MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Title: T-Test Analysis**
**Overview of Study:**
- **Objective:** To determine if there is a difference between two conditions using a t-test.
- **Participants:** 8 individuals divided into two groups:
- Group 1 (Congruent condition)
- Group 2 (Incongruent condition)
**Data Collected:**
| Subject | Total Score (X) | Group |
|---------|----------------|-------|
| 1 | 10 | 1 |
| 2 | 6 | 1 |
| 3 | 9 | 1 |
| 4 | 3 | 1 |
| 5 | 20 | 2 |
| 6 | 12 | 2 |
| 7 | 15 | 2 |
| 8 | 9 | 2 |
**Research Questions:**
1. Is there a difference between conditions?
2. What is the 95% confidence interval of the mean difference?
3. What is the effect size?
**Statistical Analysis:**
1. **Standard Deviation (s):**
\[
s = \sqrt{\frac{\sum (X - M)^2}{N-1}}
\]
2. **T-statistic (t):**
\[
t = \frac{\overline{X}_1 - \overline{X}_2}{\hat{S}_{\overline{X}_1 - \overline{X}_2}}
\]
3. **Pooled Standard Deviation (\(\hat{S}_{\text{pooled}}\)):**
\[
\hat{S}_{\text{pooled}} = \sqrt{\frac{(n_1 - 1)\hat{S}_1^2 + (n_2 - 1)\hat{S}_2^2}{(n_1 - 1) + (n_2 - 1)}}
\]
4. **Effect Size (d):**
\[
d = \frac{M_X - M_Y}{S_{\text{pooled}}}
\]
**Confidence Interval (CI) Formula:**
\[
CI = \text{Mean Difference} \pm t_{\text{critical}}(\hat{S}_{\overline{X](https://content.bartleby.com/qna-images/question/1ffb0219-9c91-4db5-8eec-6f48496f58b1/fbfc47ca-ad2d-48bc-8471-f92466a744ff/wqouba_processed.jpeg)
Transcribed Image Text:**Title: T-Test Analysis**
**Overview of Study:**
- **Objective:** To determine if there is a difference between two conditions using a t-test.
- **Participants:** 8 individuals divided into two groups:
- Group 1 (Congruent condition)
- Group 2 (Incongruent condition)
**Data Collected:**
| Subject | Total Score (X) | Group |
|---------|----------------|-------|
| 1 | 10 | 1 |
| 2 | 6 | 1 |
| 3 | 9 | 1 |
| 4 | 3 | 1 |
| 5 | 20 | 2 |
| 6 | 12 | 2 |
| 7 | 15 | 2 |
| 8 | 9 | 2 |
**Research Questions:**
1. Is there a difference between conditions?
2. What is the 95% confidence interval of the mean difference?
3. What is the effect size?
**Statistical Analysis:**
1. **Standard Deviation (s):**
\[
s = \sqrt{\frac{\sum (X - M)^2}{N-1}}
\]
2. **T-statistic (t):**
\[
t = \frac{\overline{X}_1 - \overline{X}_2}{\hat{S}_{\overline{X}_1 - \overline{X}_2}}
\]
3. **Pooled Standard Deviation (\(\hat{S}_{\text{pooled}}\)):**
\[
\hat{S}_{\text{pooled}} = \sqrt{\frac{(n_1 - 1)\hat{S}_1^2 + (n_2 - 1)\hat{S}_2^2}{(n_1 - 1) + (n_2 - 1)}}
\]
4. **Effect Size (d):**
\[
d = \frac{M_X - M_Y}{S_{\text{pooled}}}
\]
**Confidence Interval (CI) Formula:**
\[
CI = \text{Mean Difference} \pm t_{\text{critical}}(\hat{S}_{\overline{X
Expert Solution
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Step 1
Given Information:
4 individuals were tested in the Memory test in the congruent condition.
Another 4 individuals were tested in the incongruent condition.
The data is:
| Group 1 | Group 2 |
| 10 | 20 |
| 6 | 12 |
| 9 | 15 |
| 3 | 9 |
Enter the data in Excel. Use the Excel function "=AVERAGE()" to obtain the sample mean for each group.
Use the function "=STDEV.S()" to obtain the sample standard deviation for each group.
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what is the 95%CI upper and lower?
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what is the 95%CI upper and lower?
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