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 The reduction in diastolic blood pressure is noted in these patients after a 1-month period and are given in the table below. Group 1 Group 2 Group 3 4.2 4.5 1.2 4.2 2.1 −0.3 3.4 2.3 0.6 2.8 Using the data above, we want to use Fisher's LSD method to test the following hyptheses at the 1% significance level: H0 : μ1 = μ2  vs  HA : μ1 ≠ μ2 H0 : μ1 = μ3  vs  HA : μ1 ≠ μ3 H0 : μ2 = μ3  vs  HA : μ2 ≠ μ3 (a) Find the value of LSD for each of the above three hypotheses (in the above order). (b) Which pairs of means are significantly different (using Fisher's LSD test at the 1% significance level)? (A) none of them (B) all of them (C) 1 and 2, 1 and 3 only (D) 1 and 2 only (E) 1 and 3 only (F) 1 and 2, 2 and 3 only (G) 2 and 3 only (H) 1 and 3, 2 and 3 only

Answer 1

(A)

Here the ANOVA table is given below

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Group 1	3	11.8	3.933333	0.213333
Group 2	3	8.9	2.966667	1.773333
Group 3	4	4.3	1.075	1.7025
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	14.93917	2	7.469583	5.757961	0.033223	4.737414
Within Groups	9.080833	7	1.297262
Total	24.02	9

Here for the group 1 and group 2

the value of LSD is

​

Here dFW = 7 so

t_{0.025, 7} = 3.4995

LSD(1-2) = 3.4995 * sqrt [1.297262 * (1/3 + 1/3)] = 3.2544

LSD(1-3) = 3.4995 * sqrt [1.297262 * (1/3 + 1/4)] = 3.0442

LSD(2-3) =  3.4995 * sqrt [1.297262 * (1/3 + 1/4)] =3.0442

(b) Here mean difference between group 1 and group 2 = 3.93-2.9667 = 0.9667

which is less than LSD so there is no significant difference.

Here mean difference between group 1 and group 3 = 3.93- 1.075 = 2.5853

which is less than LSD so there is no a significant difference.

Here mean difference between group 2 and group 3 = 2.9667 - 1.075 =1.8917

which is less than LSD so there is not a significant difference.

None of them is significant