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8. The following data are from a repeated-measures study examining the effect of a treatment by measur- ing a group of n = 9 participants before and after they receive the treatment.

8. The following data are from a repeated-measures study examining the effect of a treatment by measur- ing a group of n = 9 participants before and after they receive the treatment.

MATLAB: An Introduction with Applications
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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**Study Description:** The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of *n* = 9 participants before and after they receive the treatment. **Explanation:** In this study, the same group of nine participants is measured at two different points in time, once before they receive a treatment and once after. This design allows researchers to assess the impact of the treatment by comparing the participants' scores at both measures. Repeated-measures studies are useful for controlling subject variability because each participant serves as their own control.
Transcribed Image Text:**Study Description:** The following data are from a repeated-measures study examining the effect of a treatment by measuring a group of *n* = 9 participants before and after they receive the treatment. **Explanation:** In this study, the same group of nine participants is measured at two different points in time, once before they receive a treatment and once after. This design allows researchers to assess the impact of the treatment by comparing the participants' scores at both measures. Repeated-measures studies are useful for controlling subject variability because each participant serves as their own control.
### Instructions for Analysis #### a. Calculate the Difference Scores and \( M_D \) - **Difference Scores**: Subtract the "Before Treatment" score from the "After Treatment" score for each participant. - **\( M_D \)**: Calculate the mean of the difference scores. #### b. Compute \( SS \), Sample Variance, and Estimated Standard Error - **\( SS \) (Sum of Squares)**: Sum of squared deviations of each difference score from the mean difference score. - **Sample Variance**: \( \text{Variance} = \frac{SS}{n-1} \), where \( n \) is the number of participants. - **Estimated Standard Error**: Square root of the Sample Variance divided by \( n \). #### c. Test for Significant Treatment Effect - Use a two-tailed test with \( \alpha = 0.05 \) to determine if there is a significant treatment effect. ### Data Table | Participant | Before Treatment | After Treatment | |-------------|------------------|-----------------| | A | 82 | 89 | | B | 64 | 67 | | C | 76 | 79 | | D | 6 | 8 | | E | 38 | 40 | | F | 150 | 147 | | G | 10 | 14 | | H | 4 | 11 | | I | 16 | 18 | ### Explanation of Analysis Process 1. **Calculate the Difference for Each Participant**: For each row, subtract the "Before Treatment" value from the "After Treatment" value to get the difference score. 2. **Calculate the Mean of the Differences (\( M_D \))**: Add all the difference scores and divide by the number of participants. 3. **Compute \( SS \), Sample Variance, and Standard Error**: These measures show the variability and reliability of your sample data. 4. **Significance Test**: Use a t-test for paired samples to determine if the treatment had a statistically significant effect.
Transcribed Image Text:### Instructions for Analysis #### a. Calculate the Difference Scores and \( M_D \) - **Difference Scores**: Subtract the "Before Treatment" score from the "After Treatment" score for each participant. - **\( M_D \)**: Calculate the mean of the difference scores. #### b. Compute \( SS \), Sample Variance, and Estimated Standard Error - **\( SS \) (Sum of Squares)**: Sum of squared deviations of each difference score from the mean difference score. - **Sample Variance**: \( \text{Variance} = \frac{SS}{n-1} \), where \( n \) is the number of participants. - **Estimated Standard Error**: Square root of the Sample Variance divided by \( n \). #### c. Test for Significant Treatment Effect - Use a two-tailed test with \( \alpha = 0.05 \) to determine if there is a significant treatment effect. ### Data Table | Participant | Before Treatment | After Treatment | |-------------|------------------|-----------------| | A | 82 | 89 | | B | 64 | 67 | | C | 76 | 79 | | D | 6 | 8 | | E | 38 | 40 | | F | 150 | 147 | | G | 10 | 14 | | H | 4 | 11 | | I | 16 | 18 | ### Explanation of Analysis Process 1. **Calculate the Difference for Each Participant**: For each row, subtract the "Before Treatment" value from the "After Treatment" value to get the difference score. 2. **Calculate the Mean of the Differences (\( M_D \))**: Add all the difference scores and divide by the number of participants. 3. **Compute \( SS \), Sample Variance, and Standard Error**: These measures show the variability and reliability of your sample data. 4. **Significance Test**: Use a t-test for paired samples to determine if the treatment had a statistically significant effect.
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