3) Researchers want to test a new anti-anxiety medication. They measure the anxi

Question

3) Researchers want to test a new anti-anxiety medication. They measure the anxiety of 36 participants on different dosages of the medication: Omg, 50mg, and 100mg. Participants are also divided based on what school they are attending, which researchers hypothesize will also affect anxiety levels. Anxiety is rated on a scale of 1-10, with 10 being "high anxiety" and 1 being "low anxiety". The data are presented below: Omg 50mg 100mg High School Students 9 2 College Students For this problem, G = 177 and 2x2 = 1081 a) Analyze the data using the appropriate analysis of variance and report F-ratios. (15 pts.)

Explanation / Answer

Solution:

Here, we have to use the two way analysis of variance or ANOVA for the given data. From the given data, we have the means for dosage and class as below:

(Calculations are carried out by using excel)

Dosage

Mean

0 mg

2.5

50 mg

4.42

100 mg

7.83

Class

Mean

High school

5.17

College

4.67

Required ANOVA table is given as below:

(Calculations are carried out by using excel)

Total DF = n – 1 = 36 – 1 = 35

DF for dosage = k – 1 = 3 – 1 = 2

(K = types of dosage = 3)

DF for class = m – 1 = 2 – 1 = 1

(m = types of class = 2)

DF for interaction = DF for dosage * DF for class = 2*1 = 2

MS = SS/DF

F = respective MS / MSE

MSE = MS for error

Source

DF

SS

MS

P-value

Dosage

2

175.167

87.5835

0

Class

1

2.25

2.25

0.05

Interaction

2

17.167

8.5835

0

Error

30

16.167

Total

35

210.75

P-values are calculated by using F-table or excel.

We assume the level of significance or alpha value for this test as 5% or 0.05.

For the variable dosage, the p-value is given as 0.00, so we reject the null hypothesis that the average anxiety score is same for the given three types of dosage. This means, there is sufficient evidence to conclude that the anxiety scores for the given three types of dosage are not same.

For the variable class, the p-value is given as 0.05, so we reject the null hypothesis that the average anxiety score is same for the high school students and college students. There is sufficient evidence to conclude that the anxiety scores for the high school students and college students are not same.

The p-value for the interaction due to three types of dosage and two types of class is given as 0.00, so we reject the null hypothesis that the given interaction is not statistically significant. There is sufficient evidence to conclude that the interaction is statistically significant.

(Decision rule: We reject the null hypothesis if the p-value is less than the given level of significance or alpha value, and we do not reject the null hypothesis if the p-value is greater than the given level of significance or alpha value.)

Dosage

Mean

0 mg

2.5

50 mg

4.42

100 mg

7.83

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