below lists what each means.

<table class="table" style="width: auto !important; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:center;background-color: #181818 !important;"> Icon </th>
   <th style="text-align:left;background-color: #181818 !important;"> Description </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:center;width: 10em; background-color: #181818 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:
#4682b4;overflow:visible;position:relative;"><path d="M52.51 440.6l171.5-142.9V214.3L52.51 71.41C31.88 54.28 0 68.66 0 96.03v319.9C0 443.3 31.88 457.7 52.51 440.6zM308.5 440.6l192-159.1c15.25-12.87 15.25-36.37 0-49.24l-192-159.1c-20.63-17.12-52.51-2.749-52.51 24.62v319.9C256 443.3 287.9 457.7 308.5 440.6z"></path></svg> </td>
   <td style="text-align:left;width: 40em; background-color: #181818 !important;"> Indicates that an example continues on the following slide. </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; background-color: #181818 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ff6347;overflow:visible;position:relative;"><path d="M384 128v255.1c0 35.35-28.65 64-64 64H64c-35.35 0-64-28.65-64-64V128c0-35.35 28.65-64 64-64H320C355.3 64 384 92.65 384 128z"></path></svg> </td>
   <td style="text-align:left;width: 40em; background-color: #181818 !important;"> Indicates that a section using common syntax has ended. </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; background-color: #181818 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#5cb85c;overflow:visible;position:relative;"><path d="M172.5 131.1C228.1 75.51 320.5 75.51 376.1 131.1C426.1 181.1 433.5 260.8 392.4 318.3L391.3 319.9C381 334.2 361 337.6 346.7 327.3C332.3 317 328.9 297 339.2 282.7L340.3 281.1C363.2 249 359.6 205.1 331.7 177.2C300.3 145.8 249.2 145.8 217.7 177.2L105.5 289.5C73.99 320.1 73.99 372 105.5 403.5C133.3 431.4 177.3 435 209.3 412.1L210.9 410.1C225.3 400.7 245.3 404 255.5 418.4C265.8 432.8 262.5 452.8 248.1 463.1L246.5 464.2C188.1 505.3 110.2 498.7 60.21 448.8C3.741 392.3 3.741 300.7 60.21 244.3L172.5 131.1zM467.5 380C411 436.5 319.5 436.5 263 380C213 330 206.5 251.2 247.6 193.7L248.7 192.1C258.1 177.8 278.1 174.4 293.3 184.7C307.7 194.1 311.1 214.1 300.8 229.3L299.7 230.9C276.8 262.1 280.4 306.9 308.3 334.8C339.7 366.2 390.8 366.2 422.3 334.8L534.5 222.5C566 191 566 139.1 534.5 108.5C506.7 80.63 462.7 76.99 430.7 99.9L429.1 101C414.7 111.3 394.7 107.1 384.5 93.58C374.2 79.2 377.5 59.21 391.9 48.94L393.5 47.82C451 6.731 529.8 13.25 579.8 63.24C636.3 119.7 636.3 211.3 579.8 267.7L467.5 380z"></path></svg> </td>
   <td style="text-align:left;width: 40em; background-color: #181818 !important;"> Indicates that there is an active hyperlink on the slide. </td>
  </tr>
  <tr>
   <td style="text-align:center;width: 10em; background-color: #181818 !important;"> <svg aria-hidden="true" role="img" viewbox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#5cb85c;overflow:visible;position:relative;"><path d="M384 48V512l-192-112L0 512V48C0 21.5 21.5 0 48 0h288C362.5 0 384 21.5 384 48z"></path></svg> </td>
   <td style="text-align:left;width: 40em; background-color: #181818 !important;"> Indicates that a section covering a concept has ended. </td>
  </tr>
</tbody>
</table>

---

# Using bars

Now that we know how to pivot, we can just `group_by` genre type and then `tally`

```r
* ggplot2movies::movies
```
]
 
