'You Draw It' Validation Applet

Eye Fitting Straight Lines in the Modern Era

Peception of Logrithmic Scales

Shiny front-end/testing framework for 'You Draw It' with r2d3 package

Emily Robinson, Susan VanderPlas, Reka Howard

Experiment Name

• Conducted: April 2021 - Present
• Platform: Shiny App
• Recruitment Method: ISU Graphics Group, Twitter, Reddit, Direct Email, etc.
• Trend Types: Simulated Linear; Simulated Exponential (linear/log scale)

Data Simulation

• Data was simulated for each individual upon start of experiment.
• See code/data-generation.R for data simulation functions.
• See Data Validation for 100 simulation reps.

Linear Data

• Parameter combinations were selected to simulate data that replicates the data sets (S, F, V, N) in Eye Fitting Straight Lines (1981).

Algorithm: Linear Data Generation linearDataGen()

In parameters: y_xbar, slope, sigma, N = 30, xmin, xmax, xby = 0.25

Out: data list of point data and line data

1. Randomly select and jitter N = 30 x-values along the domain.
2. Determine y-intercept at x = 0 from the provided slope and y-intercept at the mean of x (y_xbar).
   • Slope-intercept form: y - y_xbar = m(x-xbar)
3. Generate "good" errors based on N(0,sigma).
   • Set constraint of the mean of the first N/3 = 10 errors less than |2*sigma|
4. Simulate point data based on
   • y = yintercept + slope*x + error
5. Obtain least squares regression coefficients
   • lm(y ~ x, data = point_data)
6. Simulate least squares regression line data
   • y = yintercepthat + slopehat*x
7. Output data list of point data and line data

• Specific r2d3 options:
  • aspect ratio = 1
  • linear = "true"
  • free_draw = TRUE
  • points = "full",
  • x_by = 0.25
  • draw_start = NA
  • show_finished = T - graphics group / F
  • x_range = c(0,20)
  • y_range = range(all eye fitting data)*c(1.1, 1.1)

Exponential Data

Algorithm: Exponential Data Generation expDataGen()

In parameters: beta, sd, points_choice = "partial", points_end_scale, N = 30, xmin = 20, xmax = 20, xby = 0.25

Out: data list of point data and line data

1. Randomly select and jitter N = 30 x-values along the domain.
2. Generate "good" errors based on N(0,sd).
   • Set constraint of the mean of the first N/3 = 10 errors less than |2*sd|
3. Simulate point data based on
   • y = exp(x*beta + errorVals)
4. Obtain starting value for beta
   • lm(log(y) ~ x, data = point_data)
5. Use NLS to fit a better line to the point data
   • nls(y ~ exp(x*beta), data = point_data, ...)
6. Simulate nonlinear least squares line data
   • y = exp(x*betahat)
7. Output data list of point data and line data

• Specific r2d3 options:
  • aspect ratio = 1
  • linear =
  • free_draw = FALSE
  • points = "partial",
  • x_by = 0.25
  • draw_start_scale = 0.5 (start drawing at x = 10)
  • show_finished = T - graphics group / F
  • x_range = c(0,20)
  • y_range = range(y-points)*c(0.5, 2)

Plot Generation

• See www/js/shinydrawr-d3v5.js for D3.js source code.

Experimental Design

Treatment Design

• Linear (Eye Fitting Straight Lines): 1-way ANOVA with 4 treatments

  • 4 Treatments
    • S: positive slope, low variance (y_xbar = 3.88, slope = 0.66, sigma = 1.3, xrange = (0,20))
    • F: positive slope, high variance (y_xbar = 3.9, slope = 0.66, sigma = 1.98, xrange = (0,20))
    • V: steep positive slope (y_xbar = 3.89, slope = 1.98, sigma = 1.5, xrange = (4,18))
    • N: negative slope, high variance (y_xbar = 4.11, slope = -0.70, sigma = 2.5, xrange = (0,20))

• Exponential (Linear/Log): 2 x 2 x 2 Factorial

  • Beta: 0.1 (sd. 0.09); 0.23 (0.25)
  • Points End: 0.5; 0.75
  • Scale: Linear; Log

Experimental Design

• See code/randomization.R.
• 8 data sets were generated for each individual upon start of experiment (4 Linear + 4 Exponential)
• 12 you draw it task plots were shown to each individual (4 Linear + (4 Exponential x 2 Scales))
• The order of each of the 12 plots was randomly assigned for each individual in a CRD.

Data Files

• Data file can be found in you_draw_it_data.db.
• Field descriptions can be found in data-manifest.md.

Results

• Presentations:
  • You Draw It with r2d3 - ISU Graphics Group 04-08-2021
  • Eye Fitting Straight Lines in the Modern - Midwest Women in Science Conference Era
  • Human perception of Statistical Charts: An Introduction to Graphical Testing - UNL Nerd Nite @ Saro Cider Methods
  • Can 'You Draw It'? Eye Fitting Straight Lines in the Modern - ISU Graphics Group Era
  • Can 'You Draw It' - Job Talk
• Papers:
  • Eye Fitting Straight Lines in the Modern Era
  • UNL Dissertation
  • JSM 2022 Student Paper Competition
  • SDSS 2022 Extended Abstract
• Preliminary Analyses:
  • ISU Graphics Group (04/08/2021): Exponential Prediction, Eye Fitting Straight Lines
  • Twitter/Reddit/Direct Email Pilot Study (05/03/2021): Exponential Prediction, Eye Fitting Straight Lines