Question

1. Researchers at a trauma center wished to develop a program to help brain-damaged trauma victims
regain an acceptable level of independence. An experiment involving subjects with the same degree of
brain damage was conducted. The objective was to compare different combinations of psychiatric
treatment and physical therapy. Each subject was assigned to one of 24 different combinations of four
types of psychiatric treatment and six physical therapy programs. The response variable is the number
of months elapsing between initiation of therapy and time at which the patient was able to function
independently. The results are given below.
		Psychiatric Treatment
Physical Therapy Program	A	B	C	D
I.	11.0	9.4	12.5	13.2
II.	11.5	10.5	11.8	14.6
III.	11.8	11.5	11.8	12.8
IV.	10.5	9.1	13.5	15.0
V.	11.0	11.2	14.4	13.0
VI.	10.8	10.8	11.5	11.8
Test both the physical therapy program and the psychiatric treatment as major effects in a two-way ANOVA.

Put your answers in column B using the standard format : hypotheses and conclusions relative to the hypotheses.

Hypotheses:

Ho

Ha

Ho

Ha

Ho

Ha

Conclusion relative to the hypothesis:

Answer 1

To perform a 2-way ANOVA of the problem

H₀: The number of months elapsing between initiation of therapy and time at which the patient was able to function independently is same for both the programs

H₁: Significant effect of independent variables on number of months elapsed.

To perform the 2-way analysis using minitab we proceed as follows:

Enter the data in minitab as follows:

	Psychiatric Treatment
Physical Therapy Program	A	B	C	D
I.	11.0	9.4	12.5	13.2
II.	11.5	10.5	11.8	14.6
III.	11.8	11.5	11.8	12.8
IV.	10.5	9.1	13.5	15.0
V.	11.0	11.2	14.4	13.0
VI.	10.8	10.8	11.5	11.8

In the following 3 columns give headings as 'physical therapy program', 'psychiartic treatment', 'months' ->Data -> Stack -> Columns ->a dialogue box appears -> in 'Stack the following columns' enter A-D -> in 'Columns of current worksheet' enter months -> in 'store subscripts in' enter 'psychiartic treatment' -> Ok ->Calc -> Make Patterned Data -> Text values ->a dialogue box appears -> In 'Store patterned Data in' enter ''physical therapy program'' -> in 'Text values' enter 'I. II. III. IV. V. VI. VII. ' -> in 'Number of times to list the sequence' enter 4 ->ok -> Stat ->ANOVA -> Balanced ANOVA ->a dialogue box appears -> in 'Responses' enter 'months' -> in Model enter 'psychiartic treatment' 'physical therapy program' -> ok .

The output appears in the session window as follows:

ANOVA: months versus psychiartic treatment, physical therapy program

Factor Type Levels Values
psychiartic treatment fixed 4 A, B, C, D
physical therapy program fixed 7 I., II., III., IV., V., VI., VII.

Analysis of Variance for months

Source DF SS MS F P
psychiartic treatment 3 32.1411 10.7137 10.81 0.000
physical therapy program 6 5.0636 0.8439 0.85 0.548
Error 18 17.8364 0.9909
Total 27 55.0411

S = 0.995446 R-Sq = 67.59% R-Sq(adj) = 51.39%

So there is significant effect of psychiartic treatment in the brain damaged trauma victims since p-value<0.05