Question

1. A research study was conducted to examine the clinical efficacy of a new antidepressant. Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a moderate dose of the drug, and a group that received a high dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient. The data are presented below. Use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 1-way ANOVA test for the data in the following table:

Placebo	Moderate Dose	High Dose
42	22	10
52	19	14
39	8	12
33	23	19
41	31	10

1. What is your computed answer?
2. What would be the null hypothesis in this study?
3. What would be the alternate hypothesis?
4. What level of significance did you choose and why?
5. What is your F_crit?
6. Is there a significant difference between the groups?
7. If there is a significant difference, where specifically are the differences?
8. Interpret your answer in the context of the problem statement.

Answer 1

Solution: As specifically mentioned in the question, we will use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 1-way ANOVA test, by following the steps as mentioned below:

Step 1: Prepare the following table in the same cells as mentioned in the below-mentioned screenshot:

Step 2: Go to Data Tabe > Analysis > Data Analysis as mentioned in the below screenshot:

Step 3: After clicking the Data-Analysis, you will find the following pop-up, wherein you have to select Anova Single Factor as mentioned in the below table:

Step 4: Now, fill the same data as mentioned in the below screenshot in the pop-up window of ANOVA Sinle Factor:

(Note: As no specific information is mentioned in the question, we have taken Alpha = 0.05)

Then, pressing the 'OK' will show the result as mentioned below:

Now, we will answer the given questions one by one from the Outcome Table of ANOVA Single-Factor as mentioned below:

Answer 1: The computed Answer = Computed F-Ratio = 24.82695 (2,12)

The p-value is .000054.

Answer 2: Null Hypothesis for the given study = = There will be no difference in depression levels between the three groups.

Answer 3: Alternative Hypothesis for the given study = = There will be a difference somewhere in depression levels between the three levels of drug groups.

Answer 4: We chose the level of significance p = 0.01. Because there is a risk involved with a Type I error and we do not want to erroneously say the drug works and then later find out that it doesn't.

Answer 5: The value of F-Critical = 3.885294

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