Review

• A data visualisation consists of data symbols (and guides) and labels.

• We create a data symbol by mapping data values to the visual features of a shape.

• Which visual feature we choose depends on:

  • Whether we have quantitative or qualitative data.
  • The accuracy and capacity of the visual feature.
  • The question we are interested in answering.

Review

• We have so far focused on a single mapping from data values to a visual feature (and back).

Combining Visual Features

• All data visualisations employ multiple visual features, but we have so far assumed that those features operate independently.

• We have also largely assumed that we are only interested in mapping back to the raw data.

• In this section we will begin to consider more complex mappings between data values and visual features.

Combining Visual Features

• Describing Mappings

• Visual Summaries

• Redundant Mappings

• Independent Visual Features

• Visual Features that Interact

• Other Types of Interaction

Rugby World Cup

• The RWCperGame data frame contains measures of performance at the Rugby World Cup of 2023 for different countries, plus the hemisphere that each country is from.

  head(tibble(RWCperGame))

  ## # A tibble: 6 × 11
  ##   country   hemisphere yellowcards redcards cleanbreaks
  ##   <chr>     <fct>            <dbl>    <dbl>       <dbl>
  ## 1 Namibia   South             1        0.5         2.5 
  ## 2 Romania   North             1.25     0           2.75
  ## 3 Chile     South             1.25     0           3.75
  ## 4 Samoa     South             1.25     0.25        3.75
  ## 5 Australia South             0.5      0           5.25
  ## 6 Georgia   North             0.5      0           5.25
  ## # ℹ 6 more variables: tackles <dbl>, points <dbl>,
  ## #   conversions <dbl>, offloads <dbl>, tries <dbl>,
  ## #   runs <dbl>

A Simple Mapping

• The simplest case involves mapping one data value from one variable to one visual feature of one data symbol.

• The number of cleanbreaks for one country maps to the position of one point.

A Simple Mapping

• The number of cleanbreaks for one country maps to the position of one point.

ggplot(RWCperGame) + 
    geom_point(aes(x=cleanbreaks, y=""),
               position=position_jitter(width=0, height=.1, seed=123))

A Simple Mapping

• The simplest case involves mapping one data value from one variable (a) to one visual feature (x) of one data symbol.

A Simple Mapping

• The simplest case involves mapping back from the visual feature to the raw data.

A Simple Mapping

• The position of each point allows us to compare the cleanbreaks of different countries.

  • One country makes 2.5 cleanbreaks per game.
  • One country makes 10 more cleanbreaks.
  • Some countries make twice the number of cleanbreaks compared to others.

Visual Summaries

• We can also perceive visual summaries from a visual feature:

  • The range of cleanbreaks.
  • The average number of cleanbreaks.
  • The mode of cleanbreaks.

Visual Summaries

• We can map back from a visual feature to the raw data.

• We can also map back from visual summaries to data statistics.

An effective data visualisation will produce visual summaries of the data.

• An effective visual summary relies on rapid parallel processing of multiple basic data symbols and features.

• An effective visual summary does not require conscious attention to each individual data symbol.

Visual summaries provide less precision, but more detail than a typical mathematical summary.

Redundant Mappings

• We can map one data value from one variable to two visual features of one data symbol.

• The number of cleanbreaks for one country maps to the position and colour of one point.

Redundant Mappings

• The number of cleanbreaks for one country maps to the position and colour of one point.

ggplot(RWCperGame) + 
    geom_point(aes(x=cleanbreaks, y="", colour=cleanbreaks),
               position=position_jitter(width=0, height=.1, seed=123))

Redundant Mappings

• We can map one data value from one variable (a) to two visual features (x and y) of one data symbol.

Redundant Mappings

• A redundant mapping provides multiple paths from the visual features back to the raw data.

It can be effective to map a data value to multiple visual features.

• A colour-blind viewer who is unable to map colour back to data values may be able to map another visual feature.

Independent Visual Features

• We can map data values from two variables to two visual features of a data symbol.

• The cleanbreaks and the hemisphere from one country maps to the position and colour of one point.

Independent Visual Features

• The cleanbreaks and the hemisphere from one country maps to the position and colour of one point.

ggplot(RWCperGame) + 
    geom_point(aes(x=cleanbreaks, y="", colour=hemisphere),
               position=position_jitter(width=0, height=.1, seed=123))

Independent Visual Features

• We can map data values from two variables (a and b) to two visual features (x and y) of one data symbol.

