Data og Tidyverse

class: center, middle, inverse, title-slide

# Data og Tidyverse
### Niels Richard Hansen
### 8. september, 2022

---

## Tidyverse pakker

```r
library("tidyverse")  # Must be installed!
```

```
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──
```

```
## ✓ ggplot2 3.3.5     ✓ purrr   0.3.4
## ✓ tibble  3.1.4     ✓ dplyr   1.0.7
## ✓ tidyr   1.1.3     ✓ stringr 1.4.0
## ✓ readr   2.0.1     ✓ forcats 0.5.1
```

```
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
```

Tidyverse pakken loader et antal R pakker, som udgør en sammenhængende og 
effektiv ramme til håndtering, transformering og visualisering af data.

---
## Kernepakker

<div id="htmlwidget-b099ccff6119d342b3c4" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-b099ccff6119d342b3c4">{"x":{"filter":"none","vertical":false,"data":[["tibble","dplyr","tidyr","readr","purrr","ggplot2","stringr","forcats"],["A data structure for tabular data","Rearrange, filter, transform and join data tibbles","Pivot tables to make them tidy","Read and write tabular data","Functional programming","Graphics","Operations on text strings","Tools for categorical variables (factors)"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th>Package<\/th>\n      <th>Functionality<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"ordering":false,"searching":false,"lengthChange":false,"info":false,"paging":false,"columnDefs":[{"className":"dt-head-left","targets":"_all"}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

Vi vil i dag fokusere på pakkerne `dplyr`, `tidyr` og `readr`. Der vil 
komme en separat video om visualisering og `ggplot2`.

---
## Datatabeller

Vi organiserer data i tabeller.

Generiske termer: **data frame** eller **datatabel**

<div id="htmlwidget-7ea2345b48daef2df9d7" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-7ea2345b48daef2df9d7">{"x":{"filter":"none","vertical":false,"data":[["Base R","Tidyverse (R)","data.table (R)","pandas (Python)"],["data.frame","tibble","data.table","DataFrame"],["Stability","Coherence","Efficiency","Python!"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th>Sprog<\/th>\n      <th>Datastruktur<\/th>\n      <th>Bemærkning<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"ordering":false,"searching":false,"lengthChange":false,"info":false,"paging":false,"columnDefs":[{"className":"dt-head-left","targets":"_all"}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

```r
library(nycflights13) # Must be installed!
class(flights)        # This is a tibble
```

```
## [1] "tbl_df"     "tbl"        "data.frame"
```

---
## flights data

```r
flights
```

```
## # A tibble: 336,776 × 19
##     year month   day dep_time sched_dep_time dep_delay arr_time sched_arr_time
##    <int> <int> <int>    <int>          <int>     <dbl>    <int>          <int>
##  1  2013     1     1      517            515         2      830            819
##  2  2013     1     1      533            529         4      850            830
##  3  2013     1     1      542            540         2      923            850
##  4  2013     1     1      544            545        -1     1004           1022
##  5  2013     1     1      554            600        -6      812            837
##  6  2013     1     1      554            558        -4      740            728
##  7  2013     1     1      555            600        -5      913            854
##  8  2013     1     1      557            600        -3      709            723
##  9  2013     1     1      557            600        -3      838            846
## 10  2013     1     1      558            600        -2      753            745
## # … with 336,766 more rows, and 11 more variables: arr_delay <dbl>,
## #   carrier <chr>, flight <int>, tailnum <chr>, origin <chr>, dest <chr>,
## #   air_time <dbl>, distance <dbl>, hour <dbl>, minute <dbl>, time_hour <dttm>
```

