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Exploratory Data Analysis

Lesson 1: Graphs

 

Principles of Analytic Graphics

  1. Show comparisons

    • Evidence for a hypothesis is always relative to another competing hypothesis

    • Always ask “Compared to what?”

  2. Show causality, mechanism, explanation, systematic structure

    • Explain why the results are actually happening.

  3. Show multivariate data

    • Multivariate = >2 variables

    • The real world is multivariate

    • Need to “escape flatland”

  4. Integrate evidence

    • Completely integrate words, numbers, images and diagrams

    • Data graphics should make use of many modes of data presentation

    • Don’t let the tool drive the analysis

  5. Describe and document the evidence with appropriate labels, scales, sources, etc.

    • A data graphic should tell a complete story that is credible

  6. Content is king

    • Analytical presentations ultimately stand or fall depending on the quality, relevance and integrity of their content

    • If you don’t have an interesting story to tell, you’re going nowhere.

REFERENCE: Edward Tufte (2006). Beautiful Evidence, Graphics Press LLC.

 

Exploratory Graphs Part 1

Graphs you make for yourself to help:

  • understand data properties

  • find patterns

  • suggest modeling strategies

  • “debug” analyses

  • communicate results

 

Characteristics of exploratory graphics include:

  • speedily made

  • many are made

  • the goal of their existence is for understanding

  • Axes/legends are generally cleaned up later

  • Color/sizes are used primarily for information

 

Some simple 1-Dimensional summaries of the data include

  • Five-number summary summary(table$col)

  • boxplots boxplot(table$col)

  • histograms hist(table$col)

  • density plot

  • barplot barplot(table$col)

abline(h = 12) overlays a line on the last graph, in this case y=12.

 

Exploratory Graphics Part 2

2-Dimensional graphics include

  • Multiple/overlayed 1-D plots (Lattice/ggplot2)

  • Scatterplots

  • Smooth scatterplots

Plots that exceed 2-D include:

  • Overlayed/Multiple 2-D plots; coplots

  • Adding color, size and shape to add dimension

  • Spinning plots

  • Actual 3-D plots (not all that useful)

 

Multiple Box Plots

boxplot(pm25 ~ region, data = pollution, col = “red”)

 

Multiple Histograms

par(mfrow=c(2,1), mar = c(4,4,2,1))
hist(subset(pollution, region == "east")$pm25)
hist(subset(pollution, region == "west")$pm25)

Scatterplot

with(pollution, plot(latitude, pm25, col = region))
abline(h = 12, lwd = 2, lty = 2)

Multiple scatterplots

par(mfrow = c(1,2), mar = (c(5,4,2,1))
with(subset(pollution, region =="west"), plot(latitude, pm25, main = "West"))
with(subset(pollution, region =="east"), plot(latitude, pm25, main = "East"))

Lesson 2: Plotting

###Plotting Systems in R