Suppose a hypertension trial is mounted and 18 participants are
-
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 |
|
|
|
|
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.
——————————————–
Do the following problems using SPSS and provide a copy of the ANOVA table for each as your answer:
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
-
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.
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