Question

1. 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

Answer 1

(a) Research question: Three treatments  (aspirin, ibuprofen and acetaminophen) are equally effective or not i.e. we want to test

(b)

Null hypothesis, Ho : μ,-μ2-13us. Alternative hypothesis. Hi : at least one μίǐs different. where, m-true mean effect due to aspirin. μ2-true mean effect due to ibuprofen. u3- true mean ef fect due to acetaminophen

One-way ANOVA: Body temperatures versus Treatment

Source DF SS MS F P
Treatment 2 4.079 2.039 7.11 0.007
Error 15 4.303 0.287
Total 17 8.382

Since p-value=0.007<0.05 so we reject H0 and conclude that there is at least one treatment has different effect than others. For finding the treatment or treatments which is/are responsible for this rejection we perform Tukey's HSD test.

Grouping Information Using Tukey Method

Treatment N Mean Grouping
Aspirin 5 1.2600 A
Ibuprofen 6 1.2017 A
Acetaminophen 7 0.2529 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Treatment

Individual confidence level = 97.97%

The simultaneous confidence intervals for treatments differences are:

Aspirin-Acetaminophen: (0.1933, 1.8210)
Ibuprofen-Acetaminophen: (0.1755, 1.7221)
(Ibuprofen-Aspirin): (-0.9000, 0.7833)

c. Since C.I.s for Aspirin-Acetaminophen and Ibuprofen-Acetaminophen contain only positive values and C.I. for (Ibuprofen-Aspirin) contains zero so the difference between mean effects of  Ibuprofen and Aspirin is insignificant whereas effect of Acetaminophen is significantly different from other two, so we recommend Acetaminophen to reduce a fever for this population.

d. Multiple comparison tests can be used. Here we use Tukey's Method to answer Question c.

e. We use this test because in this situation, Probability of Type I error<= level of significance. Actually it controls the Type I error.