5. A psychologist at a private psychiatric hospital was asked to determine whether there was any clear difference in the length of stay of patients with different categories of diagnosis. Looking at the last four patients in each of the three major categories, the results (in terms of weeks of stay) were as follows: Diagnosis Category Affective Disorders Cognitive Disorders Drug-Related Conditions 12 8. 10 9. 12 11 10 Mı=6 M2 = 10 M3 = 10 %3D %3D SS 2 SS2 = 10 SS2 = 8 SSBetween = 42.67 a. What test are you going to perform? b. List the hypotheses c. List the decision rule d. Perform the ANOVA e. Complete the ANOVA table Source SS df MS Between Within Total

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**Problem Description:**

A psychologist at a private psychiatric hospital conducted a study to determine whether there was any significant difference in the length of stay for patients with different categories of diagnosis. The data collected included the length of stay (in weeks) for the last four patients in each of three major categories:

- **Affective Disorders:**
  - 7 weeks
  - 6 weeks
  - 5 weeks
  - 6 weeks

- **Cognitive Disorders:**
  - 12 weeks
  - 8 weeks
  - 9 weeks
  - 11 weeks

- **Drug-Related Conditions:**
  - 8 weeks
  - 10 weeks
  - 12 weeks
  - 10 weeks

**Means and Sums of Squares:**
- \( M_1 = 6 \), \( SS_1 = 2 \)
- \( M_2 = 10 \), \( SS_2 = 10 \)
- \( M_3 = 10 \), \( SS_3 = 8 \)
- \( SS_{Between} = 42.67 \)

**Tasks:**

a. **Test to Perform:**
   - Conduct an ANOVA (Analysis of Variance).

b. **List the Hypotheses:**
   - Null Hypothesis (\( H_0 \)): There is no significant difference in the length of stay among the three diagnosis categories.
   - Alternative Hypothesis (\( H_1 \)): There is a significant difference in the length of stay among the three diagnosis categories.

c. **Decision Rule:**
   - Decide on the significance level (commonly 0.05) to determine the critical value. Reject the null hypothesis if the calculated F-value is greater than the critical F-value from the F-distribution table.

d. **Perform the ANOVA:**
   - Calculate the necessary values for the ANOVA table.

e. **Complete the ANOVA Table:**

| Source    | SS       | df  | MS    | F    |
|-----------|----------|-----|-------|------|
| Between   | 42.67    | 2   |       |      |
| Within    |          |     |       |      |
| Total     |          |     |       |      |

- Note: Fill in MS (Mean Square) and F-ratio after computing them.

f. **Report your ANOVA result
Transcribed Image Text:**Problem Description:** A psychologist at a private psychiatric hospital conducted a study to determine whether there was any significant difference in the length of stay for patients with different categories of diagnosis. The data collected included the length of stay (in weeks) for the last four patients in each of three major categories: - **Affective Disorders:** - 7 weeks - 6 weeks - 5 weeks - 6 weeks - **Cognitive Disorders:** - 12 weeks - 8 weeks - 9 weeks - 11 weeks - **Drug-Related Conditions:** - 8 weeks - 10 weeks - 12 weeks - 10 weeks **Means and Sums of Squares:** - \( M_1 = 6 \), \( SS_1 = 2 \) - \( M_2 = 10 \), \( SS_2 = 10 \) - \( M_3 = 10 \), \( SS_3 = 8 \) - \( SS_{Between} = 42.67 \) **Tasks:** a. **Test to Perform:** - Conduct an ANOVA (Analysis of Variance). b. **List the Hypotheses:** - Null Hypothesis (\( H_0 \)): There is no significant difference in the length of stay among the three diagnosis categories. - Alternative Hypothesis (\( H_1 \)): There is a significant difference in the length of stay among the three diagnosis categories. c. **Decision Rule:** - Decide on the significance level (commonly 0.05) to determine the critical value. Reject the null hypothesis if the calculated F-value is greater than the critical F-value from the F-distribution table. d. **Perform the ANOVA:** - Calculate the necessary values for the ANOVA table. e. **Complete the ANOVA Table:** | Source | SS | df | MS | F | |-----------|----------|-----|-------|------| | Between | 42.67 | 2 | | | | Within | | | | | | Total | | | | | - Note: Fill in MS (Mean Square) and F-ratio after computing them. f. **Report your ANOVA result
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