Question

Please give a detailed explanation how to solve this with excel

1)This problem demonstrates a possible (though rare) situation that can occur with group comparisons. The groups are sections and the dependent variable is an exams score.

Section 1	Section 2	Section 3
84.9	58.5	74.1
70.6	57.6	81.5
76.4	65.8	74.9
62.5	84.1	79
81.2	80.5	72.3
67.5	44.4	65.8
75.5	68.6	71
68.6	41.8	67.8
79.2	64.8	75.5

Run a one-way ANOVA (fixed effect) with α=0.05α=0.05. Round the F-ratio to three decimal places and the p-value to four decimal places. Assume all population and ANOVA requirements are met.

F=
p=

2. Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.

Low Moderate	High Moderate	Moderately Severe	Severe
1.5	3.9	3.6	2.8
1.7	2.3	3.6	4.9
0.2	0.5	2.4	2.3
2	3.1	3.1	3.3
1.1	3.5	2.3	4
0	3	2.5	3.8

From this table, conduct an one-way ANOVA. Calculate the F-ratio and p-value. Be sure to round your answers to three decimal places. Assume all population and ANOVA requirements are met.

F-ratio:  
p-value:  



What is your final conclusion? Use a significance level of α=0.02

• There is not enough evidence to determine a difference between the treatments.
• There is sufficient evidence that there exists a significant difference between treatments.

Answer 1

Answer(1):

We have to test:

H0: there is no difference in scores of three sections

H1: there is significant difference in scores of at least two sections

In Excel we can run a one-way ANOVA as below:

Paste the data in excel > go to Data tab > go to data analysis tool pack > select the “ANOVA: Single Factor” > select the data > click ok

The output of the excel ANOVA is as below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Section 1	9	666.4	74.044	52.613
Section 2	9	566.1	62.900	204.827
Section 3	9	661.9	73.544	25.003
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	713.259	2	356.629	3.788	0.0372	3.403
Within Groups	2259.544	24	94.148
Total	2972.803	26

F=3.788

p=0.0372

We can observe that the p-value is less than α=0.05 which indicates that we have enough evidence against null hypothesis to reject it at 0.05 level, so we to reject the null hypothesis and we can conclude that there is significant difference in scores of at least two sections.

The Screen shot of Excel steps is as below:

Answer(2):

Answer(2):

We have to test:

H0: There is no difference in between treatments

H1: There is significant difference between treatments

In Excel we can run a one-way ANOVA as below:

Paste the data in excel > go to Data tab > go to data analysis tool pack > select the “ANOVA: Single Factor” > select the data > click ok

The output of the excel ANOVA is as below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Low Moderate	6	6.5	1.083	0.670
High Moderate	6	16.3	2.717	1.466
Moderately Severe	6	17.5	2.917	0.358
Severe	6	21.1	3.517	0.854
ANOVA
Source of Variation	SS	Df	MS	F	P-value	F crit
Between Groups	19.485	3	6.495	7.763	0.001	3.098
Within Groups	16.733	20	0.837
Total	36.218	23

F-ratio: 7.763

p-value: 0.001

We can observe that the p-value is less than α=0.02 which indicates that we have strong evidence against null hypothesis to reject it at 0.02 level, so we reject the null hypothesis and we can conclude that there is significant difference Between the treatments.

The Screen shot of Excel steps is as below: