Question

In order to reduce hostility levels, twelve students were randomly assigned to three different types of therapy. After completing a therapy, each student was given a test that recorded hostility level. A lower score indicates lower hostility and vice-versa.

	Therapy
1	2	3
80	74	62
92	81	71
87	78	72
85	77	62

Calculate the sample variance (or standard deviation) for each therapy.

For Hartley's test of homogenity

Ho: σ²1 = σ²2 = σ²3 Ha: Population variances are not all equal.

calculate the test statistic F'.

For σ = 0.05, specify the critical region for Hartley's test of homogeneity and make a decision about H_o.

Find the P-value and compare to σ = 0.05.

Answer 1

Sol:

Calcuations for variances

Therapy1(X)	xbar	x-xbar	(x-xbar)^2
80	86	-6	36
92	86	6	36
87	86	1	1
85	86	-1	1
		total	74

variance=s1^2=74/4-1=74/3=24.6667

Therapy2(X)	xbar	x-xbar	(x-xbar)^2
74	77.5	-3.5	12.25
81	77.5	3.5	12.25
78	77.5	0.5	0.25
77	77.5	-0.5	0.25
		total	25

variance=s2^2=25/4-1=25/3=8.3333

Therapy3(X)	xbar	x-xbar	(x-xbar)^2
62	66.75	-4.75	22.5625
71	66.75	4.25	18.0625
72	66.75	5.25	27.5625
62	66.75	-4.75	22.5625
		total	90.75

variance=s3^2=90.75/4-1=90.75/3=30.25

create a data frame DF in R

Load PMCMRplus package

and use hartleytest

Rcode:

DF=read.table(header = TRUE, text ="
Therapy   Hostility_score
1   80
1   92
1   87
1   85
2   74
2   81
2   78
2   77
3   62
3   71
3   72
3   62

"
  
)
DF
summary(DF)

library(PMCMRplus)

hartleyTest(Hostility_score ~ Therapy , data = DF)

output:

F=3.63

p=0.568

p>0.05

Do not reject Ho.
Accept Ho