Homework
I. A trial evaluated the fever-inducing effects of three substances. Study subjects were adults seen in an emergency room with diagnoses of the flu and body temperatures between 100.0 and 100.9ºF. The three treatments (aspirin, ibuprofen and acetaminophen) were assigned randomly to study subjects. Body temperatures were reevaluated 2 hours after administration of treatments. The below table lists the data.
Data Table: Decreases in body temperature (degrees Fahrenheit) for each patient
|
|
|
|
|
|
|
|
Mean
|
|
Group 1 (aspirin)
|
0.95
|
1.48
|
1.33
|
1.28
|
|
|
1.26
|
|
Group 2 (ibuprofen)
|
0.39
|
0.44
|
1.31
|
2.48
|
1.39
|
|
1.20
|
|
Group 3 (acetaminophen)
|
0.19
|
1.02
|
0.07
|
0.01
|
0.62
|
-0.39
|
0.25
|
The ANOVA table that corresponds to this data is below.
a) State the research question that this ANOVA answers.
b) Answer your research question using the means in the Data Table and the ANOVA results.
c) Which treatment(s) would you recommend to reduce a fever for this population?
d) What type of tests could you conduct that would allow you to compare each treatment group to the other (2 at a time) without inflating the type I error (α)?
e) Why is it important to make sure you do not increase the type I error?
ANOVA Table:
|
Fev_red
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
Between groups
|
3.426
|
2
|
1.713
|
4.777
|
0.030
|
|
Within groups
|
4.303
|
12
|
0.359
|
|
|
|
Total
|
7.729
|
14
|
|
|
|
II. Evidence of nonrandom differences between group means occurs when the variance between groups is ________ the variance within groups.
III. Why are scatterplots helpful when investigating the association between quantitative variables?
IV. The Pearson correlation statistic, r, is always greater than or equal to _____ and less than or equal to _____. Absolutely no association is present when r = ___. Between r = -0.56 and r = +0.46, the stronger correlation is _____.
V. A Pearson correlation statistic is only valid when the relationship between the two quantitative (continuous) variables is ____________.
VI. Explain why it is true that the slope of a line is related to the Pearson correlation statistic, r.
II. Create a scatterplot to investigate the association between the amount of fluoride in domestic water (ppm) and the number of dental caries in permanent teeth per 100 children for 21 cities. The data are below.
a. Create the scatterplot
b. Describe the association you see in your scatterplot.
c. The value of r is -0.86, -0.36, 0.36, or 0.86?
|
CityID
|
FLUORIDE (ppm)
|
CARIES
|
|
1
|
1.9
|
236
|
|
2
|
2.6
|
246
|
|
3
|
1.8
|
252
|
|
4
|
1.2
|
258
|
|
5
|
1.2
|
281
|
|
6
|
1.2
|
303
|
|
7
|
1.3
|
323
|
|
8
|
0.9
|
343
|
|
9
|
0.6
|
412
|
|
10
|
0.5
|
444
|
|
11
|
0.4
|
556
|
|
12
|
0.3
|
652
|
|
13
|
0.0
|
673
|
|
14
|
0.2
|
703
|
|
15
|
0.1
|
706
|
|
16
|
0.0
|
722
|
|
17
|
0.2
|
733
|
|
18
|
0.1
|
772
|
|
19
|
0.0
|
810
|
|
20
|
0.1
|
823
|
|
21
|
0.1
|
1037
|
Data from Dean, H.T., Arnold, F. A., Jr., & Elvove, E. (1942). Domestic water and dental caries. Public Health Reports, 57, 1155-1179.
Format your homework according to the following formatting requirements:
(1) The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
(2) The response also includes a cover page containing the title of the homework, the student's name, the course title, and the date. The cover page is not included in the required page length.
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