Login
📚 Online Statistics Education
Chapters ▾
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
⇩ Download ▾
⇩ This section (Typst)

12.8 Correlated t Simulation

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 null hypothesis for a correlated t test
  2. State the effect of increasing r on power

Instructions
This simulation demonstrates the t test for correlated observations. When you click the "sample" button, 12 subjects with scores in two conditions are sampled from a population. Each population is normally distributed with a standard deviation of 4. The mean for condition 1 is 15 and the mean for condition 2 is 13. The initial population correlation between conditions is 0.5, although you can change that. The data from the sample of 12 subjects is graphed with a line connecting the two data points for a subject. The difference scores (Condition A - Condition B) are computed and graphed as well and shown in a table. The bottom of simulation displays the mean difference score, the standard deviation of the difference scores, the standard error of the mean difference score, the value of t, and the value of p.

Illustrated Instructions
Video Demo
The video begins by running simulations with the population correlation set to.5. More simulation are run with the correlation set to.1. As you watch the video and run simulations for yourself see if you can determine a correspondence between an aspect of the graph and the standard deviation of the difference scores. Specifically, look at the degree to which the lines diverge from being parallel and the standard deviation. What effect does increasing the correlation have on the parallel lines and the standard deviation? What effect does increasing the correlation have?

Video Demo

You can change the population correlation below.

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.