---
## Kategorisering af variable

<div id="htmlwidget-fc0bd9c59ee827f32b60" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-fc0bd9c59ee827f32b60">{"x":{"filter":"none","vertical":false,"data":[["Kategorisk","Ordinal","Numerisk"],["Endelig mængde","Endelig ordnet mængde","Reelle tal"],["character/factor","factor","double/integer"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th>Variabel<\/th>\n      <th>Udfaldsrum<\/th>\n      <th>Datatype<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"ordering":false,"searching":false,"lengthChange":false,"info":false,"paging":false,"columnDefs":[{"className":"dt-head-left","targets":"_all"}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

```
## # A tibble: 336,776 × 5
##   carrier distance dep_delay tailnum flight
##   <chr>      <dbl>     <dbl> <chr>    <int>
## 1 UA          1400         2 N14228    1545
## 2 UA          1416         4 N24211    1714
## 3 AA          1089         2 N619AA    1141
## # … with 336,773 more rows
```

* `carrier` er en kategorisk variabel, datatypen er `character`

* `distance` er en numerisk variabel, datatypen er `double`

* `dep_delay` er en numerisk variabel, datatypen er `double` (kunne være `integer`)

* `tailnum` er en **kategorisk** variabel, datatypen er `character`

* `flight` (number) er en **kategorisk** variabel, datatypen er `integer`!

---
## Filtrering

```r
# Alaska Airlines
filter(flights, carrier == "AS")
```

```
## # A tibble: 714 × 19
##    year month   day dep_time sched_dep_time dep_delay arr_time sched_arr_time
##   <int> <int> <int>    <int>          <int>     <dbl>    <int>          <int>
## 1  2013     1     1      724            725        -1     1020           1030
## 2  2013     1     1     1808           1815        -7     2111           2130
## 3  2013     1     2      722            725        -3      949           1030
## # … with 711 more rows, and 11 more variables: arr_delay <dbl>, carrier <chr>,
## #   flight <int>, tailnum <chr>, origin <chr>, dest <chr>, air_time <dbl>,
## #   distance <dbl>, hour <dbl>, minute <dbl>, time_hour <dttm>
```

```r
flights
```

```
## # A tibble: 336,776 × 19
##    year month   day dep_time sched_dep_time dep_delay arr_time sched_arr_time
##   <int> <int> <int>    <int>          <int>     <dbl>    <int>          <int>
## 1  2013     1     1      517            515         2      830            819
## 2  2013     1     1      533            529         4      850            830
## 3  2013     1     1      542            540         2      923            850
## # … with 336,773 more rows, and 11 more variables: arr_delay <dbl>,
## #   carrier <chr>, flight <int>, tailnum <chr>, origin <chr>, dest <chr>,
## #   air_time <dbl>, distance <dbl>, hour <dbl>, minute <dbl>, time_hour <dttm>
```

---
## Filtrering

Forskellige betingelser kan kombineres i logiske udtryk.

```r
filter(flights, (carrier == "AS" | carrier == "AA") & tailnum == "N200AA")
```

```
## # A tibble: 34 × 19
##     year month   day dep_time sched_dep_time dep_delay arr_time sched_arr_time
##    <int> <int> <int>    <int>          <int>     <dbl>    <int>          <int>
##  1  2013     1     4       NA           1430        NA       NA           1735
##  2  2013     1    21      913            920        -7     1245           1245
##  3  2013    10     7     1233           1230         3     1430           1405
##  4  2013    10    22     1711           1715        -4     2013           2015
##  5  2013    10    31     1705           1715       -10     1841           1905
##  6  2013    11    14      927            929        -2     1220           1234
##  7  2013    11    16     1220           1225        -5     1513           1510
##  8  2013    12    31     1718           1720        -2     2027           2030
##  9  2013     2    19     1316           1300        16     1439           1440
## 10  2013     3     5     1900           1910       -10     2146           2215
## # … with 24 more rows, and 11 more variables: arr_delay <dbl>, carrier <chr>,
## #   flight <int>, tailnum <chr>, origin <chr>, dest <chr>, air_time <dbl>,
## #   distance <dbl>, hour <dbl>, minute <dbl>, time_hour <dttm>
```

Flyvninger, hvor fly N200AA har fløjet for enten Alaska Airlines eller 
American Airlines.

