visualization lecture notes - 7com1079 team research and

Visualization – Lecture notes7COM1079 – Team Research and Development Project

Dr. John NollUniversity of Hertfordshire

Part 1: Types of Visualization

Visualization – Lecture notes 7COM1079 | Dr. John Noll

Learning Objectives

The aim of this lecture is to understand when various kinds of datavisualizations are useful.

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Scatterplots–Relations Between VariablesA scatterplot plots points (x, y) to show the relationship betweentwo variables:

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Example: Runs vs Innings

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Boxplots–Variability

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I The rectangle (“box”) isbounded by the first andthird quartiles.

I The line across the box isat the median (secondquartile).

I “Whiskers” represent themaximum or minimumvalues within 1.5 times the“Interquartile Range” (theheight of the box) beyondthe top or bottom edges.

I Points are extreme valuesoutside the InterquartileRange. 6 of 38


Boxplot with points

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Shows where your data fall in relation to the quartiles.

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Example: Runs vs Batting Hand

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Runs vs Batting Hand

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Barplots–Frequency of categories

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Number of left and right handed batters

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Barplots–ProportionsA

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Histogram–Distribution

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Summary


Summary

1. Use scatterplots to visualize possible correlation of interval orordinal data.

2. Use boxplots to visualize variability, of interval or ordinal datawithin categories.

3. Use barplots to visualize frequencies of nominal data.4. Use histograms to visualize distribution, of interval data.

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End Part 1

Part 2: Visualization in R


Learning Objectives

The aim of this part is to understand how to create various usefulvisualizations:

I Scatterplots (with linear model).I Boxplots.I Barplots.I Histograms.

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Scatterplot

Basic scatterplot (using the ‘mtcars’ dataset)

1 x <- mtcars$wt2 y <- mtcars$mpg3 # Plot with main and axis titles4 # Change point shape (pch = 19) and include frame.5 plot(x # independent variable (weight)6 , y # dependent variable (miles per gallon)7 , main = "MPG vs Weight" # chart title8 , xlab = "Weight" # x-axis label9 , ylab = "MPG" # y-axis label

10 , pch = 19 # point shape (filled circle)11 , frame = T # surround chart with a frame12 )13 model <- lm(y ~ x, data = mtcars) # compute the linear model14 abline(model, col = "blue") # draw the model as a blue line

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Scatterplot

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Boxplots (with points)

1 d <- read.csv("icc_world_cup_2019_batting_stats.csv")2 x <- d$Batting.Hand # independent, nominal variable3 y <- d$Runs # dependent, interval variable4

5 plot(y ~ x # plot Runs vs Batting.Hand6 , main = "Runs vs Batting Hand" # main chart title7 , xlab = "Batting Hand" # x-axis label8 , ylab = "Runs" # y-axis label9 , pch = 19 # point type (filled circle)

10 , frame = T # frame around chart11 )12 points(y ~ x, col="cyan"); # overlay blue points

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Example: Runs vs Right-/Left-handed batting

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Runs vs Batting Hand

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Barplots–Frequency of categories

1 d <- read.csv("icc_world_cup_2019_batting_stats.csv")2

3 # This bit of magic counts right- and left-handed batters, using4 # the length of lists of players that are either "Left" or "Right" handed5 a <- aggregate(d$Player, list(d$Batting.Hand), FUN=length)6

7 barplot(a$x, # aggregate() puts the counts in column 'x'8 , names.arg=a$Group.1 # names under the bars9 , main = "Number of left and right handed batters" # main chart title

10 , xlab="Batting Hand" # x-axis label11 , ylab="Count" # y-axis label12 , col = c("lightblue", "mistyrose") # colors of bars13 , args.legend = list(x = "topleft") # where to put the legend14 , legend.text=a$Group.1) # what to put in the legend15 )

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Example: Left vs Right Handed batters

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Number of left and right handed batters

Batting Hand

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Histogram–Distribution

1 d <- read.csv("icc_world_cup_2019_batting_stats.dsv", sep="|")23 y <- d$Runs # variable to visualize45 h <- hist(y # variable to count6 , 6 # number of 'bins' (or bars)7 , main = "Runs Frequency" # main chart title8 , xlab = "Runs" # x-axis label9 , ylab = "Frequency" # y-axis label

10 , col="azure" # fill color for the bars11 )12 # Overlay a normal curve1314 mn <- mean(y) # mean of the data (runs)15 stdD <- sd(y) # standard deviation of the data16 x <- seq(100, 700, 1) # x-axis points: 100 to 70017 y1 <- dnorm(x, mean=mn, sd=stdD) # an idealized normal curve,18 # (frequencies are fraction of 1.0)19 y1 <- y1 * diff(h$mids[1:2]) * length(y); # calibrate the curve against actual2021 lines(x, y1, col="blue") # plot calibrated line in blue

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Example: Runs

Runs Frequency

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Summary

1. Always add a main chart title.2. Always label the x-axis.3. Always label the y-axis.4. Always label the boxplot and barplot categories.5. Use colors to make charts clear (but don’t overdo it).6. Add a legend to explain colors or point styles if they are

meaningful.7. Make sure text does not overlap or go outside the margins (see

next part).

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End Part 2

Part 3: More Advanced Examples


Stacked Barplots–ProportionsA

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I Stacked barplots are goodfor showing proportions,especially if the height of thebars is normalized to be thesame for all categories of the(nominal) independentvariable.

