Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis Ho: Pp = 0 (the %3D null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed. Complete the following table by calculating the differences and the squared differences:
Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis Ho: Pp = 0 (the %3D null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements, A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed. Complete the following table by calculating the differences and the squared differences:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Consider the following data from a repeated-measures design. You want to use a repeated-measures t test to test the null hypothesis Ho: PD = 0 (the
%3D
null hypothesis states that the mean difference for the general population is zero). The data consist of five observations, each with two measurements,
A and B, taken before and after a treatment. Assume the population of the differences in these measurements are normally distributed.
Complete the following table by calculating the differences and the squared differences:
Difference Score
Squared Difference Score
Observation
A
(D = B - A)
(D2)
2
3
3.
4.
6.
4.
6.
5.
6.
8.
The mean difference score is Mp =
For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and sMD
What is the estimated standard deviation of the difference scores?
S = V
6.80/
What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of
s.)
SMD
s/
%3D
What is the t statistic for the repeated-measures t test to test the null hypothesis Ho: Pp = 07
Mp
1.37
t Distribution
Degrees of Fedom 7
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Transcribed Image Text:The mean difference score is Mp =
For a repeated-measures t test, you need to calculate the t statistic, which requires you to calculate s and syD.
What is the estimated standard deviation of the difference scores?
6.80/
S =
What is the estimated standard error of the mean difference scores? (Note: For best results, retain at least six decimal places from your calculation of
s.)
SMD
s/
%3D
What is the t statistic for the repeated-measures t test to test the null hypothesis Ho: Pp = 0?
t =
Mp
%3D
1.37
t Distribution
Degrees of Freedom = 7
5000
2500
S00
4.0
-3.0
-2.0
-1.0
0.0
1.0
0.711
2.0
3.0
4.0
0.711
You conduct a two-tailed test at a = .05. To use the Distributions tool to find the critical values, you first need to set the degrees of freedom in the
tool. The degrees of freedom are
The critical values (the values for t scores that separate the tails from the main body of the distribution, forming the critical region) are
Finally, since the t statistic
in the critical region, you
the null hypothesis.
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