.panel2-sw1-auto[

```
## # A tibble: 58,788 × 24
##    title     year length budget rating votes    r1    r2    r3    r4    r5    r6
##    <chr>    <int>  <int>  <int>  <dbl> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1 $         1971    121     NA    6.4   348   4.5   4.5   4.5   4.5  14.5  24.5
##  2 $1000 a…  1939     71     NA    6      20   0    14.5   4.5  24.5  14.5  14.5
##  3 $21 a D…  1941      7     NA    8.2     5   0     0     0     0     0    24.5
##  4 $40,000   1996     70     NA    8.2     6  14.5   0     0     0     0     0  
##  5 $50,000…  1975     71     NA    3.4    17  24.5   4.5   0    14.5  14.5   4.5
##  6 $pent     2000     91     NA    4.3    45   4.5   4.5   4.5  14.5  14.5  14.5
##  7 $windle   2002     93     NA    5.3   200   4.5   0     4.5   4.5  24.5  24.5
##  8 '15'      2002     25     NA    6.7    24   4.5   4.5   4.5   4.5   4.5  14.5
##  9 '38       1987     97     NA    6.6    18   4.5   4.5   4.5   0     0     0  
## 10 '49-'17   1917     61     NA    6      51   4.5   0     4.5   4.5   4.5  44.5
## # … with 58,778 more rows, and 12 more variables: r7 <dbl>, r8 <dbl>, r9 <dbl>,
## #   r10 <dbl>, mpaa <chr>, Action <int>, Animation <int>, Comedy <int>,
## #   Drama <int>, Documentary <int>, Romance <int>, Short <int>
```
]

---
count: false

```r
  ggplot2movies::movies %>%
* select(Action, Animation,
*        Comedy, Drama,
*        Documentary, Romance,
*        Short)
```
]
 
.panel2-sw1-auto[

```
## # A tibble: 58,788 × 7
##    Action Animation Comedy Drama Documentary Romance Short
##     <int>     <int>  <int> <int>       <int>   <int> <int>
##  1      0         0      1     1           0       0     0
##  2      0         0      1     0           0       0     0
##  3      0         1      0     0           0       0     1
##  4      0         0      1     0           0       0     0
##  5      0         0      0     0           0       0     0
##  6      0         0      0     1           0       0     0
##  7      1         0      0     1           0       0     0
##  8      0         0      0     0           1       0     1
##  9      0         0      0     1           0       0     0
## 10      0         0      0     0           0       0     0
## # … with 58,778 more rows
```
]

---
count: false

```r
  ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
* pivot_longer(everything(),
*              names_to = "genre")
```
]
 
.panel2-sw1-auto[

```
## # A tibble: 411,516 × 2
##    genre       value
##    <chr>       <int>
##  1 Action          0
##  2 Animation       0
##  3 Comedy          1
##  4 Drama           1
##  5 Documentary     0
##  6 Romance         0
##  7 Short           0
##  8 Action          0
##  9 Animation       0
## 10 Comedy          1
## # … with 411,506 more rows
```
]

---
count: false

```r
  ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
  pivot_longer(everything(),
               names_to = "genre") %>%
* group_by(genre)
```
]
 
.panel2-sw1-auto[

```
## # A tibble: 411,516 × 2
## # Groups:   genre [7]
##    genre       value
##    <chr>       <int>
##  1 Action          0
##  2 Animation       0
##  3 Comedy          1
##  4 Drama           1
##  5 Documentary     0
##  6 Romance         0
##  7 Short           0
##  8 Action          0
##  9 Animation       0
## 10 Comedy          1
## # … with 411,506 more rows
```
]

---
count: false

```
## # A tibble: 7 × 2
##   genre           n
##   <chr>       <int>
## 1 Action       4688
## 2 Animation    3690
## 3 Comedy      17271
## 4 Documentary  3472
## 5 Drama       21811
## 6 Romance      4744
## 7 Short        9458
```
]

.right[<svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#ff6347;overflow:visible;position:relative;"><path d="M384 128v255.1c0 35.35-28.65 64-64 64H64c-35.35 0-64-28.65-64-64V128c0-35.35 28.65-64 64-64H320C355.3 64 384 92.65 384 128z"/></svg>]

