Free Statistics Help Book
An Interactive Multimedia introductory-level statistics book.
The book features interactive demos, simulations and case studies.
The book features interactive demos, simulations and case studies.
Testing Means :
Correlated t Simulation
Questions to be answered before the simulation are not yet implemented in this test version.
Begin by answering the questions, even if you have to guess. The first time you answer the questions you will not be told whether you are correct or not.
Once you have answered all the questions, answer them again using the simulation to help you. This time you will get feedback about each individual answer.
General 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 as shown in a table.
At the bottom of the display is shown 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.
Step By Step Instructions
1. Do a few simulations and 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.
2. Decrease the correlation to 0.1. What effect does that have on how non-parallel the lines are and the standard deviation.
3. Increase the correlation to 0.9. What effect does that have on the standard deviation and on how often the test is significant?
Summary
The higher the correlation between conditions, the closer the lines are to being parallel and the lower the standard deviation of the difference scores. Since the denominator of the t test is based on this standard deviation, the higher the correlation, the greater the chance of finding a significant difference between condition means.