CHOOSING A STATISTICAL TEST – EXERCISE III
REVIEW EACH OF THE FOLLOWING SCENARIOS AND INDICATE WHICH STATISTICAL TEST WOULD
BE MOST APPROPRIATE TO ANALYZE THE SCENARIO. FOR EACH SCENARIO, IDENTIFY THE
VARIABLES (AND LEVELS, AS APPLICABLE).
CHOOSE FROM THE FOLLOWING STATISTICS:
PEARSON’S PRODUCT MOMENT CORRELATION (PEARSON’S r)
SPEARMAN’S RHO (rs or )
CHI-SQUARE TEST OF INDEPENDENCE
CHI-SQUARE GOODNESS-OF-FIT
SIMPLE LINEAR (BIVARIATE) REGRESSION (USED TWICE)
SIMULTANEOUS ENTRY MULTIPLE REGRESSION (USED TWICE)
BLOCK ENTRY (HIERARCHICAL) MULTIPLE REGRESSION (USED TWICE)
1.
An educational researcher is studying the influence and relative importance of a student’s
reading speed and their aptitude on their overall academic achievement for a group of
randomly selected fifth graders. Which statistical test would you recommend she use?
2.
A study consists of a class of 40 students, where the study time for a test ranged from 30
minutes to 6 hours. The grades for the test ranged from a low of 48 to a high of 98. What
statistic describes how the variable Study Time is related to the variable Grade?
3.
Stanley Milgram researched the question, When do people submit to demands for
compliance? In one experiment, participants were told to administer a shock to another
participant, who was in another room. The experimenter gave directions to half the
participants over a telephone; the other half received directions in person. The dependent
variable was the frequency of whether or not a participant complied with the directions.
4.
A researcher is interested in testing the predictive influence of a student’s college success
(as measured by their academic majors GPA) as a function of a set of high school
measures (GPA and ACT) and a set of college measures (Standardized Test and
Freshman GPA). The study is designed to examine the combined effect and the additive
effect of the college measures over and above the high school measures.
5.
A group of athletic trainers use a test of physical conditioning that is very comprehensive,
but has the disadvantage that its administration is long and complex. A researcher
develops a shorter, simpler test of physical conditioning and administers both tests to a
group of young adult athletes. The intention is to use the shorter test as a substitute for the
longer, more complex test, but that will depend on how good a predictor the scores on the
short test are of the scores on the long test. Which statistical test would be used to answer
whether the short test can be substituted?
6.
As part of a class project, two students administered a test to undergraduate seniors which
ranked their creativity. They also obtained each student’s rank in class. In what way
could the two students determine the degree of relationship between the two variables?
7.
Tuition at a local university has gone up each of the past five years. The university
reports that it is a function of the rate of inflation. How can you predict what the tuition
will be in twenty years when your child enrolls?
CHOOSING A STATISTIC III
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8.
Research has shown (indicated) that an individuals performance (success, as measured by
their final grade) in the ABC Program is a function of what they bring into the program
training (pre-ability measures) and what they learn while in the program training
(acquired ability measures). You have been asked to investigate whether individuals’
acquired abilities offer significant additional predictive power beyond that contributed by
the individuals’ pre-abilities. What statistical test would you use for this study?
9.
Suppose a theory predicts that the proportion of people who participate in a rather
difficult exercise will drop by one-half each time the exercise is repeated. When the data
are gathered, 100 people participated on the first day. On each of the next three
occasions, fewer and fewer people participated. What statistical test could be used to
arrive at a judgment about the theory?
10.
Tuition at a local university has gone up each of the past five years. The university
reports that it is a function of the rate of inflation, the cost of maintaining the university,
and increases in staff and faculty salaries. How can you predict what the tuition will be in
twenty years when your child enrolls?
CHOOSING A STATISTIC III
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