74.3 The purpose of an investigation by Morley et al. (A-17) was to evaluate the
ID: 2932471 • Letter: 7
Question
74.3 The purpose of an investigation by Morley et al. (A-17) was to evaluate the analgesic effectiveness of a daily dose of oral methadone in patients with chronic neuropathic pain syndromes. The re searchers used a visual analogue scale (0-100mm, higher number indicates higher pain) ratings for maximum pain intensity over the course of the day. Each subject took either 20 mg of methadone or a placebo each day for 5 days. Subjects did not know which treatment they were taking. The following table gives the mean maximum pain intensity scores for the 5 days on methadone and the 5 days on placebo. Do these data provide sufficient evidence, at the .05 level of significance, to indicate that in general the maximum pain intensity is lower on days when methadone is taken? Subject Methadone Placebo 29.8 73.0 98.6 58.8 60.6 57.2 57.2 89.2 97.0 49.8 37.0 57.2 69.8 98.2 62.4 67.2 70.6 67.8 95.6 Sounce: John S. Morley, John Bridson, Tim P. Nash, JohB 98.4 Miles, Sarah White, and Matthew K. Makin LowDose 63.2 Methadone Has an Analgesic Effect in Neuropathic Pain 63.6 A Double-Blind Randomized Controlled Crossover Trial. 10 Palliative Medicine, 17 (2003), 576-587Explanation / Answer
Solution:
Here, we have to use paired t test for testing the hypothesis whether the maximum pain intensity is lower on days when methadone is taken.
Null hypothesis: H0: There is no statistically significant difference in the average maximum pain intensity when methadone and placebo are taken.
Alternative hypothesis: Ha: The average maximum pain intensity when methadone is taken is lower than the average maximum intensity when placebo is taken.
H0: µ1 = µ2 Vs H0: µ1 < µ2
This is a one tailed test. This is a left tailed test.
The level of significance is given as 0.05.
= 0.05
The test statistic formula is given as below:
t = Dbar / [Sd/sqrt(n)]
Calculation table is given as below:
Methadone
Placebo
Di
(Di - DBar)^2
29.8
57.2
-27.4
316.1930579
73
69.8
3.2
164.3057851
98.6
98.2
0.4
100.3639669
58.8
62.4
-3.6
36.2185124
60.6
67.2
-6.6
9.109421488
57.2
70.6
-13.4
14.30214876
57.2
67.8
-10.6
0.963966942
89.2
95.6
-6.4
10.35669421
97
98.4
-1.4
67.5385124
49.8
63.2
-13.4
14.30214876
37
63.6
-26.6
288.3821488
Sample size = n = 11
Degrees of freedom = n - 1 = 11 – 1 = 10
Dbar = -9.6182
Sd = 10.1096
t = -9.6182 / [10.1096/sqrt(11)]
t = -3.1554
P-value = 0.0051
(By using t-table)
P-value < = 0.05
So, we reject the null hypothesis that there is no statistically significant difference in the average maximum pain intensity when methadone and placebo are taken.
There is sufficient evidence to conclude that the average maximum pain intensity when methadone is taken is lower than the average maximum intensity when placebo is taken.
Methadone
Placebo
Di
(Di - DBar)^2
29.8
57.2
-27.4
316.1930579
73
69.8
3.2
164.3057851
98.6
98.2
0.4
100.3639669
58.8
62.4
-3.6
36.2185124
60.6
67.2
-6.6
9.109421488
57.2
70.6
-13.4
14.30214876
57.2
67.8
-10.6
0.963966942
89.2
95.6
-6.4
10.35669421
97
98.4
-1.4
67.5385124
49.8
63.2
-13.4
14.30214876
37
63.6
-26.6
288.3821488
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