Suppose A Hypertension Trial Is Mounted And 18 Participants Are Randomly Assigned To One

12 Jul Suppose A Hypertension Trial Is Mounted And 18 Participants Are Randomly Assigned To One

1. Suppose a hypertension trial is mounted and 18 participants are randomly assigned to one of the comparison treatments. Each participant takes the assigned medication and their systolic blood pressure (SBP) is recorded after 6 months on the assigned treatment. The data are as follows.

 

 

 

 

 

Standard Treatment	Placebo	New Treatment
124	134	114
111	143	117
133	148	121
125	142	124
128	150	122
115	160	128

 

 

 

Is there a difference in mean SBP among treatments? Run the appropriate test at =0.05.

 

 

 

Step 1. Set up hypotheses and determine level of significance

 

H₀: _= ₂= ₃

 

H₁: Means are not all equal =0.05

 

 

 

Step 2. Select the appropriate test statistic. F=MSB/MSE.

 

 

 

Step 3. Set up decision rule.

 

df₁=k-1=3-1=2 and df₂=N-k=18-3=15. Reject H₀ if F > 3.68.

 

 

 

Step 4. Compute the test statistic.

 

 

 

 

 

Standard	Placebo	New Treatment
n1=6	n2=6	n3=6
1= 122.7	2= 146.2	3= 121.0

 

 

 

If we pool all N=18 observations, the overall mean is = 130.0.

 

 

 

We can now compute .

 

SSB = 6(122.7-130.0)² + 6(146.2-130.0)² + 6(121.0-130.0)²

 

SSB = 2380.4.

 

Next, .

 

 

 

Standard Treatment	(X – 122.7)	(X – 122.7)2
124	1.3	1.69
111	-11.7	136.89
133	10.3	106.09
125	2.3	5.29
128	5.3	28.09
115	-7.7	59.29
		337.34

 

Thus, (X- ₁)² = 337.34.

 

 

 

Placebo	(X – 146.2)	(X – 146.2)2
134	-12.2	148.84
143	-3.2	10.24
148	1.8	3.24
142	-4.2	17.64
150	3.8	14.44
160	13.8	190.44
		384.84

 

Thus, (X- ₂)² = 384.84.

 

 

 

New Treatment	(X – 121.0)	(X – 121.0)2
114	-7	49
117	-4	16
121	0	0
124	3	9
122	1	1
128	7	49
		124

 

Thus, (X- ₃)² = 124.0

 

 

 

= 846.18.

 

 

 

We can now construct the ANOVA table.

 

Source of Variation	Sums of Squares SS	Degrees of freedom df	Mean Squares MS	F
Between Treatments	2380.4	2	1190.2	21.1
Error or Residual	846.2	15	56.4
Total	3226.6	17

 

 

 

Step 5. Conclusion.

 

We reject H₀ because 21.1 > 3.68. We have statistically significant evidence at =0.05 to show that there is a difference in mean systolic blood pressure among treatments.

 

 

 

 

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Do the following problems using SPSS and provide a copy of the ANOVA table for each as your answer:

 

Sullivan pp. 162-168:  14

 

 

 

PLUS the following problems:

 

1. A manufacturer wants to know which new coffee sells the best and distributes 3 types (Blue-Label, Green-Label and Red Label) to 6 of his stores. After letting customers taste the three types, the number of pounds purchased of each type of coffee on one day are recorded for the six stores.  Perform an ANOVA using SPSS to determine whether there is a significant difference in sales.

 

Blue-Label   Green-Label     Red-Label
13              1              5
4              1              2
10              2              2
13              2              2
11              2              6
3              4              4

 

 

 

1. Three topical antibiotics are tested to see how quickly they eliminate a rash in 4 people who have a history of repeated rashes of this type.

 

 

 

The number of days to eliminate the rash in the 4 people is given in the table below:

 

Topical antibiotic 1	Topical antibiotic 2	Topical antibiotic 3
3	5	8
9	1	2
5	2	6
11	5	4

 

 

 

Conduct a one-way ANOVA to determine whether there is a significance difference in the number of days to eliminate the rash.