R4DS

data science?

data science?

what R is (not)

special purpose programming language for data science statistical computing

• statistics
• data mining
• data visualization

authority says to tell you to not think of R as a programming language!

past & present

some basic properties

6 * 7

## [1] 42

x = c(1,2,3)
x + 1

## [1] 2 3 4

m = matrix(c(1,2,3,4), nrow = 2)
m[1,]

## [1] 1 3

# this is (usually) slow
x = c()
for (i in 1:10000) {
  x[i] = crazyFunction(i)
}

# this is (usually) faster
sapply(1:10000, function(i) crazyFunction(i))

x <- 3
3 -> y
x == y

## [1] TRUE

extensibility & community support

a lot of innovation and development takes place in packages

go browse some 12,000 packages on CRAN

install.packages('tidyverse')

library(tidyverse)

base R & package functions

base R functionality is always available

rnorm(n = 5, mean = 10) # 5 samples from a normal with mean 10 & std. dev. 1 (default)

## [1]  9.208483  9.652608 10.813054  9.724418  9.919161

packages bring extra functions

library(mvtnorm)
mvtnorm::rmvnorm(n = 3, mean = rep(10,5)) # 3 samples from a multivariate normal

##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] 10.365201  9.824756  9.502824  9.455536 10.553926
## [2,] 11.757588 10.121859 11.122611 10.619925 11.393111
## [3,]  9.769219  9.930861 10.394108 11.623506  9.759871

help

help('rmvnorm')

Mvnorm {mvtnorm}    R Documentation
Multivariate Normal Density and Random Deviates

Description

These functions provide the density function and a random number generator
for the multivariate normal distribution with mean equal to mean and 
covariance matrix sigma.

Usage

dmvnorm(x, mean = rep(0, p), sigma = diag(p), log = FALSE)
rmvnorm(n, mean = rep(0, nrow(sigma)), sigma = diag(length(mean)),
    method=c("eigen", "svd", "chol"), pre0.9_9994 = FALSE)

RStudio

integrated development environment for R

types of data

this course will focus (entirely?) on rectangular data

not covered:

• image data
• sound data
• video data
• corpora
• …

rectangular data

library(nycflights13)
nycflights13::flights

## # A tibble: 336,776 x 19
##     year month   day dep_time sched_dep_time dep_delay arr_time
##    <int> <int> <int>    <int>          <int>     <dbl>    <int>
##  1  2013     1     1      517            515        2.      830
##  2  2013     1     1      533            529        4.      850
##  3  2013     1     1      542            540        2.      923
##  4  2013     1     1      544            545       -1.     1004
##  5  2013     1     1      554            600       -6.      812
##  6  2013     1     1      554            558       -4.      740
##  7  2013     1     1      555            600       -5.      913
##  8  2013     1     1      557            600       -3.      709
##  9  2013     1     1      557            600       -3.      838
## 10  2013     1     1      558            600       -2.      753
## # ... with 336,766 more rows, and 12 more variables: sched_arr_time <int>,
## #   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>

tidy data

1. each variable is a column
2. each observation is a row
3. each value is a cell

untidy data 1

this is untidy

grades = tibble(name = c('Michael', 'Noa', 'Obioma'),
                midterm = c(3.7, 1.0, 1.3),
                final = c(4.0, 1.3, 1.0))
grades

## # A tibble: 3 x 3
##   name    midterm final
##   <chr>     <dbl> <dbl>
## 1 Michael    3.70  4.00
## 2 Noa        1.00  1.30
## 3 Obioma     1.30  1.00

to tidy up, we need to gather columns which are not variables into a new column

grades %>% gather('midterm', 'final', key = 'exam', value = 'grade')

## # A tibble: 6 x 3
##   name    exam    grade
##   <chr>   <chr>   <dbl>
## 1 Michael midterm  3.70
## 2 Noa     midterm  1.00
## 3 Obioma  midterm  1.30
## 4 Michael final    4.00
## 5 Noa     final    1.30
## 6 Obioma  final    1.00

untidy data 2

this is untidy too

results = tibble(name = c('Michael', 'Noa', 'Obioma', 'Michael', 'Noa', 'Obioma'),
                 what = rep(c('grade', 'points'), each = 3),
                 howmuch = c(3.7, 1.0, 1.0, 55, 99, 99))
results

## # A tibble: 6 x 3
##   name    what   howmuch
##   <chr>   <chr>    <dbl>
## 1 Michael grade     3.70
## 2 Noa     grade     1.00
## 3 Obioma  grade     1.00
## 4 Michael points   55.0 
## 5 Noa     points   99.0 
## 6 Obioma  points   99.0

to tidy up, we need to spread cells from a row out over several columns

results %>% spread(key = 'what', value = 'howmuch')