---

```r
*ggplot2movies::movies
```
]
 
.panel2-sw2-auto[

---
count: false

```r
ggplot2movies::movies %>%
* select(Action, Animation,
*        Comedy, Drama,
*        Documentary, Romance,
*        Short)
```
]
 
.panel2-sw2-auto[

---
count: false

```r
ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
* pivot_longer(everything(),
*              names_to = "genre")
```
]
 
.panel2-sw2-auto[

---
count: false

```r
ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
  pivot_longer(everything(),
               names_to = "genre") %>%
* group_by(genre)
```
]
 
.panel2-sw2-auto[

---
count: false

---
count: false

```r
ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
  pivot_longer(everything(),
               names_to = "genre") %>%
  group_by(genre) %>%
  tally(value) %>%
*ggplot(aes(x = genre,
*          y = n,
*          fill = -n))
```
]
 
.panel2-sw2-auto[
![](Slides-Week-9R_files/figure-html/sw2_auto_06_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
  pivot_longer(everything(),
               names_to = "genre") %>%
  group_by(genre) %>%
  tally(value) %>%
ggplot(aes(x = genre,
           y = n,
           fill = -n)) +
* geom_bar(stat='identity',
*          show.legend = FALSE)
```
]
 
.panel2-sw2-auto[
![](Slides-Week-9R_files/figure-html/sw2_auto_07_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
  pivot_longer(everything(),
               names_to = "genre") %>%
  group_by(genre) %>%
  tally(value) %>%
ggplot(aes(x = genre,
           y = n,
           fill = -n)) +
  geom_bar(stat='identity',
           show.legend = FALSE) +
* labs(title = "Count of Genre",
*      x = "Genre",
*      y = "Count")
```
]
 
.panel2-sw2-auto[
![](Slides-Week-9R_files/figure-html/sw2_auto_08_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  select(Action, Animation,
         Comedy, Drama,
         Documentary, Romance,
         Short) %>%
  pivot_longer(everything(),
               names_to = "genre") %>%
  group_by(genre) %>%
  tally(value) %>%
ggplot(aes(x = genre,
           y = n,
           fill = -n)) +
  geom_bar(stat='identity',
           show.legend = FALSE) +
  labs(title = "Count of Genre",
       x = "Genre",
       y = "Count") +
* theme_minimal()
```
]
 
.panel2-sw2-auto[
![](Slides-Week-9R_files/figure-html/sw2_auto_09_output-1.png)
]

---

# Back to the movies

Let's take a look at the ratings

```r
*ggplot2movies::movies
```
]
 
.panel2-sw3-auto[

---
count: false

```r
ggplot2movies::movies %>%
* ggplot(aes(x = rating,
*            fill = ..x..))
```
]
 
.panel2-sw3-auto[
![](Slides-Week-9R_files/figure-html/sw3_auto_02_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  ggplot(aes(x = rating,
             fill = ..x..)) +
* geom_histogram(bins = 20,
*                show.legend = FALSE)
```
]
 
.panel2-sw3-auto[
![](Slides-Week-9R_files/figure-html/sw3_auto_03_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  ggplot(aes(x = rating,
             fill = ..x..)) +
  geom_histogram(bins = 20,
                 show.legend = FALSE) +
* scale_fill_viridis(direction = -1)
```
]
 
.panel2-sw3-auto[
![](Slides-Week-9R_files/figure-html/sw3_auto_04_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  ggplot(aes(x = rating,
             fill = ..x..)) +
  geom_histogram(bins = 20,
                 show.legend = FALSE) +
  scale_fill_viridis(direction = -1) +
* theme_minimal()
```
]
 
.panel2-sw3-auto[
![](Slides-Week-9R_files/figure-html/sw3_auto_05_output-1.png)
]

---
count: false

```r
ggplot2movies::movies %>%
  ggplot(aes(x = rating,
             fill = ..x..)) +
  geom_histogram(bins = 20,
                 show.legend = FALSE) +
  scale_fill_viridis(direction = -1) +
  theme_minimal()
```
]
 
