CHOOSING A STATISTICAL TEST – EXERCISE II – KEY
REVIEW EACH OF THE FOLLOWING SCENARIOS AND INDICATE WHICH STATISTICAL ANALYSIS
WOULD BE MOST APPROPRIATE TO TEST THAT SCENARIO. FOR EACH SCENARIO, IDENTIFY THE
INDEPENDENT VARIABLE(S) (AND LEVELS, AS APPLICABLE), AND THE DEPENDENT VARIABLE.
CHOOSE FROM THE FOLLOWING STATISTICS (EACH ONLY USED ONCE):
DEPENDENT-SAMPLES T TEST
INDEPENDENT-SAMPLES T TEST
ONE-WAY ANOVA
ONE-FACTOR (ONE-WAY) REPEATED MEASURES ANOVA
ONE-FACTOR (ONE-WAY) ANALYSIS OF COVARIANCE
FACTORIAL (TWO-WAY) ANOVA
SIMPLE LINEAR (BIVARIATE) REGRESSION
SIMULTANEOUS ENTRY MULTIPLE REGRESSION
BLOCK ENTRY (HIERARCHICAL) MULTIPLE REGRESSION
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 your recommend she use?
Multiple linear regression analysis (simultaneous entry) would be used,
with one set of independent (predictor) variables (reading speed and
aptitude) and one dependent (criterion) variable (academic achievement).
2.
As part of a two-week treatment for phobias, a therapist measured the general anxiety
level of each client four times: before, after one week of treatment, at the end of the
treatment, and four months later. What statistical test would be used to determine the
effectiveness of the treatment?
A one-factor repeated-measures ANOVA will help evaluate the treatment.
Here the dependent variable is anxiety level and the independent variable
treatment times, with four occasions (before, after one week of treatment,
at the end of the treatment, and four months later).
3.
Children (mean age = 6 years) who ate breakfast at school participated in an experiment
to determine the effect of sugar on activity. On some days a particular child received
sugar with breakfast and on other days the child did not. This was true for all the children
in the study. Later in the day each child was observed and activity recorded.
A paired-samples (dependent) t test allows you to determine if activity (the
dependent variable) depends on whether or not a child eats sugar at
breakfast (the independent variable). The samples are paired – each child
serves in both conditions.
4.
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?
Simple linear (bivariate) regression analysis (used for prediction) would be
used, with one Independent (Predictor) Variable (Short Test) and one
Dependent (Criterion) Variable (Long Test).
5.
An experimenter is interested in the effect of expectations and drugs on alertness. Each
participant is given an amphetamine (stimulant) or a placebo (an inert substance). In
addition, half of each group is told that the drug taken was a stimulant and half that the
drug was a depressant. An alertness score for each participant is obtained from a
composite of measures that included a questionnaire and observation.
A 2  2 factorial ANOVA. The two independent variables are drug type
(two levels; amphetamine and placebo) and information (two levels; told it
was a stimulant and told it was a depressant), with the alertness score
being the dependent variable.
6.
The districts high school cafeteria manage is dismayed by the amount of food that is left
on plates. One way to reduce waste is to prepare the food using a tastier recipe. Suppose
that three unique recipes for the entrée are served (all other items being equal) at three
different school cafeterias (from peer schools). As the plates are cleaned in the kitchen,
the amount of entrée left on the plates is recorded. How might the manager gauge the
preference of the recipes?
One-way Analysis of Variance – with the dependent variable being the
amount of entrée left, and the independent variable being type of entrée
(with three levels).
7.
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?
Multiple linear regression analysis (hierarchical, block entry) would be
used, with the first (control) set of Independent (Predictor) Variables being
the pre-ability measures and the second set of Independent (Predictor)
Variables being the acquired ability measures. The one Dependent
(Criterion) Variable would be the performance (success).
CHOOSING A STATISTIC II – KEY
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8.
A consumer testing group compared two leading laundry detergents to determine which
got laundry whiter. White towels that had been subjected to a variety of filthy treatments
were randomly assigned to one of the two detergents. After washing, each set of towels
was tested with a photometer for the amount of light reflected (testing their cleanliness).
What is the statistical test that should be used to compare the two detergents?
An independent-samples t test, with cleanliness as the dependent variable
and laundry detergent as the independent variable (two levels; the two
leading brands).
9.
Based on research from the National High School and Beyond Study, males have been
shown to have significantly higher mathematics achievement scores than females. A
researcher wishes to explore this hypothesis; however, she contends that this difference
may be due to differences in the number of math courses taken by the male and female
students. What statistical test would she use to test mathematics achievement score
differences between males and females controlling for the effect of the number of
mathematics courses that the male and female students had previously taken.
A one-way (one-factor) analysis of covariance, with mathematics
achievement scores as the dependent variable, gender (two level; males
and females) as the independent variable, and number of mathematics
courses previously taken as the covariate.
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