---
## Filtrering og variabelselektion

```r
Alaska_flights <- filter(flights, carrier == "AS")
Alaska_flights
```

```
## # A tibble: 714 × 19
##     year month   day dep_time sched_dep_time dep_delay arr_time sched_arr_time
##    <int> <int> <int>    <int>          <int>     <dbl>    <int>          <int>
##  1  2013     1     1      724            725        -1     1020           1030
##  2  2013     1     1     1808           1815        -7     2111           2130
##  3  2013     1     2      722            725        -3      949           1030
##  4  2013     1     2     1818           1815         3     2131           2130
##  5  2013     1     3      724            725        -1     1012           1030
##  6  2013     1     3     1817           1815         2     2121           2130
##  7  2013     1     4      725            725         0     1031           1030
##  8  2013     1     4     1808           1815        -7     2101           2130
##  9  2013     1     5      725            725         0     1011           1030
## 10  2013     1     5     1803           1815       -12     2118           2130
## # … with 704 more rows, and 11 more variables: arr_delay <dbl>, carrier <chr>,
## #   flight <int>, tailnum <chr>, origin <chr>, dest <chr>, air_time <dbl>,
## #   distance <dbl>, hour <dbl>, minute <dbl>, time_hour <dttm>
```

```r
Alaska_flights <- select(
  Alaska_flights, 
  c("carrier", "distance", "dep_delay", "tailnum", "flight")
)
```

---
## Filtrering og variabelselektion

```r
Alaska_flights
```

```
## # A tibble: 714 × 5
##   carrier distance dep_delay tailnum flight
##   <chr>      <dbl>     <dbl> <chr>    <int>
## 1 AS          2402        -1 N594AS      11
## 2 AS          2402        -7 N553AS       7
## 3 AS          2402        -3 N592AS      11
## # … with 711 more rows
```

Det er muligt at udvælge variable ved hjælp af en række selektionskriterier, 
f.eks.

```r
select(flights, dep_time:dep_delay)
```

```
## # A tibble: 336,776 × 3
##   dep_time sched_dep_time dep_delay
##      <int>          <int>     <dbl>
## 1      517            515         2
## 2      533            529         4
## 3      542            540         2
## # … with 336,773 more rows
```

---
## Quiz

Hvad er resultatet af følgende filtrering?

```r
filter(flights, carrier == "AS" & carrier == "AA")
```

Hvad er dimensionerne af tabellen efter følgende selektion af variable?

```r
select(flights, year:day)
```

---
## Løsning

```r
filter(flights, carrier == "AS" & carrier == "AA")
```

```r
select(flights, year:day)
```

---
## Pipe

Vi kan kæde flere operationer sammen med **nestede funktionskald**

```r
select(
  filter(flights, (carrier == "AS" | carrier == "AA") & tailnum == "N200AA"),
  year:day
)
```

```
## # A tibble: 34 × 3
##     year month   day
##    <int> <int> <int>
##  1  2013     1     4
##  2  2013     1    21
##  3  2013    10     7
##  4  2013    10    22
##  5  2013    10    31
##  6  2013    11    14
##  7  2013    11    16
##  8  2013    12    31
##  9  2013     2    19
## 10  2013     3     5
## # … with 24 more rows
```

---
## Pipe

Pipe operatoren `%>%` er syntaktisk sukker, der gør nestede funktionskald 
læsbare.

```r
flights %>% 
  filter((carrier == "AS" | carrier == "AA") & tailnum == "N200AA") %>% 
  select(year:day)
```

---
## Aktiv vs passiv undervisning

I et eksperiment blev 157 fysikstuderende delt i to grupper på et kursus 
i statik.

I gruppen `active` inkluderede undervisningsformen aktivt de studerende.

I gruppen `passive` inkluderede undervisningsformen ikke de studerende aktivt.