.panel2-sw3-auto[
![](Slides-Week-9R_files/figure-html/sw3_auto_06_output-1.png)
]

```r
pop_hist <-
ggplot2movies::movies %>% 
  ggplot(aes(x = rating,
             fill = ..x..)) +
  geom_histogram(bins = 20,
                 show.legend = FALSE) +
  scale_fill_viridis(direction = -1) +
  theme_minimal()
```

---

# Purpose

We would like to produce a confidence interval for the population mean rating. Let's first pretend we had to take a sample of `$n=1000$` from the `$N = 58788$` movies. To do this, we'll use the `sample_n` command from the `dplyr` package.

```r
*set.seed(123)
```
]
 
.panel2-sw4-auto[

]

---
count: false

```r
set.seed(123)

*ggplot2movies::movies
```
]
 
.panel2-sw4-auto[

---
count: false

```r
set.seed(123)

ggplot2movies::movies %>%
* sample_n(1000)
```
]
 
.panel2-sw4-auto[

```
## # A tibble: 1,000 × 24
##    title     year length budget rating votes    r1    r2    r3    r4    r5    r6
##    <chr>    <int>  <int>  <int>  <dbl> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  2 Yakuza,…  1975    112 NA        6.9   550   4.5   4.5   4.5   4.5   4.5  14.5
##  3 Aprimi …  2003     93 NA        4.5    32  14.5   4.5   4.5  14.5  14.5   4.5
##  4 Zendan-…  2002    106 NA        6.8    52   4.5   0     0     4.5   4.5  24.5
##  5 Lightni…  1994     98 NA        4.8  1020   4.5   4.5   4.5  14.5  14.5  24.5
##  6 Leylase…  1995    100  7  e5    6.6    29   0     0     4.5   4.5  14.5  14.5
##  7 Ojos si…  1973     81 NA        3      12  34.5   4.5   0     4.5   0     0  
##  8 Another…  1998    101 NA        6.3  1872   4.5   4.5   4.5   4.5  14.5  14.5
##  9 Sebasti…  1990     88 NA        5.5     7  14.5   0     0     0    24.5  24.5
## 10 Shine     1996    105  5.5e6    7.6 12425   4.5   4.5   4.5   4.5   4.5   4.5
## # … with 990 more rows, and 12 more variables: r7 <dbl>, r8 <dbl>, r9 <dbl>,
## #   r10 <dbl>, mpaa <chr>, Action <int>, Animation <int>, Comedy <int>,
## #   Drama <int>, Documentary <int>, Romance <int>, Short <int>
```
]

```r
set.seed(123)

movies_sample <- 
  ggplot2movies::movies %>% 
  sample_n(1000)
```

---

Let's see what this looks like

```r
*ggplot(movies_sample,
*      aes(x = rating,
*          fill = ..x..))
```
]
 
.panel2-sw5-auto[
![](Slides-Week-9R_files/figure-html/sw5_auto_01_output-1.png)
]

---
count: false

```r
ggplot(movies_sample,
       aes(x = rating,
           fill = ..x..)) +
*      geom_histogram(color = "white",
*                     bins = 20,
*                     show.legend = FALSE)
```
]
 
.panel2-sw5-auto[
![](Slides-Week-9R_files/figure-html/sw5_auto_02_output-1.png)
]

---
count: false

```r
ggplot(movies_sample,
       aes(x = rating,
           fill = ..x..)) +
       geom_histogram(color = "white",
                      bins = 20,
                      show.legend = FALSE) +
*      scale_fill_viridis(direction = -1)
```
]
 
.panel2-sw5-auto[
![](Slides-Week-9R_files/figure-html/sw5_auto_03_output-1.png)
]

---
count: false

```r
ggplot(movies_sample,
       aes(x = rating,
           fill = ..x..)) +
       geom_histogram(color = "white",
                      bins = 20,
                      show.legend = FALSE) +
       scale_fill_viridis(direction = -1) +
*      theme_minimal()
```
]
 
