MATH1302 Practice Questions 1 Design and Analysis of Experiments
Instructions:
The following questions are based on the material from this course. These questions are not compulsory but are provided as practice the concepts that will be built on in the course and to practice with R and SAS
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Question 1
An experimenter has conducted a single-factor experiment with four levels of the factor, and each factor level has been replicated six times. The computed value of the F-statistic is 3.26. Find the p value.
Question 2
An output from ANOVA analysis is shown below. Fill in the blanks (by hand).
One-way ANOVA:
Analysis of Variance
Source DF
Factor 3
Error ??
Total 19 196.04
SS MS F-Value P-Value
36.15 ?? ?? ??
Question 3
An article in Bioelectromagnetics (¡°Electromagnetic Effects on Forearm Disuse Osteopenia: A Randomized, Double-Blind, Sham-Controlled Study¡±, Vol. 32, 2011, pp. 273-282) described a randomized, double-blind, sham controlled, feasibility and dosing study to determine if a common pulsing electromagnetic field (PEMF) treatment could moderate the substantial osteopenia that occurs after forearm disuse. Subjects were randomized into four groups after a distal radius fracture, or carpal surgery requiring immobilization in a cast. Active or identical sham PEMF transducers were worn on the distal forearm for 1, 2 or 4 h/day for 8 weeks starting after cast removal (¡°baseline¡±) when bone density continues to decline. Bone mineral density (BMD) and bone geometry were measured in the distal forearm by dual energy X-ray absorptiometry (DXA) and peripheral quantitative computed tomography (pQCT). The data below are the percent losses in BMD measurements on the radius after 16 weeks for patients wearing the active or sham PEMF transducers for 1, 2 or 4 h/day (data were constructed to match the means and standard deviations read from a graph in the paper).
a) Is there evidence to support a claim that PEMF usage affects BMD loss? If so, analyse the data to determine which specific treatments produce the differences.
b) Analyse the residuals from this experiment and comment on the underlying assumptions and model adequacy.
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