138 CATEGORICAL DATA: PROPORTIONSstatement will produce tables that give you the proportions needed to test the equality
of the two porportions. SPSS allows you to specify which variables are nonimal
using the variable view of the data editor and the Measure option. Any question with
numerous missing values or “do not know” responses should be examined to see if
there was something wrong with the question.
Note that in many computer programs a variable that has numerous missing values
can result in the data for many patients being excluded even through that particular
variable is not used in the current analysis. To avoid this loss of patients in the analysis,
the variable with the missing values should be explicitly noted as not used or dropped.
PROBLEMS
10.1 Table A. 1 lists random digits between 0 and 9. Assume that an even number is
a success and an odd number is a failure. Draw three samples of size 10 and
write down the proportion of successes. Make a frequency table with all the
sample proportions from the entire class. Compute the mean and variance of all
the sample proportions. What do you expect the population 7r to equal? Using
5~ what is the variance of an observation? What is the variance of the mean of
10 observations? How does this compare with the result from the frequency
table?
10.2 If the proportion of people with a certain illness who recover under a given
treatment is actually .8, what percentage of sample proportions obtained from
repeated samples of size 64 would be between .7 and .9?
10.3 The proportion of 200 children age 19-35 months from families in poverty
who had inadequate polio vaccinations was found to be .21 in community A.
Community B, which has a special program in place to increase vaccination of
children from families in poverty, measured their vaccination proportion and
found it to be. 12 among 150 children. Test the null hypothesis of equal propor-
tions in the two communities using a: = .05. Also compute a 95% confidence
limit for the difference in the two proportions. Contrast what statements can
be made from the test and the confidence limits.
10.4 If the proportion of patients who recover from a certain illness under a given
treatment is actually .9, what is the probability that < 75% of a sample of 100
patients recover?
10.5 One hundred patients are available to participate in an experiment to compare
two cold remedies. As in the example in the text, the physician divides them
into two equal groups, gives each treatment to 50 patients, and finds that the
percentages of patients who recover within 10days are 90 and 80%. Give a
95% confidence interval for the difference between the population recovery
rates. What can you conclude from this confidence interval?
10.6 An experiment was performed to determine if a new educational program given
by pharmacists could reduce the prescribing of a widely used analgesic that had
been proven to be inferior to aspirin. The physicians were randomly assigned