A school psychologist is interested in determining if children with attention deficit hyperactivity disorder (ADHD) learn better if English literature is read to them rather than having them read the material alone by themselves. A random sample of 10 sixth graders with ADHD is selected and divided into two groups of n=9. One of the groups has a story read to them (Listening Group) and the other reads the story alone by themselves (Reading Group). A test on the story is given after each group has finished reading or hearing the story. The following scores were obtained with 20 being a perfect score. What is the r^2?
A school psychologist is interested in determining if children with attention deficit hyperactivity disorder (ADHD) learn better if English literature is read to them rather than having them read the material alone by themselves. A random sample of 10 sixth graders with ADHD is selected and divided into two groups of n=9. One of the groups has a story read to them (Listening Group) and the other reads the story alone by themselves (Reading Group). A test on the story is given after each group has finished reading or hearing the story. The following scores were obtained with 20 being a perfect score. What is the r^2?
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A school psychologist is interested in determining if children with attention deficit hyperactivity disorder (ADHD) learn better if English literature is read to them rather than having them read the material alone by themselves. A random sample of 10 sixth graders with ADHD is selected and divided into two groups of n=9. One of the groups has a story read to them (Listening Group) and the other reads the story alone by themselves (Reading Group). A test on the story is given after each group has finished reading or hearing the story. The following scores were obtained with 20 being a perfect score.
What is the r^2?
Transcribed Image Text:**Two-sample t-test, independent groups**
The table below contains data for a two-sample t-test comparing the means of a Reading Group and a Listening Group.
### Group Data
| | Reading Group | Listening Group |
|--------|---------------|-----------------|
| 10 | 15 |
| 10 | 12 |
| 7 | 13 |
| 12 | 11 |
| 8 | 10 |
| 9 | 9 |
| 10 | 11 |
| 9 | 10 |
| 11 | 11 |
### Summary Statistics
| | Reading Group | Listening Group |
|-----------|---------------|-----------------|
| Count (n) | 9 | 9 |
| Mean | 9.444444444 | 11.33333333 |
| DEVSQ(SS) | 20.22222222 | 26 |
| STDEV.S | 1.589898669 | 1.802775638 |
| df | 8 | 8 |
### Calculations
- **S(M1-M2)**: 0.8011
- **alpha**: 0.05
- **t_crit**: 2.1199
- **t_obs**: 3.5389
### Decision
Since t_obs (3.5389) > t_crit (2.1199), **Reject Ho**.
### Effect Size
- **Cohen's d**: 1.1113
### Interpretation
Based on the t-test results, we reject the null hypothesis (Ho), indicating a significant difference between the Reading and Listening Groups. The effect size measured by Cohen's d is 1.1113, which is considered a large effect size.
This data analysis and results can be helpful in determining the effectiveness of different learning methods (reading vs. listening).
Transcribed Image Text:### t-Test: Two-Sample Assuming Equal Variances
#### Group Statistics
| Statistics | G1 | G2 |
|-------------------|-------------|-------------|
| **Mean** | 8.777777778 | 11.44444444 |
| **Variance** | 3.944444444 | 3.277777778 |
| **Observations** | 9 | 9 |
| **Pooled Variance** | 3.611111111 | |
| **Hypothesized Mean Difference** | 0 | |
| **Degrees of Freedom (df)** | 16 | |
#### t-Test Results
| Results | Value |
|-------------------------------|---------------|
| **t Statistic** | -2.97683363 |
| **P(T<=t) one-tail** | 0.004495533 |
| **t Critical one-tail** | 1.745883676 |
| **P(T<=t) two-tail** | 0.008899105 |
| **t Critical two-tail** | 2.119905299 |
### Explanation of t-Test
A t-test is performed to determine if there is a significant difference between the means of two groups (G1 and G2). This particular t-test assumes that the variances of the two groups are equal.
- **G1 and G2 Statistics**: The table lists the mean, variance, and number of observations for both groups.
- **Pooled Variance**: This is the combined variance of the two groups, calculated since the t-test assumes equal variances.
- **Degrees of Freedom**: This is the total number of observations in both groups minus 2.
### Interpretation of Results:
- **t Statistic**: A value of -2.97683363 indicates the calculated t-value from the t-test.
- **P-Value (one-tail)**: The one-tailed p-value of 0.004495533 indicates the probability of observing the test results under the null hypothesis.
- **Critical t-Value (one-tail)**: The critical value for the one-tailed test is 1.745883676. Since the absolute t statistic is greater than this value, the null hypothesis can be rejected in a one-tailed test scenario.
- **P-Value (two-tail)**: A two
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