Independent Visual Features

• Position and colour do not interact.

• We can perceive the positions of points independently of the colour of the points.

Independent Visual Features

• This is also true for a combination of position and length.

An effective data visualisation allows each individual visual feature to map back to the corresponding data values.

Visual Features that Interact

• We can map data values from two variables to two visual features of a data symbol.

Visual Features that Interact

• The cleanbreaks and the tries from one country map to the horizontal and vertical position of one point.

• The cleanbreaks and the tries from one country map to the horizontal and vertical position of one point.

ggplot(RWCperGame) + 
    geom_point(aes(x=cleanbreaks, y=tries))

Visual Features that Interact

• The horizontal and vertical position interact to produce position in space (2D).

Visual Features that Interact

• Position in space allows us to perceive interactions between the original data values.

• Position in space provides visual summaries.

  • Clusters or groups of points (proximity).
  • The correlation between cleanbreaks and tries.

Some combinations of visual features can be effective by producing additional visual features.

• The additional visual features can map back to information about interactions between data variables.

Youth Crime

• The crimeEthnicity data frame contains the crime rate and the population for different ethnicitys over multiple years.

head(crimeEthnicity)

##   ethnicity year count      prop   yearDate
## 1     Māori 2011  5957 46.451965 2011-06-30
## 2  Pasifika 2011  1092  8.515284 2011-06-30
## 3     Asian 2011   243  1.894885 2011-06-30
## 4     MELAA 2011    99  0.771990 2011-06-30
## 5     Other 2011    58  0.452277 2011-06-30
## 6  European 2011  5375 41.913600 2011-06-30

Visual Features that Interact

• We can map the pop and rate to the horizontal and vertical length (width and height) of rectangles.

• We can map the pop and rate to the horizontal and vertical length (width and height) of rectangles.

ggplot(crimeGroup) +
    geom_tile(aes(x=year, y=group, width=pop/200000, height=rate/1500))

• Horizontal and vertical length interact to produce area and shape.

• In this case, area allows us to perceive count.

• In this case, the additional shape feature makes it harder to perceive the separate length features.

Some combinations of visual features can be effective by producing additional visual features.

• Additional visual features map back to data statistics.

• We may not be able to map back to the raw data.

Accidental Interaction

• Is there a correlation between country and cleanbreaks?

An effective data visualisation combines visual features that generate additional visual features only on purpose.

• We want to combine visual features that interact when the interaction is useful.

• We want to combine visual features that are independent when interaction is not useful.

Visual Features that Interact

• The perception of correlation is affected by the amount of white space.

Visual Features that Interact

• The perception of correlation is affected by the amount of white space.

Interaction Between Data Symbols

• The interaction between visual features can be weakened or broken by the presence of other data symbols.

Proximity

• Gestalt proximity says that items that are close together are seen as a group.

• Discretised data values can create columns or rows of data symbols.

Summary

• We can perceive visual summaries that map back to data statistics.

• When we combine visual features, the features may act independently, or the features may interact.

• Interactions between features can produce additional visual features.

• We want to select visual features that interact only when we want to produce the additional visual effects.

• The interaction between visual features can be sensitive to context.

Exercise

• The RWCperGame data frame contains measures of performance at the Rugby World Cup of 2023 for different countries, plus the hemisphere that each country is from.

• We can also calculate the conversionRate for each country.

  RWCperGame$conversionRate <- 
      RWCperGame$conversions/RWCperGame$tries

Exercise

• We want to explore the conversionRate
  • Comparing one country with another.
  • Is there a correlation with the number of tries?

head(RWCperGame[c("country", "tries", "conversionRate")])

##      country tries conversionRate
## 11   Namibia  0.75      0.6666667
## 14   Romania  1.00      0.7500000
## 3      Chile  1.00      0.5000000
## 15     Samoa  2.75      0.7272727
## 2  Australia  2.75      0.6363636
## 7    Georgia  1.75      0.5714286

cor(RWCperGame$tries, RWCperGame$conversionRate)

## [1] 0.3820937

• Comparing one country with another.

  • Do the visual features interact or are they independent?
  • Are there any additional visual features?
  • Are there any visual summaries?

• Is there a correlation with the number of tries?

  • Do the visual features interact or are they independent?
  • Are there any additional visual features?
  • Are there any visual summaries?

Exercise

• Can you write {ggplot2} code to produce the previous two data visualisations?

Exercise