I This is the right way tovisualize a comparison ofproportions problem

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Stacked Barplots–Step 1

Transform (“wrangle”) the data: we need a tabulation of theproportions (fractions) of Left- and Right-handed batters on eachteam:

1 d <- read.csv("icc_world_cup_2019_batting_stats.csv")2 # Aggregate by Team and Batting.Hand to get number of Left and Right-handers3 a.Team.Batting.Hand <-aggregate(Player ~ Team + Batting.Hand, d, FUN=length)4 # Aggregate by Team to get number of Players5 a.Team.Size <-aggregate(Player ~ Team, d, FUN=length)6 # Merge the two aggregations, to enable proportion calculation7 a <- merge(a.Team.Batting.Hand, a.Team.Size, by = "Team") # 'join' on Team8 # Rename columns to make meaning more clear9 colnames(a) <- c("Team", "Batting.Hand", "Batting.Hand.Count", "Total.Count")

10 # Create a cross-tabulation of *fraction* of Left/Right-hand batters11 xtab <- xtabs(Batting.Hand.Count / Total.Count ~ Team + Batting.Hand, a)

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Why xtabs()?Our aggregation looks like this:> a

Team Batting.Hand Batting.Hand.Count Total.Count1 Afghanistan Left 2 42 Afghanistan Right 2 43 Australia Right 4 64 Australia Left 2 65 Bangladesh Right 3 66 Bangladesh Left 3 67 England Right 4 68 England Left 2 69 India Right 5 510 New Zealand Left 1 411 New Zealand Right 3 412 Pakistan Left 3 613 Pakistan Right 3 614 South Africa Right 3 415 South Africa Left 1 416 Sri Lanka Right 2 417 Sri Lanka Left 2 418 Windies Left 3 519 Windies Right 2 5

We need the hand fraction perteam, which is thecross-tabulation of theBatting.Hand.Count divided bythe Total.Count per Team andBatting.Hand:> xtabs(Batting.Hand.Count / Total.Count ~

Team + Batting.Hand, a)

Batting.HandTeam Left Right

Afghanistan 0.5000000 0.5000000Australia 0.3333333 0.6666667Bangladesh 0.5000000 0.5000000England 0.3333333 0.6666667India 0.0000000 1.0000000New Zealand 0.2500000 0.7500000Pakistan 0.5000000 0.5000000South Africa 0.2500000 0.7500000Sri Lanka 0.5000000 0.5000000Windies 0.6000000 0.4000000

The cross-tabulation shows the fraction of Left- and Right-handedbatters per team.

When we plot this, it becomes clear how different teams compare interms of Left- vs Right-handed batters.

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Stacked Barplots–Step 2Plot the cross-tabulation:

1 # Create a cross-tabulation of *fraction* of Left/Right-hand batters2 xtab <- xtabs(Batting.Hand.Count / Total.Count ~ Team + Batting.Hand, a)3

4 # Extend bottom margin so team names are not cropped.5 par(mar=c(7, 4.1, 4.1, 2.1)) # First element is bottom margin (default: c(5.1, 4.1, 4.1, 2.1)).6

7 # Plot transposed xtab as stacked barplot.8 barplot(t(xtab) # transpose so Teams appear as columns9 , main = "Fraction of left and right handed batters" # chart title, as usual

10 , ylab = "Fraction of players" # y-axis label (x-axis labelled below)11 , col = c("lightblue", "mistyrose") # colors of left and right-handed segmetnt12 , las = 2 # rotate x-axis labels 90 degrees13 , legend.text=c("Left", "Right") # color key14 , args.legend = list(x = "topleft") # legend location15 , axes = F # no (vertical) axis (added below)16 )17 axis(side = 2, at = c(0,.5,1), labels = c("0%", "50%", "80%"))18 mtext("Team", side=1, line = 6) # Put xlab below labels

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Stacked Barplots–World Cup Batting HandA

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Histograms with Normal Curve

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I Plotting a normalcurve over ahistogram helpsvisualize variationand potentialnon-normality.

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Histograms with Normal Curve1 d <- read.csv("icc_world_cup_2019_batting_stats.csv")2 y <- d$Runs3

4 h <- hist(y5 , 66 , main = "Runs Frequency"7 , xlab = "Runs"8 , ylab = "Frequency"9 , col = "azure"

10 )11

12 x <- seq(100, 700, 1)13 mn <- mean(y)14 stdDev <- sd(y)15 yn <- dnorm(x, mean=mn, sd=stdDev)16 box.size <- diff(h$mids[1:2]) * length(y)17 yn <- yn * box.size18

19 lines(x, yn, col="blue") 34 of 38



Runs Frequency

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Histograms with Normal CurveWhy scale yn?

1 h <- hist(y, 6, main = "Runs Frequency", xlab = "Runs", ylab = "Frequency", col="azure")23 x <- seq(100, 700, 1)4 mn <- mean(y)5 print(mn)6 yn <- dnorm(x, mean=mn, sd=sd(y))7 bin.size <- diff(h$mids[1:2]) * length(y)8 yn <- yn * bin.size

1. dnorm() yields a probability density curve for the normaldistribution.

2. hist() produces a distribution of frequencies.3. To convert the density curve to a frequency curve we have to

scale the density by the size of the bins:1 bin.size <- diff(h$mids[1:2]) * length(y)

I diff(h$mids[1:2]) is the width of the binI length(y) is the number of points in the sample, and hence

the height of the bin if all the points fell into it. 36 of 38

Notes:Points on the curve are the probability that a single sample chosen at random from thepopulation will have the x-axis value. This is why the mean of a normal population is alsocalled the expected value: it is the most likely.



To see this, consider two histograms for the same data with differentbin sizes:

Histogram of y

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I With six bins (blue plot), themiddle bins are taller.

I With ten bins (pink plot), thebins are shorter, and thedistribution is clearly skewed.

I With many bins (grey plot),the distribution looks almostrandom.

I The boxes, and curves, aredifferent heights, and the redand black curves are “fatter”.

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End Part 3

visualization lecture notes - 7com1079 team research and

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