Week 02 - What can we learn from visualizing distributions?

Prof. C. Austin Davis

Spring 2025

Roadmap for today

• Syllabus quiz
• Review math assessment
• A look back at last week
• Visualizing and understanding distributions
  • Histogram / frequency distribution
  • Density
  • Cumulative distribution
• Preview of next time

Syllabus quiz

Math assessment*

Start with summation notation, open for questions

A look back at last week

• What is data? Unit of analysis? Variable?
• What types of variable will we encounter?
• Translating between concepts and measurement
• Console vs. source pane
• Our first R script

What is data?

• Data is systematic observation of many “units” / pieces of information structured to facilitate analysis and comparison.
• The type of entity about which observation is gathered.
• A property or characteristic that can take on different values for different units.

What types of variables will we encounter?

• Categorical
• Binary
• Continuous

Translating between concepts and measurement

• Ask for examples from prior class in military power, poverty, free speech, mental health, trauma.

Console vs. source pane - Console is direct access to R - Displays commands and output - Keeps a complete log of everything you’ve done since you opened R Studio - Best for experimentation

• Source pane is a specialized text editor
• Displays commands and comments (or notes)
• Saves only what you want
• Best for building, documenting, sharing analysis

Our first R script - Walk them through

What can we learn from visualizing distributions?

Synthesizing large quantities of information to establish general, actionable facts about the world

UCB Admissions by Gender*

• What is this figure called? Frequency distribution or histogram.
• What does the horizontal axis capture?
• What does each bar height capture?
• What do you infer about admissions by gender during this year at UCB?

Tools we’ll need*

• Reading in data: read_dta() and read_csv()
• Inspecting data: tibbles, summary(), and View()
• Picking observations: filter() and the pipe operator %>%
• Plotting: ggplot(), geom_bar(), geom_histogram(), geom_density()

• Go to Canvas and download today’s .R script
• Recipe for reading data: [OBJECT NAME] <- read_dta(“[FILE PATH]”)
• Go to Week 2 exercise to demonstrate tibbles, summary() and View()
• Recipe for picking observations: [NEW OBJECT NAME] <- [OLD OBJECT NAME] %>% filter([VARIABLE] [CONDITION] [VALUE])
• Recipe for ggplot: [NEW OBJECT NAME] <- ggplot(data=[OBJECT NAME],aes(x=[VARIABLE NAME])) + [PLOT_TYPE]
• Density is a smoothed histogram suitable for continuous variables
• Pros: smoothing / binning automatic, facilitates visual comparisons
• Cons: degree of smoothing is discretionary, can be deceptive

UCB Applicant Test Scores by Gender*

Intermission

Mental health in a refugee setting*

Understanding your data*

Codebooks / questionnaires

Other documentation

Income growth in the US*

Preview of next time

From pictures to numbers: rank statistics, mean, variance, and the tidyverse syntax.

Questions to ponder

• How could you tell if an embassy was using too much electricity?
• What statistical tool could help you measure income inequality?