Buffering Capacity
Group Medium High
Cerebral palsy 2 8
Control 3 7
Source: J. F. Tahmassebi and M. E. J. Curzon, “The Cause of Drooling in Children with Cerebral Palsy—
Hypersalivation or Swallowing Defect?” International Journal of Paediatric Dentistry, 13 (2003), 106–111.
Test for a significant difference between cerebral palsied children and controls with respect to high
or low buffering capacity. Let and find the p value.
12.6.2 In a study by Xiao and Shi (A-14), researchers studied the effect of cranberry juice in the treat-
ment and prevention of Helicobacter pylori infection in mice. The eradication of Helicobacter
pylori results in the healing of peptic ulcers. Researchers compared treatment with cranberry juice
to “triple therapy (amoxicillin, bismuth subcitrate, and metronidazole) in mice infected with Heli-
cobacter pylori. After 4 weeks, they examined the mice to determine the frequency of eradication
of the bacterium in the two treatment groups. The following table shows the results.
No. of Mice with Helicobacter pylori Eradicated
Yes N o
Triple therapy 8 2
Cranberry juice 2 8
Source: Shu Dong Xiao and Tong Shi, “Is Cranberry Juice Effective in the Treatment and Prevention of
Helicobacter Pylori Infection of Mice,” Chinese Journal of Digestive Diseases, 4 (2003), 136–139.
May we conclude, on the basis of these data, that triple therapy is more effective than cranberry
juice at eradication of the bacterium? Let and find the p value.
12.6.3 In a study by Shaked et al. (A-15), researchers studied 26 children with blunt pancreatic injuries.
These injuries occurred from a direct blow to the abdomen, bicycle handlebars, fall from height,
or car accident. Nineteen of the patients were classified as having minor injuries, and seven were
classified as having major injuries. Pseudocyst formation was suspected when signs of clinical
deterioration developed, such as increased abdominal pain, epigastric fullness, fever, and increased
pancreatic enzyme levels. In the major injury group, six of the seven children developed pseudo-
cysts while in the minor injury group, three of the 19 children developed pseudocysts. Is this suf-
ficient evidence to allow us to conclude that the proportion of children developing pseudocysts is
higher in the major injury group than in the minor injury group? Let
12.7 RELATIVE RISK, ODDS RATIO, AND
THE MANTEL–HAENSZEL STATISTIC
In Chapter 8 we learned to use analysis of variance techniques to analyze data that arise
from designed experiments, investigations in which at least one variable is manipulated
in some way. Designed experiments, of course, are not the only sources of data that are
a = .01.
a = .05
a = .05
634 CHAPTER 12 THE CHI-SQUARE DISTRIBUTION AND THE ANALYSIS OF FREQUENCIES