Background on 3D graphics

In 1990, Microsoft Excel 3 introduced the ability to create 3D charts (Walkenbach 2020). Multiple studies have shown the downsides to unnecessarily using these types of charts.

• 2D graphs had more confident answers and novice participants were more accurate with 2D graphs than 3D graphs (Barfield and Robless 1989)

• Visual appeal for 2D and 3D graphs were approximately equal, and simple graphs were preferred for extracting information (Fisher, Dempsey, and Marousky 1997)

Background on 3D graphics

Overview

Research questions:

1. How do 3D printed charts compare to 2D and 3D digital charts?
2. Can we extend on the findings from Cleveland and McGill’s study on elementary perceptual tasks?

Replicating Cleveland and McGill

Our study draws influence from Cleveland and McGill’s 1984 paper, specifically from their position-length experiment with graph types 1 and 3 (Cleveland and McGill 1984).

• Overall goal was to establish which graphical elements are the most important for extracting information

• Types 1-3 measure position, and types 4-5 measure length

Graph types for position-length experiment from Cleveland and McGill

In their study, participants were asked which of the marked bars were smaller and by approximately how much.

Replicating Cleveland and McGill

Values involved in comparison judgments are

\[V_i=10\cdot10^{(i-1)/12}\quad i=1,\dots, 10\]

To closely replicate values, we made three assumptions about the comparisons from Cleveland and McGill

1. Match the exact ratios that were used

2. No value was used more than twice

3. All other values are randomly generated

Study Design

Design of each kit

Study Design

Each subject receives a kit of 3D printed charts with instructions that direct users to a Shiny app

Shiny App

Shiny App

Shiny App

Shiny App

Shiny App

Shiny App

Model

\[y_{ijklm}=\mu+S_i+R_j+G(R)_{(k)j}+T_l+\epsilon_{ijklm}\]

where

• \(y_{ijklm}=\log_2(|\text{Judged Percent} - \text{True Percent}|+1/8)\)

• \(S_i\sim N(0,\sigma^2_S)\) is the effect of the \(i^{th}\) subject

• \(R_j\) is the effect of the \(j^{th}\) ratio

• \(G(R)_{(k)j}\) is the effect of the \(k^{th}\) graph type nested in the \(j^{th}\) ratio

• \(T_l\) is the effect of the \(l^{th}\) comparison type

• \(\epsilon_{ijklm}\sim N(0,\sigma^2_\epsilon)\) is the random error

Results

• Few responses incorrectly identified the smaller bar and were removed from the data

• Plot within ratio was not statistically significant, nor was anything else

• Cleveland and McGill showed an increase in error from Type 1 to Type 3

Bootstrap Confidence Intervals

In Cleveland and McGill, confidence intervals were calculated using bootstrap sampling of subjects using the means of the midmeans. The same process is used here, although each subject did not receive each treatment combination.

A Contemporary Approach with GLMMs

The responses from the previous analysis used the log errors, but Generalized Linear Mixed Models are a modern option to analyze the data. Adjusting for the ratios as covariates, a beta regression model with unequal slopes is fit below:

\[\eta_{ijkl}=S_i+\beta_j R_{jk}+G_k+T_l\]

• \(\eta_{ijkl}\) is the participant response

• \(S_i\sim N(0,\sigma^2_S)\) is the effect of the \(i^{th}\) subject

• \(\beta_j\) is the effect of the \(j^{th}\) true ratio

• \(R_{jk}\) is the \(j^{th}\) ratio for the \(k^{th}\) graph type

• \(T_l\) is the effect of the \(l^{th}\) comparison type

• \(y_i|S_i\sim Beta(\mu_{ijkl}, \phi)\)

• Link function: \(\eta_{ijkl}=\log[\mu_{ijkl}/(1-\mu_{ijkl})]\)

GLMM Results

Beta regression does not have easily interpretable results. These results are averaged over all ratios. Generally, the expected proportion responses follow that 2D digital > 3D printed > 3D digital

Results averaged over ratio, holding the comparison type constant

Future work

• Include static 3D charts (similar to Microsoft Excel)
• Explore other types of visualizations, such as 3D printed heat maps

No results were significant, but what if we could incorporate the study at a larger scale?