A researcher wants to understand the depression scores reported by patients enrolled in two drug trials. The levels of depression were measured next day and midweek after the drug consumption. Which test the researcher should use to understand the effect of the drug on the days? (use Data1.csv) (i) Given is the study table tabulated by researcher for patients on a new drug. Compute the odds ratio for survival.

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  1. A researcher wants to understand the depression scores reported by patients enrolled in two drug trials. The levels of depression were measured next day and midweek after the drug consumption. Which test the researcher should use to understand the effect of the drug on the days? (use Data1.csv)
  2. (i) Given is the study table tabulated by researcher for patients on a new drug. Compute the odds ratio for survival.
**Question 5: Solve both the questions:**

**A.** A researcher wants to understand the depression scores reported by patients enrolled in two drug trials. The levels of depression were measured the next day and midweek after the drug consumption. Which test should the researcher use to understand the effect of the drug on the days? (use Data1.csv)

**B.** (i) Given is the study table tabulated by the researcher for patients on a new drug. Compute the odds ratio for survival.

| Treatments | Drug1 | Drug2 | Odds Ratio |
|------------|-------|-------|------------|
| Survived   | 250   | 100   |            |
| Died       | 150   | 20    |            |

### Explanation

**A. Analysis Requirement**

The researcher needs to compare depression scores on two different days for two drug trials. An appropriate statistical test to use would be a repeated measures ANOVA or a paired t-test, depending on the distribution and nature of the data within Data1.csv. These tests help in comparing means across different times or conditions for the same subjects.

**B. Odds Ratio Calculation**

To calculate the odds ratio for survival between Drug1 and Drug2:

1. **Odds of Survival with Drug1**: Number of Survived (Drug1) / Number of Died (Drug1)
   = 250 / 150
   
2. **Odds of Survival with Drug2**: Number of Survived (Drug2) / Number of Died (Drug2)
   = 100 / 20

3. **Odds Ratio (OR)**: (Odds with Drug1) / (Odds with Drug2)

The odds ratio provides a measure of the association between drug treatment and survival outcome. If the odds ratio is greater than 1, survival is more likely with Drug1 relative to Drug2. If less than 1, Drug2 is more effective.
Transcribed Image Text:**Question 5: Solve both the questions:** **A.** A researcher wants to understand the depression scores reported by patients enrolled in two drug trials. The levels of depression were measured the next day and midweek after the drug consumption. Which test should the researcher use to understand the effect of the drug on the days? (use Data1.csv) **B.** (i) Given is the study table tabulated by the researcher for patients on a new drug. Compute the odds ratio for survival. | Treatments | Drug1 | Drug2 | Odds Ratio | |------------|-------|-------|------------| | Survived | 250 | 100 | | | Died | 150 | 20 | | ### Explanation **A. Analysis Requirement** The researcher needs to compare depression scores on two different days for two drug trials. An appropriate statistical test to use would be a repeated measures ANOVA or a paired t-test, depending on the distribution and nature of the data within Data1.csv. These tests help in comparing means across different times or conditions for the same subjects. **B. Odds Ratio Calculation** To calculate the odds ratio for survival between Drug1 and Drug2: 1. **Odds of Survival with Drug1**: Number of Survived (Drug1) / Number of Died (Drug1) = 250 / 150 2. **Odds of Survival with Drug2**: Number of Survived (Drug2) / Number of Died (Drug2) = 100 / 20 3. **Odds Ratio (OR)**: (Odds with Drug1) / (Odds with Drug2) The odds ratio provides a measure of the association between drug treatment and survival outcome. If the odds ratio is greater than 1, survival is more likely with Drug1 relative to Drug2. If less than 1, Drug2 is more effective.
The table presents data on the effect of two drugs (A and B) measured over two days, Sunday and Wednesday, for 20 participants. The columns are as follows:

- **Column A (Participant):** Lists the participant number from 1 to 20.
- **Column B (Drug):** Indicates which drug was administered to each participant (either A or B).
- **Column C (Sunday):** Shows the measurement taken on Sunday for each participant.
- **Column D (Wednesday):** Shows the measurement taken on Wednesday for each participant.

### Detailed Data:

- **Participants 1 to 11:** Administered Drug A.
  - Measurements range from:
    - **Sunday:** 13 to 35
    - **Wednesday:** 24 to 39

- **Participants 12 to 20:** Administered Drug B.
  - Measurements range from:
    - **Sunday:** 2 to 20
    - **Wednesday:** 3 to 36

This table allows for comparison of the efficacy or impact of the two drugs over a short period by observing changes in measurements from Sunday to Wednesday.
Transcribed Image Text:The table presents data on the effect of two drugs (A and B) measured over two days, Sunday and Wednesday, for 20 participants. The columns are as follows: - **Column A (Participant):** Lists the participant number from 1 to 20. - **Column B (Drug):** Indicates which drug was administered to each participant (either A or B). - **Column C (Sunday):** Shows the measurement taken on Sunday for each participant. - **Column D (Wednesday):** Shows the measurement taken on Wednesday for each participant. ### Detailed Data: - **Participants 1 to 11:** Administered Drug A. - Measurements range from: - **Sunday:** 13 to 35 - **Wednesday:** 24 to 39 - **Participants 12 to 20:** Administered Drug B. - Measurements range from: - **Sunday:** 2 to 20 - **Wednesday:** 3 to 36 This table allows for comparison of the efficacy or impact of the two drugs over a short period by observing changes in measurements from Sunday to Wednesday.
Expert Solution
Step 1

A)

Chi-square test of independence:

A single simple random sampling is done with each individual being classified based on the two categorical variables. Then, the hypothesis testing is carried out to check whether there is any relationship between the two categorical variables. This test is called as chi-square test of independence.

In the given situation, the researcher should use to understand the effect of the drug on the days.

Hence, we can use the chi-square test.

 

 

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