De studerende tog efterfølgende en test og evaluerede underviseren ved at 
svare på, i hvor høj grad de var enige i udsagnet

*The instructor was effective at teaching*

Testscoren er numerisk i intervallet `$[0,1]$` og evalueringen antager de 
fem værdier

`Strongly disagree`  
`Disagree`  
`Neither agree nor disagree`  
`Agree`  
`Strongly agree`

---
## Aktiv vs passiv undervisning

Data er i tabellen `statics`

```r
statics
```

```
## # A tibble: 157 × 3
##    Format Score Evaluation                
##    <chr>  <dbl> <chr>                     
##  1 active  0.78 Strongly agree            
##  2 active  0.47 Strongly agree            
##  3 active  0.65 Neither agree nor disagree
##  4 active  0.62 Agree                     
##  5 active  0.73 Agree                     
##  6 active  0.9  Agree                     
##  7 active  0.78 Neither agree nor disagree
##  8 active  0.71 Disagree                  
##  9 active  0.73 Strongly agree            
## 10 active  0.68 Strongly agree            
## # … with 147 more rows
```

Spørgsmål 1: Betyder undervisningsformen noget for, hvordan de studerende 
evaluerer underviseren?

---
## Tabulering

```r
summarize(statics, count = n())
```

```
## # A tibble: 1 × 1
##   count
##   <int>
## 1   157
```

```r
statics %>% 
group_by(Evaluation) %>% 
  summarize(count = n())
```

```
## # A tibble: 5 × 2
##   Evaluation                 count
##   <chr>                      <int>
## 1 Agree                         38
## 2 Disagree                      10
## 3 Neither agree nor disagree    19
## 4 Strongly agree                85
## 5 Strongly disagree              5
```

Stof til eftertanke: Hvordan er det lige at værdierne er ordnede? (MathDive 
Exercise 1.2)

---
## Tabulering for de to undervisningsformer

.small[

```r
statics %>% 
* filter(Format == "active") %>%
  group_by(Evaluation) %>% 
  summarize(count = n())
```

```
## # A tibble: 5 × 2
##   Evaluation                 count
##   <chr>                      <int>
## 1 Agree                         22
## 2 Disagree                       9
## 3 Neither agree nor disagree    12
## 4 Strongly agree                35
## 5 Strongly disagree              2
```
]

.small[

```r
statics %>% 
* filter(Format == "passive") %>%
  group_by(Evaluation) %>% 
  summarize(count = n())
```

```
## # A tibble: 5 × 2
##   Evaluation                 count
##   <chr>                      <int>
## 1 Agree                         16
## 2 Disagree                       1
## 3 Neither agree nor disagree     7
## 4 Strongly agree                50
## 5 Strongly disagree              3
```

]

Kan vi ikke gøre det nemmere?

---
## Krydstabulering

```r
statics %>% 
  group_by(Format, Evaluation) %>% 
  summarize(count = n())
```

```
## # A tibble: 10 × 3
## # Groups:   Format [2]
##    Format  Evaluation                 count
##    <chr>   <chr>                      <int>
##  1 active  Agree                         22
##  2 active  Disagree                       9
##  3 active  Neither agree nor disagree    12
##  4 active  Strongly agree                35
##  5 active  Strongly disagree              2
##  6 passive Agree                         16
##  7 passive Disagree                       1
##  8 passive Neither agree nor disagree     7
##  9 passive Strongly agree                50
## 10 passive Strongly disagree              3
```

---
# Pause

---
## Opsummering

* `filter()` udvælger **rækker** (observationer), som opfylder en betingelse.

Betingelser formuleres som logiske udtryk i termer af variable i data.

* `select()` udvælger **søjler** (variable) i henhold til et `tidy-select` udtryk.

Et udtryk kan være variabelnavne, men også meget andet.

* `%>%` (pipe) kombinerer to eller flere operationer.

Ækvivalent med nestede funktionskald, men lettere at læse.

* `summarize(count = n())` tæller.

I kombination med `group_by()` indenfor hver kombination af værdier for 
en eller flere variable.

* `read_csv()` indlæser data fra en tekstfil med "comma separated variables".

