Rstudio

• Make a folder on your computer where you want to keep files to use in Rstudio. Do NOT use Danish characters æ, ø, å in the folder name (or anywhere in the path to the folder).
• Set the working directory to this folder: Session -> Set Working Directory -> Choose Directory (shortcut: Ctrl+Shift+H).
• Make the change permanent by setting the default directory in: Tools -> Global Options -> Choose Directory.

R extensions

• The functionality of R can be extended through libraries or packages (much like plugins in browsers etc.). Some are installed by default in R and you just need to load them.
• To install a new package in Rstudio use the menu: Tools -> Install Packages
• You need to know the name of the package you want to install. You can also do it through a command:

install.packages("mosaic")

• When it is installed you can load it through the library command:

library(mosaic)

• This loads the mosaic package which has a lot of convenient functions for this course (we will get back to that later). It also prints a lot of info about functions that have been changed by the mosaic package, but you can safely ignore that.

R help

• You get help via ?<command>:

?sum

• Use tab to make Rstudio guess what you have started typing.
• Search for help:

help.search("plot")

• You can find a cheat sheet with the R functions we use for this course here.

Data example

We use data about pengiuns from the R package palmerpenguins

pingviner <- palmerpenguins::penguins
pingviner

## # A tibble: 344 × 8
##    species island    bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
##    <fct>   <fct>              <dbl>         <dbl>             <int>       <int>
##  1 Adelie  Torgersen           39.1          18.7               181        3750
##  2 Adelie  Torgersen           39.5          17.4               186        3800
##  3 Adelie  Torgersen           40.3          18                 195        3250
##  4 Adelie  Torgersen           NA            NA                  NA          NA
##  5 Adelie  Torgersen           36.7          19.3               193        3450
##  6 Adelie  Torgersen           39.3          20.6               190        3650
##  7 Adelie  Torgersen           38.9          17.8               181        3625
##  8 Adelie  Torgersen           39.2          19.6               195        4675
##  9 Adelie  Torgersen           34.1          18.1               193        3475
## 10 Adelie  Torgersen           42            20.2               190        4250
## # ℹ 334 more rows
## # ℹ 2 more variables: sex <fct>, year <int>

• What is fundamentally different about the the variables (columns) species and body_mass_g?

Data types

Quantitative variables

• The measurements have numerical values.

• Quantative data often comes about in one of the following ways:

  • Continuous variables: measurements of time, length, size, age, mass, etc.
  • Discrete variables: counts of e.g. words in a text, hits on a webpage, number of arrivals to a queue in one hour, etc.

• Measurements like this have a well-defined scale and in R they are stored as the type numeric.

• It is important to be able to distinguish between discrete count variables and continuous variables, since this often determines how we describe the uncertainty of a measurement.

• Are any of the measurements in our data set quantitative?

Categorical/qualitative variables

• The measurement is one of a set of given categories, e.g. sex (male/female), social status, satisfaction score (low/medium/high), etc.
• The measurement is usually stored (which is also recommended) as a factor in R. The possible categories are called levels. Example: the levels of the factor “sex” is male/female.
• Factors have two so-called scales:
  • Nominal scale: There is no natural ordering of the factor levels, e.g. sex and hair color.
  • Ordinal scale: There is a natural ordering of the factor levels, e.g. social status and satisfaction score. A factor in R can have a so-called attribute assigned, which tells if it is ordinal.
• Are any of the measurements in our data set categorical/qualitative?

Scatterplot

• To study the relation between two quantitative variables a scatterplot is used:

gf_point(bill_length_mm ~ bill_depth_mm, color = ~ species, data = pingviner)

• We could also draw the graph for each species:

gf_point(bill_length_mm ~ bill_depth_mm | species, color = ~ species, data = pingviner)

• If we want a regression line along with the points we can do:

gf_point(bill_length_mm ~ bill_depth_mm, color = ~ species, data = pingviner) %>% 
  gf_lm()

Histogram

• For a single quantitative variable a histogram offers more details:

gf_histogram( ~ bill_length_mm, data = pingviner)

• How to make a histogram for some variable x:
  • Divide the interval from the minimum value of x to the maximum value of x in an appropriate number of equal sized sub-intervals.
  • Draw a box over each sub-interval with the height being proportional to the number of observations in the sub-interval.