## # A tibble: 3 x 3
##   name    grade points
##   <chr>   <dbl>  <dbl>
## 1 Michael  3.70    55.
## 2 Noa      1.00    99.
## 3 Obioma   1.00    99.

overview

truth-value judgement task

test your intuitions

“Some of the circles are black.”

rating scale task

design

• replication/extension of previous work
  • van Tiel & Geurts (2014), van Tiel (2014), Degen & Tanenhaus (2015)
• 4 experimental variants:
  • binary truth-value judgements vs. 7-point rating scale
  • include filler sentences with \(\textit{many}\) and \(\textit{most}\) or not
• participants recruited via Amazon’s Mechanical Turk
  • each subject rated 3 sentences with some
  • pseudo-randomized order; fully randomized visual displays

dummy

read data

d = readr::read_csv('../data/00_typicality_some.csv') # from package 'readr'

## Parsed with column specification:
## cols(
##   id = col_integer(),
##   language = col_character(),
##   rt = col_integer(),
##   type = col_character(),
##   response = col_integer(),
##   nr_black = col_integer(),
##   variant = col_character(),
##   comments = col_character()
## )

inspect data

d

## # A tibble: 5,112 x 8
##       id language    rt type   response nr_black variant comments
##    <int> <chr>    <int> <chr>     <int>    <int> <chr>   <chr>   
##  1     1 English   3930 filler        1        5 C       No      
##  2     1 English   3108 most          0        5 C       No      
##  3     1 English   2599 filler        1        8 C       No      
##  4     1 English   4405 many          1        7 C       No      
##  5     1 English   2574 some          1        6 C       No      
##  6     1 English   1917 filler        1        3 C       No      
##  7     1 English   2471 filler        0        3 C       No      
##  8     1 English   2495 many          0        6 C       No      
##  9     1 English   2093 some          1        9 C       No      
## 10     1 English   1767 filler        0        2 C       No      
## # ... with 5,102 more rows

any comments?

levels(factor(d$comments))[1:20]

##  [1] "bonuses always help with a toddler in the home ;)"                                                                         
##  [2] "Cheers."                                                                                                                   
##  [3] "cool!"                                                                                                                     
##  [4] "Easy HIT thanks!"                                                                                                          
##  [5] "Everything worked fine, thanks"                                                                                            
##  [6] "fun"                                                                                                                       
##  [7] "Fun and interactive. Thank you!"                                                                                           
##  [8] "fun fun fun"                                                                                                               
##  [9] "Fun study"                                                                                                                 
## [10] "Fun study, thanks"                                                                                                         
## [11] "fun survey"                                                                                                                
## [12] "Fun, thanks!"                                                                                                              
## [13] "good hit"                                                                                                                  
## [14] "Good luck with your research!"                                                                                             
## [15] "great hit"                                                                                                                 
## [16] "Great hit, good luck with your research."                                                                                  
## [17] "Great HIT!"                                                                                                                
## [18] "Great survey. Thank you!"                                                                                                  
## [19] "Hi"                                                                                                                        
## [20] "I accidentally clicked \"false\" on one of the \"some are black\" statements.  It was the one where around half were black"

self-reported native languages

table(d$language)

## 
## American English          Egnlish          Enblish         Englashi 
##                8               13                8                8 
##          english          English          ENGLISH          englsih 
##             2410             2457              103               26 
##          englush         Enlglish           FRENCH         Japanese 
##               13                8               13                8 
##          Russian          Spanish            Tamil            white 
##                8                8                8               13

filter non-native speakers of Enblush

d = dplyr::filter(d, ! language %in% c("FRENCH", "Japanese", "Russian", "Spanish", "Tamil", "white"))
table(d$language)

## 
## American English          Egnlish          Enblish         Englashi 
##                8               13                8                8 
##          english          English          ENGLISH          englsih 
##             2410             2457              103               26 
##          englush         Enlglish 
##               13                8

select relevant columns & rows

d = d %>% dplyr::filter(type == "some") %>% 
          dplyr::select(-language, -comments, -type)
d

## # A tibble: 1,449 x 5
##       id    rt response nr_black variant
##    <int> <int>    <int>    <int> <chr>  
##  1     1  2574        1        6 C      
##  2     1  2093        1        9 C      
##  3     1  2543        1        3 C      
##  4     2  1857        4        5 B      
##  5     2 11454        4       10 B      
##  6     2  2053        4        3 B      
##  7     3  1479        1       10 D      
##  8     3  1640        0        0 D      
##  9     3  1199        1        7 D      
## 10     4  4828        6        6 B      
## # ... with 1,439 more rows

more intelligible column names

d = d %>% dplyr::rename(condition = nr_black)
d

## # A tibble: 1,449 x 5
##       id    rt response condition variant
##    <int> <int>    <int>     <int> <chr>  
##  1     1  2574        1         6 C      
##  2     1  2093        1         9 C      
##  3     1  2543        1         3 C      
##  4     2  1857        4         5 B      
##  5     2 11454        4        10 B      
##  6     2  2053        4         3 B      
##  7     3  1479        1        10 D      
##  8     3  1640        0         0 D      
##  9     3  1199        1         7 D      
## 10     4  4828        6         6 B      
## # ... with 1,439 more rows

adding columns

d = d %>% dplyr::mutate(dependent.measure = ifelse(variant %in% c("A", "B"), "ordinal", "binary"),
                        alternatives = factor(ifelse(variant %in% c("A", "C"), "present", "absent"))) %>% 
          dplyr::select(- variant)
d