.panel2-sw5-auto[
![](Slides-Week-9R_files/figure-html/sw5_auto_04_output-1.png)
]

---

```r
rand_sample <- 
  ggplot(movies_sample, 
         aes(x = rating,
             fill = ..x..)) +
  geom_histogram(color = "white", 
                 bins = 20,
                 show.legend = FALSE) +
  scale_fill_viridis(direction = -1) +
  theme_minimal()
```

---

# Population Estimation

We can think of the histogram as an estimate of our population distribution histogram that we plotted earlier so a population mean rating will provide a good estimate. To estimate a plausible range of values, we can start by using the mean of the sample.

A good way to to this is to add parentheses around a variable declaration like so

```r
*movies_sample
```
]
 
.panel2-sw6-auto[

---
count: false

```r
movies_sample %>%
*  summarize(mean = mean(rating))
```
]
 
.panel2-sw6-auto[

```
## # A tibble: 1 × 1
##    mean
##   <dbl>
## 1  5.97
```
]

This values is only a single estimation. What you did earlier was top keep sampling from the population, or what is known as **sampling with replacement**.

.right[<svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#4682b4;overflow:visible;position:relative;"><path d="M52.51 440.6l171.5-142.9V214.3L52.51 71.41C31.88 54.28 0 68.66 0 96.03v319.9C0 443.3 31.88 457.7 52.51 440.6zM308.5 440.6l192-159.1c15.25-12.87 15.25-36.37 0-49.24l-192-159.1c-20.63-17.12-52.51-2.749-52.51 24.62v319.9C256 443.3 287.9 457.7 308.5 440.6z"/></svg>]

---

# Sampling with Replacement

To do this, we can use the `resample` command from the `mosaic` package. Let's see one instance of this.

```r
*resample(movies_sample)
```
]
 
.panel2-sw7-auto[

]

---
count: false

```r
resample(movies_sample) %>%
* arrange(orig.id)
```
]
 
.panel2-sw7-auto[

```
## # A tibble: 1,000 × 25
##    title     year length budget rating votes    r1    r2    r3    r4    r5    r6
##    <chr>    <int>  <int>  <int>  <dbl> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  2 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  3 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  4 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  5 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  6 Thief o…  1952     78 NA        5       8  14.5   0     0     0    45.5   0  
##  7 Shine     1996    105  5.5e6    7.6 12425   4.5   4.5   4.5   4.5   4.5   4.5
##  8 Shine     1996    105  5.5e6    7.6 12425   4.5   4.5   4.5   4.5   4.5   4.5
##  9 Scalps    1983     82 NA        3      52  24.5  14.5  24.5   4.5   4.5   4.5
## 10 Tenness…  1942    103 NA        7.1    57   0     4.5   4.5   4.5   4.5  14.5
## # … with 990 more rows, and 13 more variables: r7 <dbl>, r8 <dbl>, r9 <dbl>,
## #   r10 <dbl>, mpaa <chr>, Action <int>, Animation <int>, Comedy <int>,
## #   Drama <int>, Documentary <int>, Romance <int>, Short <int>, orig.id <chr>
```
]

---
count: false

```r
resample(movies_sample) %>%
  arrange(orig.id) %>%
* summarize(mean = mean(rating))
```
]
 
.panel2-sw7-auto[

```
## # A tibble: 1 × 1
##    mean
##   <dbl>
## 1  5.99
```
]

But again, this is only one sample mean.

---

To do a whole bunch we can run a `do` command with parentheses like so

```r
*do(10)
```
]
 
.panel2-sw8-auto[

```
## An object of class "repeater"
## Slot "n":
## [1] 10
## 
## Slot "cull":
## NULL
## 
## Slot "mode":
## [1] "default"
## 
## Slot "algorithm":
## [1] 1
## 
## Slot "parallel":
## [1] TRUE
```
]

---
count: false

```r
do(10) *
* (resample(ggplot2movies::movies) %>%
*    summarize(mean = mean(rating)))
```
]
 