---
## Indlæsning af data

```r
statics <- read_csv(
  "../Data/statics.csv",
  col_types = cols(
    Evaluation = col_factor(
      levels = c(
        "Strongly disagree", 
        "Disagree", 
        "Neither agree nor disagree", 
        "Agree", 
        "Strongly agree"
      )
    )
  )
)
```

---
## Evaluation som faktor

```r
statics
```

```
## # A tibble: 157 × 3
##    Format Score Evaluation                
##    <chr>  <dbl> <fct>                     
##  1 active  0.78 Strongly agree            
##  2 active  0.47 Strongly agree            
##  3 active  0.65 Neither agree nor disagree
##  4 active  0.62 Agree                     
##  5 active  0.73 Agree                     
##  6 active  0.9  Agree                     
##  7 active  0.78 Neither agree nor disagree
##  8 active  0.71 Disagree                  
##  9 active  0.73 Strongly agree            
## 10 active  0.68 Strongly agree            
## # … with 147 more rows
```

```r
statics$Evaluation[1:4]
```

```
## [1] Strongly agree             Strongly agree            
## [3] Neither agree nor disagree Agree                     
## 5 Levels: Strongly disagree Disagree Neither agree nor disagree ... Strongly agree
```

---
## Krydstabulering igen

```r
long_tab <- statics %>% 
  group_by(Format, Evaluation) %>% 
  summarize(count = n())
```

```r
long_tab
```

```
## # A tibble: 10 × 3
## # Groups:   Format [2]
##    Format  Evaluation                 count
##    <chr>   <fct>                      <int>
##  1 active  Strongly disagree              2
##  2 active  Disagree                       9
##  3 active  Neither agree nor disagree    12
##  4 active  Agree                         22
##  5 active  Strongly agree                35
##  6 passive Strongly disagree              3
##  7 passive Disagree                       1
##  8 passive Neither agree nor disagree     7
##  9 passive Agree                         16
## 10 passive Strongly agree                50
```

---
## Pivoting

```r
long_tab %>% 
  pivot_wider(names_from = Format, values_from = count)
```

```
## # A tibble: 5 × 3
##   Evaluation                 active passive
##   <fct>                       <int>   <int>
## 1 Strongly disagree               2       3
## 2 Disagree                        9       1
## 3 Neither agree nor disagree     12       7
## 4 Agree                          22      16
## 5 Strongly agree                 35      50
```

En "bred" tabel er ikke tidy! Søjler er ikke variable, men værdier for en 
variabel.

"Lange" tabeller er tidy.

---
## Søjlediagrammer (bar plots)

```r
long_tab %>% 
  filter(Format == "active") %>% 
  ggplot(aes(x = Evaluation, y = count)) +
  geom_col()
```

---
## Søjlediagrammer (bar plots)

```r
*statics %>%
  filter(Format == "active") %>% 
  ggplot(aes(x = Evaluation)) +
* geom_bar()
```

---
## Quiz

Hvad sker der, hvis vi ikke filtrerer?

```r
statics %>% 
*# filter(Format == "active") %>%
  ggplot(aes(x = Evaluation)) +
  geom_bar()
```

Og hvad viser følgende figur?

```r
statics %>% 
  ggplot(aes(x = Evaluation, fill = Format)) +
  geom_bar()
```

---
## Løsning

```r
statics %>% 
*# filter(Format == "active") %>%
  ggplot(aes(x = Evaluation)) +
  geom_bar()
```

---
## Løsning

```r
statics %>% 
  ggplot(aes(x = Evaluation, fill = Format)) +
  geom_bar()
```

---
## Vejrdata

```r
weather  # In nycflights13 package
```

```
## # A tibble: 26,115 × 15
##    origin  year month   day  hour  temp  dewp humid wind_dir wind_speed
##    <chr>  <int> <int> <int> <int> <dbl> <dbl> <dbl>    <dbl>      <dbl>
##  1 EWR     2013     1     1     1  39.0  26.1  59.4      270      10.4 
##  2 EWR     2013     1     1     2  39.0  27.0  61.6      250       8.06
##  3 EWR     2013     1     1     3  39.0  28.0  64.4      240      11.5 
##  4 EWR     2013     1     1     4  39.9  28.0  62.2      250      12.7 
##  5 EWR     2013     1     1     5  39.0  28.0  64.4      260      12.7 
##  6 EWR     2013     1     1     6  37.9  28.0  67.2      240      11.5 
##  7 EWR     2013     1     1     7  39.0  28.0  64.4      240      15.0 
##  8 EWR     2013     1     1     8  39.9  28.0  62.2      250      10.4 
##  9 EWR     2013     1     1     9  39.9  28.0  62.2      260      15.0 
## 10 EWR     2013     1     1    10  41    28.0  59.6      260      13.8 
## # … with 26,105 more rows, and 5 more variables: wind_gust <dbl>, precip <dbl>,
## #   pressure <dbl>, visib <dbl>, time_hour <dttm>
```

```r
temperature <- select(weather, c("month", "temp"))
```

