Graphical Data Analysis on the Circle: Wrap-Around Time Series Plots for (Interrupted) Time Series Designs

Area of Science:

• Statistics
• Data Visualization
• Time Series Analysis

Background:

• Time series data often exhibits circular patterns (seasonal, cyclical).
• Traditional graphical methods primarily use linear plots, which may obscure circular trends.
• Existing circular methods like rose diagrams offer some visualization but have limitations.

Purpose of the Study:

• To introduce and evaluate circular graphical methods for time series analysis.
• To propose and develop a new method, Wrap-Around Time Series Plots (WATS Plots).
• To demonstrate the utility of WATS Plots for interrupted time series designs.

Main Methods:

• Utilized rose diagrams (circular histograms) via the RRose software system.
• Developed and applied novel Wrap-Around Time Series Plots (WATS Plots).
• Applied WATS Plots to interrupted time series data on Oklahoma birth rates surrounding the Oklahoma City bombing.

Main Results:

• WATS Plots were compared with traditional linear time series plots.
• Smoothing and error bands were overlaid on both linear and WATS Plots.
• WATS Plots more clearly revealed the existence and effect size of a fertility differential following the bombing.

Conclusions:

• Circular graphical methods, particularly WATS Plots, enhance time series analysis.
• WATS Plots provide superior visualization for interrupted time series designs compared to linear plots.
• The proposed WATS Plots effectively illustrate significant changes in time series data, as demonstrated by the Oklahoma birth rate example.