Woo and McKenna investigated the effect of broadband ultraviolet B (UVB) therapy
ID: 3309277 • Letter: W
Question
Woo and McKenna investigated the effect of broadband ultraviolet B (UVB) therapy and topical calcipotriol cream used together on areas of psoriasis. One of the outcome variables is the Psoriasis Area and Severity Index (PASI). The following table give the PASI scores for 20 subjects measured at the baseline and after 8 treatments. Do these data provide sufficient evidence, at the .01 level of significance, to indicate that the combination therapy reduces PASI scores?
Subject
Baseline
After 8 Treatments
1
5.9
5.2
2
7.6
12.2
3
12.8
4.6
4
16.5
4
5
6.1
0.4
6
14.4
3.8
7
6.6
1.2
8
5.4
3.1
9
9.6
3.5
10
11.6
4.9
11
11.1
11.1
12
15.6
8.4
13
6.9
5.8
14
15.2
5
15
21
6.4
16
5.9
0
17
10
2.7
18
12.2
5.1
19
20.2
4.8
20
6.2
4.2
7.a. State the null hypothesis in words and in symbol. (I have highlighted an important word in the main question above. Pay attention to that while doing the null hypothesis.)
7.b. State the alternative hypothesis in words and in symbol.
7.c. Perform paired sample t test using the SPSS. Copy and paste two tables from the output: (1) Paired Samples Statistics, and (2) Paired Samples Test.
7.d. Based on the t statistic and p value in output tables, would you reject or retain the null hypothesis? Obtain the critical value using the online software (QuickCalcs GraphPad) and compare t statistic with it. Make sure to enter the right level and the df.
Subject
Baseline
After 8 Treatments
1
5.9
5.2
2
7.6
12.2
3
12.8
4.6
4
16.5
4
5
6.1
0.4
6
14.4
3.8
7
6.6
1.2
8
5.4
3.1
9
9.6
3.5
10
11.6
4.9
11
11.1
11.1
12
15.6
8.4
13
6.9
5.8
14
15.2
5
15
21
6.4
16
5.9
0
17
10
2.7
18
12.2
5.1
19
20.2
4.8
20
6.2
4.2
Explanation / Answer
QUestion 7
(a) Null HYpothesis : H0 : There is no difference between Psoriasis Area and Severity Index (PASI) measured at the baseline and after 8 treatments of broadband ultraviolet B (UVB) therapy and topical calcipotriol cream. d = 0
Altenative Hypothesis : Ha : There is sufficient reduction in Psoriasis Area and Severity Index (PASI) measured at the baseline and after 8 treatments of broadband ultraviolet B (UVB) therapy and topical calcipotriol cream. d > 0
where d is the difference of PASI score between baseline and 8 treatments score.
(b) Here the difference Table is
Average difference dbar = 6.22
Standard deviation of differnece sd = 5.04
so standard error of difference se0 = sd /sqrt(n) = 5.04/ sqrt(20) = 1.127
Test statistic
t = 6.22/ 1.127 =5.5188
here for dF = 19 and alpha = 0.01
tcritical = 2.5395
p - value = 0.000013
so t > tcritical so we shall reject the null hypothesis and can conclude that There is sufficient reduction in Psoriasis Area and Severity Index (PASI) measured at the baseline and after 8 treatments of broadband ultraviolet B (UVB) therapy and topical calcipotriol cream.
NOTE: here i have not used the SPSS. But i have used EXCEL. The excel results are given below.
Subject Baseline After 8 Treatments Difference 1 5.9 5.2 0.7 2 7.6 12.2 -4.6 3 12.8 4.6 8.2 4 16.5 4 12.5 5 6.1 0.4 5.7 6 14.4 3.8 10.6 7 6.6 1.2 5.4 8 5.4 3.1 2.3 9 9.6 3.5 6.1 10 11.6 4.9 6.7 11 11.1 11.1 0 12 15.6 8.4 7.2 13 6.9 5.8 1.1 14 15.2 5 10.2 15 21 6.4 14.6 16 5.9 0 5.9 17 10 2.7 7.3 18 12.2 5.1 7.1 19 20.2 4.8 15.4 20 6.2 4.2 2 Average 6.22 STDEV 5.040322Related Questions
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