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📚 Online Statistics Education
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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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12.2 t Distribution Demo

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

Learning Objectives

  1. State the difference between the shape of the t distribution and the shape of the normal distribution.
  2. State how the degrees of freedom affect the difference between the t and normal distributions.

Instructions
This demonstration allows you to compare the t distribution to the standard normal distribution. At the start, the standard normal distribution is compared to a t distribution with three degrees of freedom. You can change the degrees of freedom of the t distribution with the slider. The 3 and the 50 mark the ends of the slider. The "current" degrees of freedom are shown at the bottom where it says "t distribution with df=3." As you change the slider, the df are shown by this last line. The "zoom in" button allows you to change the scale of the graph to see the tails of the distribution in more detail.

Illustrated Instructions
Video Demo
In the video the slider is used to increase the degrees of freedom. Notice how the t-distribution change as the degrees of freedom increase. The video concludes with the tails of the tails of the graphs being zoomed into via the "zoom in" button and the degrees of freedom being decreased.

Video Demo

You can change the shape of the t-distribution by adjusting the degrees of freedom with the sliders.

Watch the video demonstration (onlinestatbook.com)

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.