Lecture 24

Clutter is Your Enemy!

Byeong-Hak Choe

SUNY Geneseo

November 1, 2024

Happy Halloween, everyone! 🎃👻🎃👻🎃👻🎃👻🎃👻🎃👻

Every element added to a page or screen demands cognitive load
- Cognitive load: the mental effort needed to process information
Extra elements = extra brain power for the audience to process
- Example: Overly complex slides or graphs can overwhelm viewers
Excessive load can lead to disengagement and confusion
- Goal: a graphic should display as much information as it can, with the lowest possible cognitive strain to the viewer.

Clutter: Visual elements that occupy space but do not improve understanding
Clutter makes information harder to process and can confuse the viewer
Strive for clarity: Simplified visuals encourage engagement and improve comprehension
- Less clutter = clearer message, more focused audience
Tips
- Avoid having the data all skewed to one side or the other of your graph.
- Avoid too many superimposed elements, such as too many curves (>4) in the same graphing space.

Problem: When data points are densely packed, it can obscure insights
- Often due to extreme values or skewed distributions
- Dense clusters of points become visual clutter, hiding patterns
Solution: Apply a log transformation!
- Reduces clutter: Points become evenly distributed across the plot
  - Prevents overlapping data points and enhances readability
- Reduces influence of outliers, clarifying patterns
  - Improves interpretability by revealing underlying relationships
- Supports focused, informative data communication without extra elements

$\log_{10}\,(\,100\,)$: the base $10$ logarithm of $100$ is $2$, because $10^{2} = 100$
$\log_{e}\,(\,x\,)$: the base $e$ logarithm is called the natural log, where $e = 2.718\cdots$ is the mathematical constant, the Euler’s number.
$\log\,(\,x\,)$ or $\ln\,(\,x\,)$: the natural log of $x$ .
$\log_{e}\,(\,7.389\cdots\,)$: the natural log of $7.389\cdots$ is $2$, because $e^{2} = 7.389\cdots$.
In R,
- log(x): log of x with base e, called natural log.
- log10(x): log of x with base 10.

Consider using a logarithmic scale when percentage changes are more meaningful than changes in absolute units.

Percentage changes are widely used in various fields to better interpret relative differences. Examples include:
- Stock prices: Percentage changes reflect the magnitude of gains or losses relative to the initial price.
- Housing prices: Percentage changes show market trends consistently across different neighborhoods or regions.
- GDP growth: Expressed as a percentage to indicate economic performance over time.
- Income levels: A $1,000 increase has a greater impact on a lower-income individual compared to someone with a significantly higher income.

\[ \Delta \log(x) = \log(x_{1}) - \log(x_{0}) \approx \frac{x_{1} - x_{0}}{x_{0}} = \frac{\Delta x}{x_{0}}. \]

One percent increase in GDP per capita is associated with an increase in life expectancy by 0.084 year (30.66 days)!