1. A step-by-step hypothesis test for a repeated-measures design Consider the following data from a repeated-measures design. You want to use a repeated- measures t test to test the null hypothesis H,: PD = 0 (the 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 (D = B - A) Observation (D²) 12 10 11 12 3 17 16 4 10 11 16 18 The mean difference score is M= 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? v 10.80 / 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/ What is the t statistic for the repeated-measures t test to test the null hypothesis Hạ: Hu = 0? 0.27 t Distribution Degrees of Freedom -1.0 -2.0 -1.0 4.711 1.0 0.711 1.0 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.
1. A step-by-step hypothesis test for a repeated-measures design Consider the following data from a repeated-measures design. You want to use a repeated- measures t test to test the null hypothesis H,: PD = 0 (the 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 (D = B - A) Observation (D²) 12 10 11 12 3 17 16 4 10 11 16 18 The mean difference score is M= 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? v 10.80 / 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/ What is the t statistic for the repeated-measures t test to test the null hypothesis Hạ: Hu = 0? 0.27 t Distribution Degrees of Freedom -1.0 -2.0 -1.0 4.711 1.0 0.711 1.0 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.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:1. A step-by-step hypothesis test for a repeated-measures design
Consider the following data from a repeated-measures design. You want to use a repeated-
measures t test to test the null hypothesis H,: PD = 0 (the 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
(D = B - A)
Observation
(D²)
12 10
11
12
3
17
16
4
10
11
16
18
The mean difference score is M=
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?
v 10.80 /
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/
What is the t statistic for the repeated-measures t test to test the null hypothesis Hạ: Hu = 0?
0.27
t Distribution
Degrees of Freedom
-1.0
-2.0
-1.0
4.711
1.0
0.711
1.0
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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