Question

- Strategies for treating hypertensive patients by nonpharmacologic methods are compared by establishing three groups of hypertensive patients who receive the following types of nonpharmacologic therapy: Group 1: Patients receive counseling for weight reduction Group 2: Patients receive counseling for meditation Group 3: Patients receive no counseling at all month period and are given in the The reduction in diastolic blood pressure is noted in these patients after a table below. 4.2 Group 1 Group 2 Group 3 4.5 1.2 4.7 2.9 -0.3 3.4 2.3 2.3 0.1

Answer 1

treatment	I	II	III
count, ni =	3	3	4
mean , x̅ i =	4.100	3.23	0.825
std. dev., si =	0.656	1.137	1.170
sample variances, si^2 =	0.430	1.293	1.369
total sum	12.3	9.7	3.3		25.3	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				2.53
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	2.465	0.495	2.907
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	7.395	1.484	11.628		20.50683
SS(within ) = SSW = Σ(n-1)s² =	0.860	2.587	4.108		7.554

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   10
df within = N-k =   7
  
mean square between groups , MSB = SSB/k-1 =    10.2534
  
mean square within groups , MSW = SSW/N-k =    1.0792
  
F-stat = MSB/MSW =    9.5012

anova table
	SS	df	MS	F	p-value
Between:	20.507	2	10.2534	9.501	0.0101
Within:	7.554	7	1.0792
Total:	28.061	9

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The Bonferroni correction sets the significance cut-off at α/n = 0.06/3 = 0.02

MSE=   1.079

test statistic = ( x̅ i -x̅ j) /√(MSE(1/ni+1/nj))

answer: 1.02 , 4.13 , 3.04

b)

α=0.02

no. of treatments,k=   3
DF error =N-k=   7
t-critical value,t(α/2,df)=   2.9980

if test stat > critical value, means are significantly different

		t-critical value	test statistic		result
µ1-µ2		2.998	1.02		means are not different
µ1-µ3		2.998	4.13		means are different
µ2-µ3		2.998	3.04		means are different

answer: option H)