## # A tibble: 1,449 x 6
##       id    rt response condition dependent.measure alternatives
##    <int> <int>    <int>     <int> <chr>             <fct>       
##  1     1  2574        1         6 binary            present     
##  2     1  2093        1         9 binary            present     
##  3     1  2543        1         3 binary            present     
##  4     2  1857        4         5 ordinal           absent      
##  5     2 11454        4        10 ordinal           absent      
##  6     2  2053        4         3 ordinal           absent      
##  7     3  1479        1        10 binary            absent      
##  8     3  1640        0         0 binary            absent      
##  9     3  1199        1         7 binary            absent      
## 10     4  4828        6         6 ordinal           absent      
## # ... with 1,439 more rows

rescale responses

d = d %>% mutate(response = purrr::map2_dbl(dependent.measure, response, 
                                            function(x,y) { ifelse(x == "ordinal", (y-1)/6, y) } ))
d

## # A tibble: 1,449 x 6
##       id    rt response condition dependent.measure alternatives
##    <int> <int>    <dbl>     <int> <chr>             <fct>       
##  1     1  2574    1.00          6 binary            present     
##  2     1  2093    1.00          9 binary            present     
##  3     1  2543    1.00          3 binary            present     
##  4     2  1857    0.500         5 ordinal           absent      
##  5     2 11454    0.500        10 ordinal           absent      
##  6     2  2053    0.500         3 ordinal           absent      
##  7     3  1479    1.00         10 binary            absent      
##  8     3  1640    0.            0 binary            absent      
##  9     3  1199    1.00          7 binary            absent      
## 10     4  4828    0.833         6 ordinal           absent      
## # ... with 1,439 more rows

get mean RTs for dependent measures

d %>% dplyr::group_by(dependent.measure) %>% 
      dplyr::summarize(mean.response = mean(response))

## # A tibble: 2 x 2
##   dependent.measure mean.response
##   <chr>                     <dbl>
## 1 binary                    0.785
## 2 ordinal                   0.600

get mean responses

resp.summary = d %>% dplyr::group_by(dependent.measure, alternatives, condition) %>% 
                     dplyr::summarize(mean.response = mean(response))
resp.summary

## # A tibble: 44 x 4
## # Groups:   dependent.measure, alternatives [?]
##    dependent.measure alternatives condition mean.response
##    <chr>             <fct>            <int>         <dbl>
##  1 binary            absent               0        0.0909
##  2 binary            absent               1        0.478 
##  3 binary            absent               2        0.778 
##  4 binary            absent               3        0.958 
##  5 binary            absent               4        0.964 
##  6 binary            absent               5        1.00  
##  7 binary            absent               6        0.938 
##  8 binary            absent               7        0.980 
##  9 binary            absent               8        0.929 
## 10 binary            absent               9        0.967 
## # ... with 34 more rows

a naked plot

ggplot()

plotting mean responses

ggplot(data = resp.summary, aes(x = condition, y = mean.response)) +
  geom_point()

plotting mean responses per treatment

ggplot(data = resp.summary, aes(x = condition, y = mean.response, color = alternatives)) +
  geom_point()

plotting mean responses per treatment & depentend measure

ggplot(data = resp.summary, aes(x = condition, y = mean.response, color = alternatives)) +
  geom_point() + geom_line() + facet_grid( . ~ dependent.measure)

some cosmetics

ggplot(data = resp.summary, aes(x = condition, y = mean.response, color = alternatives)) +
  geom_point() + geom_line() + facet_grid( . ~ dependent.measure) + 
  xlab("number of black balls") + ylab("mean response") +
  scale_x_continuous(breaks = 0:10) + scale_color_manual(values = c("darkgrey", "firebrick"))

homework

• dive into R for Data Science

• extend your implementation of the (cat) picture rating task in the following way:
  • each time the experiment starts the participant is allocated at random to either a 2-button forced choice task or a slider rating task
    • you can find different response measures implemented in the ResponseTypeTemplate
  • in the 2-button forced choice task, everything stays as it is
  • in the slider rating task, participants see all of your lovely pictures but rate them on a slider scale rather than make a forced choice