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1 Introduction2 Graphing Distributions3 Summarizing Distributions4 Describing Bivariate Data5 Probability6 Research Design7 Normal Distribution8 Advanced Graphs9 Sampling Distributions10 Estimation11 Logic of Hypothesis Testing12 Tests of Means13 Power14 Regression15 Analysis of Variance16 Transformations17 Chi Square18 Distribution Free Tests19 Effect Size
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3.16 Comparing Distributions Demo

This section is an interactive demonstration. The live simulation runs on the original site: open the demonstration at onlinestatbook.com.

Learning Objectives

  1. Become more familiar with collecting data and presenting statistics from this data.
  2. Learn how one might compare data from two distributions.

Instructions
This demonstration collects response time data from you and computes various descriptive statistics. It also displays histograms and box plots. After you click the button to begin, a rectangle will appear to the right of the button. Move the cursor to the rectangle and click. The time it takes you to click on the rectangle is recorded. Half of the time the rectangle is small and half of the time it is big. After two practice trials and 40 regular trials, the descriptive statistics and graphs will be displayed.

Illustrated Instructions
The simulation is started by clicking the button in the lower left of the screen. Clicking this button begins a series of trials where a another button appears on the right and you will be asked to click this button as quickly as possible.Screenshot of the reaction-time experiment used by the comparing-distributions demo, shown twice with a red arrow between. Above, the Start Screen: instructions explaining that clicking the button makes another button appear on the right, that the time taken to click it is recorded, that the target is large on half the trials and small on the other half, and that data are analyzed after 2 practice and 40 regular trials, with a Click to begin button at the bottom left. Below, the same screen after clicking: an empty target square has appeared at the lower right.
Half of the buttons will large and half will be small. Once you complete 40 trials, the simulation will show you descriptive statistics about the reaction time data for each button size (see screenshot below).
Screenshot of the demo's analysis output comparing reaction times to Small and Large targets, N = 20 each. The statistics table gives Small versus Large: mean 916.75 vs 728.50, median 857 vs 713, trimean 895.06 vs 717.25, minimum 675 vs 545, maximum 1522 vs 905, 25th percentile 827 vs 676, 75th percentile 1039.25 vs 767, sd 192.75 vs 89.45, sem 43.10 vs 20.00, skew 1.62 vs 0.34, kurtosis 4.14 vs 0.41. Two histograms on the right share an axis from 552 to 1498: the Small distribution is spread out with an isolated case near 1500, the Large distribution is compact between about 550 and 900. Box plots at the lower left show the same contrast, with an outside value above each box.

There are no questions for this simulation.

Follow the instructions accompanying the simulation. Compare the two distributions after completing the 40 trials. Are the differences what you expected?

Adapted from Online Statistics Education: A Multimedia Course of Study (onlinestatbook.com), Project Leader: David M. Lane, Rice University. Developed with NSF support. The original work is in the public domain; it is cited here at the authors' request. Changes were made: reformatted as an accessible XYZ web edition with native MathML. License: Public-Domain.