.panel2-sw8-auto[

```
##        mean
## 1  5.937487
## 2  5.936739
## 3  5.930409
## 4  5.921472
## 5  5.934427
## 6  5.934444
## 7  5.930503
## 8  5.944598
## 9  5.933162
## 10 5.929152
```
]

---

But a sample of 10 is so tiny. Let's try 1000 like before

```r
* do(1000)
```
]
 
.panel2-sw9-auto[

```
## An object of class "repeater"
## Slot "n":
## [1] 1000
## 
## Slot "cull":
## NULL
## 
## Slot "mode":
## [1] "default"
## 
## Slot "algorithm":
## [1] 1
## 
## Slot "parallel":
## [1] TRUE
```
]

---
count: false

```r
  do(1000) *
* summarize(resample(ggplot2movies::movies),
*           mean = mean(rating))
```
]
 
.panel2-sw9-auto[

```
##          mean
## 1    5.947217
## 2    5.936438
## 3    5.936428
## 4    5.942277
## 5    5.942965
## 6    5.935548
## 7    5.925339
## 8    5.936348
## 9    5.947751
## 10   5.929229
## 11   5.929606
## 12   5.934994
## 13   5.922717
## 14   5.923758
## 15   5.932064
## 16   5.936353
## 17   5.931591
## 18   5.930556
## 19   5.935526
## 20   5.938646
## 21   5.936723
## 22   5.937902
## 23   5.934175
## 24   5.930826
## 25   5.941469
## 26   5.928256
## 27   5.926160
## 28   5.932947
## 29   5.941658
## 30   5.933526
## 31   5.930333
## 32   5.943244
## 33   5.940425
## 34   5.925890
## 35   5.932255
## 36   5.932330
## 37   5.926226
## 38   5.927002
## 39   5.940163
## 40   5.932752
## 41   5.926255
## 42   5.944388
## 43   5.941323
## 44   5.929312
## 45   5.930256
## 46   5.927108
## 47   5.932406
## 48   5.921350
## 49   5.935080
## 50   5.930722
## 51   5.931119
## 52   5.934590
## 53   5.926835
## 54   5.930726
## 55   5.927291
## 56   5.931534
## 57   5.931062
## 58   5.930049
## 59   5.917743
## 60   5.936717
## 61   5.942478
## 62   5.928650
## 63   5.935941
## 64   5.933709
## 65   5.932842
## 66   5.935053
## 67   5.932507
## 68   5.929253
## 69   5.938806
## 70   5.937700
## 71   5.917427
## 72   5.941497
## 73   5.929120
## 74   5.930865
## 75   5.944475
## 76   5.935824
## 77   5.930843
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## 81   5.921409
## 82   5.937373
## 83   5.944126
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## 85   5.941342
## 86   5.935380
## 87   5.936043
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## 89   5.935300
## 90   5.938945
## 91   5.939845
## 92   5.943779
## 93   5.931199
## 94   5.936916
## 95   5.934373
## 96   5.927140
## 97   5.931743
## 98   5.926914
## 99   5.938011
## 100  5.929601
## 101  5.925515
## 102  5.929008
## 103  5.935529
## 104  5.932075
## 105  5.932056
## 106  5.928484
## 107  5.926393
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## 109  5.936895
## 110  5.926187
## 111  5.916383
## 112  5.939556
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## 114  5.925136
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## 119  5.938778
## 120  5.927422
## 121  5.934203
## 122  5.931008
## 123  5.941823
## 124  5.933162
## 125  5.932905
## 126  5.930135
## 127  5.937297
## 128  5.929594
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## 130  5.929113
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## 132  5.921312
## 133  5.931243
## 134  5.937593
## 135  5.948670
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## 137  5.942580
## 138  5.927358
## 139  5.936089
## 140  5.929663
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## 144  5.923074
## 145  5.930023
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## 148  5.931481
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## 216  5.937559
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## 239  5.936211
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## 243  5.924296
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## 248  5.924808