Percentiles

• The \(p\)th percentile is a value such that at least \(p\)% of the sample lies below or at this value and at least \((100-p)\)% of the sample lies above or at the value.

Q <- quantile(bill_length_mm ~ species, data = pingviner, na.rm = TRUE)
Q

##     species 0% 25% 50% 75% 100%
## 1    Adelie 32  37  39  41   46
## 2 Chinstrap 41  46  50  51   58
## 3    Gentoo 41  45  47  50   60

• 50-percentile is the median and it is a measure of the center of data as the number of data points below the median is the samme as the number above the median.
• 0-percentile is the minimum value.
• 25-percentile is called the lower quartile (Q1). Median of lower 50% of data.
• 75-percentile is called the upper quartile (Q3). Median of upper 50% of data.
• 100-percentil is the maximum value.
• Interquartile Range (IQR): a measure of variability given by the difference of the upper and lower quartiles.

Boxplot

Boxplot can be good for comparing groups (notice we put the values on the y-axis here as it is more conventional for boxplots):

gf_boxplot(bill_length_mm ~ species, color = ~ species, data = pingviner)

How to draw a box plot

• Box:
  • Calculate the median, lower and upper quartiles.
  • Plot a line by the median and draw a box between the upper and lower quartiles.
• Whiskers:
  • Calculate interquartile range and call it IQR.
  • Calculate the following values:
    • L = lower quartile - 1.5*IQR
    • U = upper quartile + 1.5*IQR
  • Draw a line from lower quartile to the smallest measurement, which is larger than L.
  • Similarly, draw a line from upper quartile to the largest measurement which is smaller than U.
• Outliers: Measurements smaller than L or larger than U are drawn as circles.

Note: Whiskers are minimum and maximum of the observations that are not deemed to be outliers.

Measures of center of data: Mean and median

• A number of numerical summaries can be retrieved using the favstats command:

favstats(bill_length_mm ~ species, data = pingviner)

##     species min Q1 median Q3 max mean  sd   n missing
## 1    Adelie  32 37     39 41  46   39 2.7 151       1
## 2 Chinstrap  41 46     50 51  58   49 3.3  68       0
## 3    Gentoo  41 45     47 50  60   48 3.1 123       1

• The observed values of bill_length_mm are \(y_1=46.1\), \(y_2=50,\ldots,y_n=49.9\), where there are a total of \(n=123\) values.

As previously defined this constitutes a sample.

• mean = 48 is the average of the sample, which is calculated by \[ \bar{y}=\frac{1}{n}\sum_{i=1}^n y_i. \] We may also call \(\bar{y}\) the (empirical) mean or the sample mean. It is calculated using mean() in R.
• median = 47 is calculated using median() in R.
• An important property of the mean and the median is that they have the same unit as the observations (e.g. millimeter).

Measures of variability of data: range, standard deviation and variance

• The range is the difference of the largest and smallest observation (range() in R).
• The (empirical) variance (var() in R) is the average of the squared deviations from the mean: \[ s^2=\frac{1}{n-1}\sum_{i=1}^n (y_i-\bar{y})^2. \]
• sd \(=\) standard deviation \(= s=\sqrt{s^2}\) (sd() in R).
• Note: If the observations are measured in mm, the variance has unit \(\text{mm}^2\) which is hard to interpret. The standard deviation on the other hand has the same unit as the observations.
• The standard deviation describes how much data varies around the (empirical) mean.

The empirical rule

If the histogram of the sample looks like a bell shaped curve, then

• about 68% of the observations lie between \(\bar{y}-s\) and \(\bar{y}+s\).
• about 95% of the observations lie between \(\bar{y}-2s\) and \(\bar{y}+2s\).
• All or almost all (99.7%) of the observations lie between \(\bar{y}-3s\) and \(\bar{y}+3s\).