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 5.7 4.5 1.2 2.8 -0.3 3.4 2.3 0.2 2.8 Using the data from Problem #6 above, we want to use Fisher's LSD method to test the following hyptheses at the 5% significance level: Ho 12vS Hạ:1 Ho 3vS HA:13 Ho 23 vs Hạ:u23 (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 5% significance level)?

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
1	4	16.1	4.025	1.575833
2	3	9.6	3.2	1.33
3	3	1.1	0.366667	0.583333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	24.10183333	2	12.05092	9.861442	0.009199	4.737414
Within Groups	8.554166667	7	1.222024
Total	32.656	9

a) LSD = t * sqrt(MSW *(1/n1 + 1/n2)
df = df within = N-k = 7
t = 2.3646
MSW = 1.222024

for first and second
LSD =2.3646 *sqrt(1.222*(1/4 + 1/3)) = 1.996418

for third
LSD =2.3646 *sqrt(1.222*(1/3 + 1/3))) = 2.13426

b)
difference in means for first = 0.825
for second = 3.6583
for third = 2.8333

if absolute difference > LSD

then difference is significant

hence

second and third pair are significantly different