Solution Found!
In the article “Assessment of Dermatopharmacokinetic
Chapter 4, Problem 8E(choose chapter or problem)
In the article “Assessment of Dermatopharmacokinetic Approach in the Bioequivalence Determination of Topical Tretinoin Gel Products” (L. Pershing, J. Nelson, et al., Journal of the American Academy of Dermatology, 2003:740–751), measurements of the concentration of an anti-fungal gel, in ng per square centimeter of skin, were made one hour after application for 49 individuals. Following are the results. The authors claim that these data are well-modeled by a lognormal distribution. Construct an appropriate probability plot, and use it to determine whether the data support this claim.
132.44 76.73 258.46 177.46 73.01 130.62 235.63
107.54 75.95 70.37 88.76 104.00 19.07 174.30
82.87 68.73 41.47 120.44 136.52 82.46 67.04
96.92 93.26 72.92 138.15 82.43 245.41 104.68
82.53 122.59 147.12 129.82 54.83 65.82 75.24
135.52 132.21 85.63 135.79 65.98 349.71 77.84
89.19 102.94 166.11 168.76 155.20 44.35 202.51
Questions & Answers
QUESTION:
In the article “Assessment of Dermatopharmacokinetic Approach in the Bioequivalence Determination of Topical Tretinoin Gel Products” (L. Pershing, J. Nelson, et al., Journal of the American Academy of Dermatology, 2003:740–751), measurements of the concentration of an anti-fungal gel, in ng per square centimeter of skin, were made one hour after application for 49 individuals. Following are the results. The authors claim that these data are well-modeled by a lognormal distribution. Construct an appropriate probability plot, and use it to determine whether the data support this claim.
132.44 76.73 258.46 177.46 73.01 130.62 235.63
107.54 75.95 70.37 88.76 104.00 19.07 174.30
82.87 68.73 41.47 120.44 136.52 82.46 67.04
96.92 93.26 72.92 138.15 82.43 245.41 104.68
82.53 122.59 147.12 129.82 54.83 65.82 75.24
135.52 132.21 85.63 135.79 65.98 349.71 77.84
89.19 102.94 166.11 168.76 155.20 44.35 202.51
ANSWER:
Solution :
Step 1 of 1:
Given, the measurement of the concentration of an anti-fungal gel, in ng per square centimeter of skin, were made one hour after application for 49 individuals.
We know that the data are well-modeled by a lognormal distribution.
Here Ylognormal distribution with the parameters mean
and standard deviation
.
So YN
.
Our goal is:
We need to construct an appropriate probability plot, and use it to determine whether the data support this claim.
Now we need to construct an appropriate probability plot, and use it to determine whether the data support this claim.
We have to use this formula to compute the pairs.
(In,
)
Where i=1,2,3,...,n and
The natural logs of the ordered observation = In.
Then the table is given below.
i |
In |
i |
In |
||||
1 |
132.44 |
4.8861 |
0.010204082 |
27 |
245.41 |
5.5029 |
0.540816327 |
2 |
76.73 |
4.3403 |
0.0 |