11 May Suppose a hypertension trial is mounted and 18 p
- 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 |
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 |
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