## 249  5.922341
## 250  5.933725
## 251  5.928399
## 252  5.937707
## 253  5.937188
## 254  5.938011
## 255  5.924432
## 256  5.935984
## 257  5.925990
## 258  5.936334
## 259  5.924808
## 260  5.939336
## 261  5.943716
## 262  5.928477
## 263  5.934235
## 264  5.931755
## 265  5.931071
## 266  5.931025
## 267  5.940900
## 268  5.937452
## 269  5.923593
## 270  5.927398
## 271  5.938249
## 272  5.939671
## 273  5.923950
## 274  5.933818
## 275  5.934400
## 276  5.932173
## 277  5.922460
## 278  5.936125
## 279  5.943077
## 280  5.940219
## 281  5.940003
## 282  5.932798
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## 284  5.923139
## 285  5.955734
## 286  5.934876
## 287  5.928371
## 288  5.932221
## 289  5.923755
## 290  5.923176
## 291  5.922374
## 292  5.930812
## 293  5.930152
## 294  5.930152
## 295  5.931100
## 296  5.935162
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## 298  5.933325
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## 300  5.923865
## 301  5.935153
## 302  5.924709
## 303  5.931624
## 304  5.929591
## 305  5.928764
## 306  5.939756
## 307  5.942041
## 308  5.930355
## 309  5.943643
## 310  5.935164
## 311  5.937916
## 312  5.938290
## 313  5.934109
## 314  5.923333
## 315  5.926153
## 316  5.935116
## 317  5.940393
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## 320  5.938414
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## 322  5.937348
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## 328  5.942168
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## 331  5.931248
## 332  5.925714
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## 338  5.935531
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## 341  5.925134
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## 345  5.938295
## 346  5.942017
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## 363  5.931421
## 364  5.926102
## 365  5.927506
## 366  5.926893
## 367  5.931617
## 368  5.937088
## 369  5.923384
## 370  5.937822
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## 372  5.937142
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## 375  5.923420
## 376  5.930040
## 377  5.931163
## 378  5.919091
## 379  5.934412
## 380  5.936291
## 381  5.927997
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## 385  5.934400
## 386  5.930576
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## 390  5.934051
## 391  5.938499
## 392  5.930591
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## 415  5.936519
## 416  5.928007
## 417  5.937611
## 418  5.932661
## 419  5.943693
## 420  5.923377
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## 827  5.935762
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## 830  5.932932
## 831  5.947265
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## 931  5.936963
## 932  5.932367
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## 935  5.934711
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## 939  5.928081
## 940  5.935123
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## 942  5.935864
## 943  5.924457
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## 946  5.932976
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## 949  5.940459
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## 957  5.930316
## 958  5.935189
## 959  5.930003
## 960  5.923500
## 961  5.931467
## 962  5.939993
## 963  5.933592
## 964  5.934429
## 965  5.935079
## 966  5.928868
## 967  5.935762
## 968  5.926869
## 969  5.931115
## 970  5.930574
## 971  5.939505
## 972  5.924449
## 973  5.938197
## 974  5.943990
## 975  5.939559
## 976  5.937708
## 977  5.919444
## 978  5.929227
## 979  5.927370
## 980  5.927446
## 981  5.922704
## 982  5.929217
## 983  5.935298
## 984  5.935339
## 985  5.938608
## 986  5.936176
## 987  5.933976
## 988  5.933958
## 989  5.939105
## 990  5.938030
## 991  5.940512
## 992  5.932056
## 993  5.924444
## 994  5.929811
## 995  5.932488
## 996  5.932015
## 997  5.931166
## 998  5.933799
## 999  5.925058
## 1000 5.937144
```
]

---

```r
not_tiny <- 
  do(1000) *
  summarize(resample(ggplot2movies::movies), 
            mean = mean(rating))
```

---

# Estimating the population

```r
*ggplot(not_tiny,
*      mapping = aes(x = mean,
*                    fill = ..x..))
```
]
 
.panel2-sw10-auto[
![](Slides-Week-9R_files/figure-html/sw10_auto_01_output-1.png)
]

