stat4arch

Petr Pajdla & Peter Tkáč

AES_707: Statistics seminar for archaeologists

Seminar 3

17. 3. 2022

Today:

  • Data visualization, plots for one variable.
  • Descriptive stats.
  • Data manipulation basics (base R and dplyr package).
  • Plotting in ggplot2.

Descriptive statistics

Characterizing centrality

Mean

mean(x)
\( \begin{aligned} \overline{x} = \frac{x_1 + x_2 + \cdots + x_n}{n} = \frac{1}{n} (\sum^n_{i=1}x_i) \end{aligned} \)

Median

median(x)
Robust, minimizes influence of outliers.

Characterizing dispersion and/or spread

Range

(rozpětí)
max(x) - min(x) or range(x)

Variance and Standard deviation

(rozptyl a směrodatná odchylka)
sd(x)
\( \begin{aligned} \sigma = \sqrt{s^2} = \sqrt{\frac{\sum(x_i-\overline{x})^2}{n-1}} \end{aligned} \)

Interquartile range

(midspread, IQR, kvantil, mezikvartilové rozpětí)
IQR(x)
Robust, minimizes influence of outliers.

Why look at data then?

Anscombe's quartet

# A tibble: 4 × 6
    set `mean(x)` `sd(x)` `mean(y)` `sd(y)` `cor(x, y)`
  <int>     <dbl>   <dbl>     <dbl>   <dbl>       <dbl>
1     1         9    3.32      7.50    2.03       0.816
2     2         9    3.32      7.50    2.03       0.816
3     3         9    3.32      7.5     2.03       0.816
4     4         9    3.32      7.50    2.03       0.817

Four sets of numerical data, all have almost identical values of descriptive statistics…

Why look at data then?

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Visualizing data

Brainstorming

  • Prečo potrebujeme vizualizovať data?
  • Aké vlastnosti má mať dobrý graf?
  • Aké prvky vieme na grafe pomenovať?

Data viz

(Minard 1869)

Data viz

(Snow 1854)

Types of graphs

Bar chart

(Sloupcový graf)
Distribution of values of a qualitative variable.

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Histogram

Distribution of values of a quantitative variable.

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Density plot

Similar to histogram, great for comparison.

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Boxplot

(Krabicový graf)
Comparison of two and more quantitative variables.

Boxplot

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Plotting in R

  • Base graphics with plot
  • Package ggplot2

Base graphics

Cvičenie s tabulkou lokality.

   lokalita objekty_ks
1 Vedrovice         27
2  Kyjovice         13
3  Pohansko         55
4 Mikulčice         29
5    Znojmo         20

barplot(lokality$objekty_ks, 
        names.arg = lokality$lokalita, 
        col = "lightblue")

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Package ggplot2

install.packages("ggplot2")

library(ggplot2)

Syntax

ggplot(data = lokality, aes(x = lokalita, y = objekty_ks)) +
  geom_bar(stat = "identity")

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Dlhý zápis:

ggplot(data = lokality, mapping = aes(x = lokalita, y = objekty_ks)) +
  geom_bar(stat = "identity")

Krátky zápis:

ggplot(lokality, aes(lokalita, objekty_ks)) +
  geom_bar(stat = "identity")

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Barplot

Cvičenie s databázou EWBurials.

library(archdata) # ?EWBurials
data(EWBurials)
hroby <- data.frame(EWBurials)
head(hroby, 4)

     Group  North  West         Age  Sex Direction Looking   Goods
011      2  96.96 90.32 Young Adult Male        42     283 Present
014      2 100.20 90.61 Young Adult Male        28     272 Present
015      2 101.74 91.62   Old Adult Male       350     219 Present
016a     2 101.00 90.47 Young Adult Male       335      60  Absent

Otázky

  • aký je pomer mužských a ženských hrobov?
  • aké je zastúpenie vekových kategórií medzi pohlaviami?
  • líšila sa prítommosť milodarov (1) v závislosti na pohlaví alebo (2) v závislosti na veku?
  • aké sú rozdiely medzi skupinami?

1. Aký je pomer mužských a ženských hrobov?

p <- ggplot(hroby, aes(x = Sex))

p + geom_bar()

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Ako by ste spravili podobný graf, zobrazujúci rozdelenie hrobov podľa veku?

p <- ggplot(hroby, aes(x = Age))

p + geom_bar()

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Labels

p <- ggplot(hroby, aes(x = Sex)) +
  geom_bar()

p + labs(x = "pohlaví", 
         y = "počet", 
         title = "Počet hrobů podle pohlaví", 
         caption = "Archdata::EWBurials")

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2. Aké je zastúpenie vekových kategórií medzi pohlaviami?

Stacked bar chart: geom_bar().

p <- ggplot(hroby, aes(x = Sex, fill = Age))

p + geom_bar()

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2. Aké je zastúpenie vekových kategórií medzi pohlaviami?

Dodged bar chart: geom_bar(position = "dodge").

p <- ggplot(hroby, aes(x = Sex, fill = Age))

p + geom_bar(position = "dodge")

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3a. Líšila sa prítommosť milodarov v závislosti na pohlaví?

p <- ggplot(hroby, aes(x = Sex, fill = Goods))

p + geom_bar()

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3b. Líšila sa prítommosť milodarov v závislosti na veku?

Absolútne čísla

p <- ggplot(hroby, aes(x = Age, fill = Goods))

p + geom_bar()

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3b. Líšila sa prítommosť milodarov v závislosti na veku?

Relatívny pomer

geom_bar(position = "fill")

p <- ggplot(hroby, aes(x = Age, fill = Goods))

p + geom_bar(position = "fill")

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4. Aké sú rozdiely medzi skupinami?

p <- ggplot(hroby, aes(x = Age))

p + geom_bar() +
  facet_grid(Sex ~ Group)

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Aby to nebolo tak jednoduché...

Aký je rozdiel medzi týmito datasetmi?

hroby

     Group  North  West         Age  Sex Direction Looking   Goods
011      2  96.96 90.32 Young Adult Male        42     283 Present
014      2 100.20 90.61 Young Adult Male        28     272 Present
015      2 101.74 91.62   Old Adult Male       350     219 Present
016a     2 101.00 90.47 Young Adult Male       335      60  Absent
018      2 101.65 90.46   Old Adult Male         3      86 Present
020      1  95.17 90.53 Young Adult Male       142      21  Absent

lokality

   lokalita objekty_ks
1 Vedrovice         27
2  Kyjovice         13
3  Pohansko         55
4 Mikulčice         29
5    Znojmo         20

p <- ggplot(hroby, aes(x = Age))
p + geom_bar()

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p <- ggplot(lokality, 
            aes(x = lokalita, 
                y = objekty_ks))
p + geom_bar(stat="identity")

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Project assignment

Where to look for data sets?

library(archdata)
?archdata # list of data sets in the package