Week 3: Visulaization

Visualization · exploratory data analysis · joins

Published

September 11, 2026

What We Did

Quiz
Examined Anscombe’s Quartet and compared summary statistics across four datasets.
Learned how to build plots using ggplot(), aes(), and geom_*().
Reviewed uncertainty in ACS estimates using margin of error (MOE), standard error (SE), and coefficient of variation (CV).
Calculated uncertainty for derived estimates and changes over time.
GO HOME!

Key Concepts

Anscombe’s Quartet

The four datasets have the same or nearly identical mean x, mean y, correlation, and regression line, but very different distributions when plotted.

How to Build a ggplot

Step 1: Assign an object and create a blank canvas

p <- ggplot(data)

# You can also start without specifying data
p <- ggplot()

Step 2: Define aesthetic mappings

aes() maps data to visual properties such as position and color.

Inside aes(): map a variable or category to a visual property.
Outside aes(): set a visual property to a fixed value.

# Map the category "blue" to color.
# This creates a legend labeled "blue";
# it does not necessarily make the points blue.
ggplot(county_data) +
  aes(x = estimate, y = moe_pct, color = "blue") +
  geom_point()

# Set all points to blue
ggplot(county_data) +
  aes(x = estimate, y = moe_pct) +
  geom_point(color = "blue")

# Color points according to the city variable
ggplot(df, aes(x = income, y = rent)) +
  geom_point(aes(color = city))

Step 3: Choose a geometry

Function	Purpose
`geom_histogram()`	Show the distribution of a variable
`geom_point()`	Show the relationship between two variables
`geom_boxplot()`	Compare distributions across groups
`geom_col()`	Compare values across groups
`geom_line()`	Show changes over time
`geom_errorbar()`	Display uncertainty

p <- ggplot(df, aes(x = income, y = rent, color = city)) +
  geom_point()

The + operator adds layers or other plot components.

ACS Error and Reliability

Standard Error (SE)

For an ACS margin of error reported at the 90% confidence level:

\[ SE = \frac{MOE}{1.645} \]

Coefficient of Variation (CV)

\[ CV = \frac{SE}{\text{Estimate}} \times 100% \]

CV thresholds from the class notes:

CV Level	Range	Interpretation
Low	< 15%	High reliability
Medium	15%–30%
High	> 30%	High sampling error

Uncertainty in Derived Estimates

When calculating sums, proportions, or ratios, account for uncertainty in the original estimates. Both the numerator and denominator may have sampling error.

Function	Purpose	Example
`moe_sum()`	Calculate the MOE of a sum	Add populations across several areas
`moe_prop()`	Calculate the MOE of a part-to-whole proportion	Population in poverty ÷ population for whom poverty status is determined
`moe_ratio()`	Calculate the MOE of a general ratio	Number of jobs ÷ number of housing units

Changes Over Time

When comparing ACS multiyear estimates, use periods with non-overlapping years.

Convert each period’s MOE to its standard error:

\[ SE_1 = \frac{MOE_1}{1.645}, \qquad SE_2 = \frac{MOE_2}{1.645} \]

Assuming the two estimates are independent, the standard error of the difference is:

\[ SE_{\text{diff}} = \sqrt{SE_1^2 + SE_2^2} \]

Define the difference as:

\[ \text{Difference} = \text{Estimate}_1 - \text{Estimate}_2 \]

The Z-score is:

\[ Z = \frac{\text{Estimate}_1 - \text{Estimate}2}{SE{\text{diff}}} \]

The 90% confidence interval for the change is:

\[ \text{Difference} \pm 1.645 \times SE_{\text{diff}} \]

Reflection

Questions I Still Have

--- title: "Week 3: Visulaization" description: "Visualization · exploratory data analysis · joins" date: 2026-09-11 --- ## What We Did - Quiz - Examined Anscombe’s Quartet and compared summary statistics across four datasets. - Learned how to build plots using ggplot(), aes(), and geom_*(). - Reviewed uncertainty in ACS estimates using margin of error (MOE), standard error (SE), and coefficient of variation (CV). - Calculated uncertainty for derived estimates and changes over time. - GO HOME! ## Key Concepts ### Anscombe’s Quartet The four datasets have the same or nearly identical mean x, mean y, correlation, and regression line, but very different distributions when plotted. ### How to Build a ggplot #### Step 1: Assign an object and create a blank canvas ```R p <- ggplot(data) # You can also start without specifying data p <- ggplot() ``` #### Step 2: Define aesthetic mappings aes() maps data to visual properties such as position and color. - Inside aes(): map a variable or category to a visual property. - Outside aes(): set a visual property to a fixed value. ```R # Map the category "blue" to color. # This creates a legend labeled "blue"; # it does not necessarily make the points blue. ggplot(county_data) + aes(x = estimate, y = moe_pct, color = "blue") + geom_point() # Set all points to blue ggplot(county_data) + aes(x = estimate, y = moe_pct) + geom_point(color = "blue") # Color points according to the city variable ggplot(df, aes(x = income, y = rent)) + geom_point(aes(color = city)) ``` #### Step 3: Choose a geometry | Function | Purpose | | --- | --- | | `geom_histogram()` | Show the distribution of a variable | | `geom_point()` | Show the relationship between two variables | | `geom_boxplot()` | Compare distributions across groups | | `geom_col()` | Compare values across groups | | `geom_line()` | Show changes over time | | `geom_errorbar()` | Display uncertainty | ```R p <- ggplot(df, aes(x = income, y = rent, color = city)) + geom_point() ``` The + operator adds layers or other plot components. ### ACS Error and Reliability #### Standard Error (SE) For an ACS margin of error reported at the 90% confidence level: $$ SE = \frac{MOE}{1.645} $$ #### Coefficient of Variation (CV) $$ CV = \frac{SE}{\text{Estimate}} \times 100% $$ CV thresholds from the class notes: | CV Level | Range | Interpretation | | --- | --- | --- | | Low | < 15% | High reliability | | Medium | 15%–30% | | | High | > 30% | High sampling error | #### Uncertainty in Derived Estimates When calculating sums, proportions, or ratios, account for uncertainty in the original estimates. Both the numerator and denominator may have sampling error. | Function | Purpose | Example | | --- | --- | --- | | `moe_sum()` | Calculate the MOE of a sum | Add populations across several areas | | `moe_prop()` | Calculate the MOE of a part-to-whole proportion | Population in poverty ÷ population for whom poverty status is determined | | `moe_ratio()` | Calculate the MOE of a general ratio | Number of jobs ÷ number of housing units | #### Changes Over Time When comparing ACS multiyear estimates, use periods with non-overlapping years. Convert each period’s MOE to its standard error: $$ SE_1 = \frac{MOE_1}{1.645}, \qquad SE_2 = \frac{MOE_2}{1.645} $$ Assuming the two estimates are independent, the standard error of the difference is: $$ SE_{\text{diff}} = \sqrt{SE_1^2 + SE_2^2} $$ Define the difference as: $$ \text{Difference} = \text{Estimate}_1 - \text{Estimate}_2 $$ The Z-score is: $$ Z = \frac{\text{Estimate}_1 - \text{Estimate}2}{SE{\text{diff}}} $$ The 90% confidence interval for the change is: $$ \text{Difference} \pm 1.645 \times SE_{\text{diff}} $$ ## Reflection ## Questions I Still Have