EXAMPLE
Illustrating the Process of Statistics
Many studies evaluate batterer treatment programs, but there are few experiments designed to
compare batterer treatment programs to non-therapeutic treatments, such as community service.
Researchers designed an experiment in which 376 male criminal court defendants who were
accused of assaulting their intimate female partners were randomly assigned into either a
treatment group or a control group. The subjects in the treatment group entered a 40-hour
batterer treatment program while the subjects in the control group received 40 hours of
community service. After 6 months, it was reported that 21% of the males in the control group
had further battering incidents, while 10% of the males in the treatment group had further
battering incidents. The researchers concluded that the treatment was effective in reducing
repeat battering offenses.
(Source: The Effects of a Group Batterer Treatment Program: A Randomized Experiment in
Brooklyn by Bruce G. Taylor, et. al. Justice Quarterly, Vol. 18, No. 1, March 2001.)
Step 1: Identify the research objective.
To determine whether males accused of batterering their intimate female partners that were
assigned into a 40-hour batter treatment program are less likely to batter again compared to those
assigned to 40-hours of community service.
Step 2: Collect the information needed to answer the question.
The researchers randomly divided the subjects into two groups. Group 1 participants received
the 40-hour batterer program, while group 2 participants received 40 hours of community
service. Six months after the program ended, the percentage of males that battered their intimate
female partner was determined.
Step 3: Organize and summarize the information.
The demographic characteristics of the subjects in the experimental and control group were
similar. After the six month treatment, 21% of the males in the control group had any further
battering incidents, while 10% of the males in the treatment group had any further battering
incidents.
Step 4: Draw conclusions from the data.
We extend the results of the 376 males in the study to all males who batter their intimate female
partner. That is, males who batter their female partner and participate in a batter treatment
program are less likely to batter again.
Example 1
According to Variety (Aug. 27, 2009), the average age of viewers of live television programs
broadcast on CBS, NBC, and ABC is 51 years. Suppose a rival network (e.g. Fox) executive
hypothesizes that the average age of Fox viewers is less than 51. To test her hypotheses, she
samples 200 Fox viewers and determines the age of each.
a. Describe the population.
The population is the set of units of interest to the TV executive, which is the set of all Fox
Viewers.
b. Describe the variable of interest.
The age (in years) of each viewer is the variable of interest.
c. Describe the sample.
The sample must be a subset of the population. In this case, it is the 200 Fox viewers selected by
the executive.
d. Describe the inference.
The inference of interest involves the generalization of the information contained in the sample
of 200 viewers to the population of all Fox viewers. In particular, the executive wants to estimate
the average age of the viewers in order to determine whether it is less than 51 years.
Example 2
“Cola Wars” is the popular term for intense competition between Coca-Cola and Pepsi displayed
in their marketing campaigns, which have featured movie and television stars, rock videos,
athletic endorsements, and claims of consumer preference based on taste tests. Suppose, as part
of a Pepsi marketing campaign, 1,000 cola consumers are given a blind taste test (i.e., a taste test
in which the two brand names are disguised). Each consumer is asked to state a preference for
Brand A or brand B.
a. Describe the population.
Since we are interested in the responses of cola consumers in taste test, a cola consumer is the
experimental unit. Thus, the population of interest is the collection or set of all cola consumers.
b. Describe the variable of interest.
The characteristic that Pepsi wants to measure is the consumer’s cola preference, as revealed
under the conditions of blind taste test, so cola preference is the variable of interest.
c. Describe the sample.
The sample is 1,000 cola consumers selected from the population of all cola consumers.
d. Describe the inference.
The inference of interest is the generalization of the cola preferences of the 1,000 sampled
consumers to the population of all cola consumers. In particular, the preferences of the
consumers in the sample can be used to estimate the percentages of cola consumers who prefer
each brand.