---
## Summarize

```r
temperature %>% 
  summarize(
    mean = mean(temp, na.rm = TRUE),
    std_dev = sd(temp, na.rm = TRUE)
  )
```

```
## # A tibble: 1 × 2
##    mean std_dev
##   <dbl>   <dbl>
## 1  55.3    17.8
```

```r
month_avg_temp <- temperature %>% 
* group_by(month) %>%
  summarize(
    mean = mean(temp, na.rm = TRUE),
    std_dev = sd(temp, na.rm = TRUE)
  )
```

---
## Summarize

```r
month_avg_temp
```

```
## # A tibble: 12 × 3
##    month  mean std_dev
##    <int> <dbl>   <dbl>
##  1     1  35.6   10.2 
##  2     2  34.3    6.98
##  3     3  39.9    6.25
##  4     4  51.7    8.79
##  5     5  61.8    9.68
##  6     6  72.2    7.55
##  7     7  80.1    7.12
##  8     8  74.5    5.19
##  9     9  67.4    8.47
## 10    10  60.1    8.85
## 11    11  45.0   10.4 
## 12    12  38.4    9.98
```

---
## Join

```r
temperature_joined <- temperature %>% 
  left_join(month_avg_temp)
```

```
## Joining, by = "month"
```

```r
temperature_joined
```

```
## # A tibble: 26,115 × 4
##    month  temp  mean std_dev
##    <int> <dbl> <dbl>   <dbl>
##  1     1  39.0  35.6    10.2
##  2     1  39.0  35.6    10.2
##  3     1  39.0  35.6    10.2
##  4     1  39.9  35.6    10.2
##  5     1  39.0  35.6    10.2
##  6     1  37.9  35.6    10.2
##  7     1  39.0  35.6    10.2
##  8     1  39.9  35.6    10.2
##  9     1  39.9  35.6    10.2
## 10     1  41    35.6    10.2
## # … with 26,105 more rows
```

---
## Standardize

```r
# No grouping needed here
temperature_joined %>%
  mutate(temp_stand = (temp - mean) / std_dev) %>% 
  select(c("month", "temp", "temp_stand"))
```

```
## # A tibble: 26,115 × 3
##    month  temp temp_stand
##    <int> <dbl>      <dbl>
##  1     1  39.0      0.331
##  2     1  39.0      0.331
##  3     1  39.0      0.331
##  4     1  39.9      0.419
##  5     1  39.0      0.331
##  6     1  37.9      0.225
##  7     1  39.0      0.331
##  8     1  39.9      0.419
##  9     1  39.9      0.419
## 10     1  41        0.525
## # … with 26,105 more rows
```

---
## Standardize

```r
temperature %>% 
* group_by(month) %>%
  mutate(temp_stand = (temp - mean(temp, na.rm = TRUE)) / sd(temp, na.rm = TRUE))
```

```
## # A tibble: 26,115 × 3
## # Groups:   month [12]
##    month  temp temp_stand
##    <int> <dbl>      <dbl>
##  1     1  39.0      0.331
##  2     1  39.0      0.331
##  3     1  39.0      0.331
##  4     1  39.9      0.419
##  5     1  39.0      0.331
##  6     1  37.9      0.225
##  7     1  39.0      0.331
##  8     1  39.9      0.419
##  9     1  39.9      0.419
## 10     1  41        0.525
## # … with 26,105 more rows
```

---
## Standardize

```r
temperature %>% 
  group_by(month) %>% 
  mutate(temp_stand = scale(temp) %>% as.numeric())
```