Statistics Problem Generator

Shiny application that generates randomized statistics problems for practice: a data set, a plot, and an answer key, for a selected statistical test.

App: https://chadcwilliams.shinyapps.io/StatsProblemGenerator/ Repo: https://github.com/chadcwilliams/StatsProblemGenerator

Overview

The app selects a statistical test, generates a random data set matching that test's requirements, computes every statistic required to solve it, and displays three outputs: the data, a plot, and the worked solution. Each click of "Generate Data" produces a new data set. A seed value can be set to reproduce a specific data set later.

The dropdowns are labeled "Psyc 300A" and "Psyc 300B" and split the 17 supported tests across a two-course sequence.

Usage

Open the app: https://chadcwilliams.shinyapps.io/StatsProblemGenerator/

1. Select a test. Choose one option from either dropdown. Selecting a test in one dropdown clears the other; only one test is active at a time.
2. Set parameters.
   • Number of Participants — sample size used to generate the data (per group, for multi-group tests).
   • Range of Values — range the generated scores are drawn from.
   • Seed — optional. See Seed.
3. Generate Data. Produces a data set and displays it in the Data panel.
4. Plot Data. Renders the plot associated with the selected test.
5. Show Answers. Displays the worked solution.
6. Download PDF. Available once a data set exists. Downloads a three-page PDF: problem data, plot, answer key. See PDF output.

Selecting a different test clears the data, plot, and answers currently on screen.

Seed

Each data set is generated using a seed value passed to set.seed().

• If the Seed field is left blank, the app generates a random seed on each click of "Generate Data" and displays it below the field as "Seed used: ".
• If a number is entered in the Seed field before clicking "Generate Data", that value is used instead.

Recording the seed value allows the same data set to be regenerated later by entering it into the Seed field. The seed used is also included in the PDF filename and as a footnote on each PDF page.

PDF output

The downloaded PDF contains three pages:

1. Problem data, as shown in the Data panel.
2. Plot, as shown after clicking "Plot Data".
3. Answer key, as shown after clicking "Show Answers".

Each page includes a footnote with the seed used to generate the data set. The filename follows the pattern <test_name>_<seed>.pdf.

Supported tests

Psyc 300A

Test	Description
Frequency Distribution	Frequency table construction
Descriptives	Mode, median, mean, range, SIQR, MAD, variance, SD, skew
Z-scores	Conversion between raw scores and z-scores
Correlation & Regression	Pearson's r and the regression line
Single Participant Z-Test	One participant's score vs. a known population
Single Sample Z-Test	Sample mean vs. a known population, σ known
Single Sample T-Test	Sample mean vs. a known population, σ unknown

Psyc 300B

Test	Description
Related Samples T-Test	Paired/repeated-measures comparison
Independent Samples T-Test	Two independent groups
Correlation (Advanced)	Significance test of a correlation coefficient
Power (calculate n)	Sample size required for a target power
Power (calculate power)	Power of a specified design
One-Way ANOVA	Comparison of 3+ group means
Multiple Comparisons	Planned comparisons and post-hoc tests (Tukey, Dunnett, Fisher's LSD, Dunn's test)
Multifactorial ANOVA	Two-way ANOVA with main effects and an interaction
Chi-Squared (Goodness of Fit)	Observed vs. expected category frequencies
Chi-Squared (Homogeneity & Independence)	Association between two categorical variables

File structure

app.R                     Server/UI setup, test switching, PDF download handler
utils/
  ui.R                    UI layout and inputs
  observe_events.R        Renders the on-screen Answer Key and Plot for the active test
  pdf_report.R            Builds the PDF; mirrors the on-screen answer key/plot logic
  stat_tests/
    freq_distribution.R
    descriptives.R
    ...                   One file per test. Generates the data, computes the
                           statistics, and populates stats/plotdata/problemdata

Each test script writes to three shared reactive objects:

• stats — computed statistics for the answer key
• plotdata — data required by the plot
• problemdata — the problem table shown in the Data panel and reused in the PDF

Answer-key rendering, plotting, and PDF generation read from these three objects and are not duplicated per test.

The PDF is built with grid/gridExtra rather than rmarkdown, to avoid a Pandoc/LaTeX dependency on the hosting server.

Local development

R packages: shiny, bslib, rhandsontable, ggplot2, dplyr, gridExtra, faux, rstatix, BSDA.

shiny::runApp()

Run from the project root (the directory containing app.R).

Author

Chad C. Williams — chadcwilliams.com