---
count: false

```r
ggplot(not_tiny,
       mapping = aes(x = mean,
                     fill = ..x..)) +
* geom_histogram(bins = 20,
*                color = "white",
*                show.legend = FALSE)
```
]
 
.panel2-sw10-auto[
![](Slides-Week-9R_files/figure-html/sw10_auto_02_output-1.png)
]

---
count: false

```r
ggplot(not_tiny,
       mapping = aes(x = mean,
                     fill = ..x..)) +
  geom_histogram(bins = 20,
                 color = "white",
                 show.legend = FALSE) +
* scale_fill_viridis(direction = -1)
```
]
 
.panel2-sw10-auto[
![](Slides-Week-9R_files/figure-html/sw10_auto_03_output-1.png)
]

---
count: false

```r
ggplot(not_tiny,
       mapping = aes(x = mean,
                     fill = ..x..)) +
  geom_histogram(bins = 20,
                 color = "white",
                 show.legend = FALSE) +
  scale_fill_viridis(direction = -1) +
* theme_minimal()
```
]
 
.panel2-sw10-auto[
![](Slides-Week-9R_files/figure-html/sw10_auto_04_output-1.png)
]

---

```r
rep_sample <- 
  ggplot(data = not_tiny , 
         mapping = aes(x = mean,
                       fill = ..x..)) +
  geom_histogram(bins = 20, 
                 color = "white",
                 show.legend = FALSE) +
  scale_fill_viridis(direction = -1) +
  theme_minimal()
```

---

# Comparison for `$n=100$`

- Left - original population distribution
- Middle - random sample distribution 
- Right - repeated sample distribution

---

# Comparison for `$n=1000$`

- Left - original population distribution
- Middle - random sample distribution 
- Right - repeated sample distribution

The repeated sample distribution does a better job for smaller samples...

---

# Comparison for `$n=10000$`

- Left - original population distribution
- Middle - random sample distribution 
- Right - repeated sample distribution

...but oversampling sample means leads to a normal distribution!

---

# Shortcut: Naming and Outputting a Data Frame

There are many approaches that you can take to shorten the number of steps taken to get what you want. While knowing the "long" way gives you the greatest flexibility, if you absolutely know where you're going then knowing shortcuts will make your life easier. Here are two ways to name a data frame and see the output at the same time:

```r
(way1 <- 
    starwars %>%
    head() %>%
    select(name, height, hair_color))
```

```
## # A tibble: 6 × 3
##   name           height hair_color 
##   <chr>           <int> <chr>      
## 1 Luke Skywalker    172 blond      
## 2 C-3PO             167 <NA>       
## 3 R2-D2              96 <NA>       
## 4 Darth Vader       202 none       
## 5 Leia Organa       150 brown      
## 6 Owen Lars         178 brown, grey
```
]

```r
way2 <- 
    starwars %>%
    head() %>%
    select(name, height, hair_color); way2
```

---

# Confidence using quantiles

We can now calculate a confidence interval using many options. Let's first isolate the middle 95% of values which corresponds to a 95% confidence interval for the population mean rating.

```r
*confint(not_tiny,
*       level = 0.95,
*       method = "quantile")
```
]
 
.panel2-sw12-auto[

```
##   name    lower    upper level     method estimate
## 1 mean 5.920575 5.946025  0.95 percentile  5.93285
```
]

Based on the sample data and bootstrapping techniques, we can be 95% confident that the true mean rating of ALL IMDB ratings is between 5.49 and about 6.13.

---

# Confidence using the standard error

Recall that the **standard error** is the standard deviation of the sampling distribution and is approximated by the bootstrap distribution or the null distribution depending on the context. To do this we can use the same function as before but only by changing the method

```r
*confint(not_tiny,
*        level = 0.95,
*        method = "stderr")
```
]
 
.panel2-sw13-auto[

```
## Warning: confint: Using df = Inf.
```

```
##   name    lower    upper level method estimate margin.of.error
## 1 mean 5.920053 5.945945  0.95 stderr  5.93285      0.01294608
```
]

The interpretation is virtually the same here.

---

## Thats it!