Listed below are several examples of using the decision-tree flowcharts to determine an appropriate statistical procedure for a given study. We will walk you through each step of the process.
DESCRIPTION: Panic disorder
patients, either with or without agoraphobia, are compared on
(1) whether they qualify for a diagnosis of depression, (2)
their age at the time of the first panic attack, and (3) the
number of panic attacks that they have had in the last 30 days.
SELECTION: We start by listing the study characteristics.
We have two independent groups in a differential study defined
by their diagnosis (panic with agoraphobia, panic without
agoraphobia). This is a differential research study with three
dependent variables. The diagnosis of depression is a nominal
measure, and the age at first panic attack and the number of
panic attacks are both ratio measures.
We always want to include descriptive statistics. We would
compute frequency counts for the diagnosis of depression and
measures of central tendency (mean, median, and mode) and
variability (variance and standard deviation) for the other two
variables.
There is no manipulation; therefore, no manipulation check is
necessary. In differential research studies, one must be very
cautious about the possibility of confounding. Therefore, we
will want to compute correlations between the dependent
variables and possible confounding variables and will want to
look for mean differences on potential confounding variables
using the same inferential statistics used to test the
hypotheses.
For the first dependent variable (presence of depression,
nominal variable), we are comparing two groups. Therefore, the
appropriate inferential statistic is a chi-square test for
independence. For the next two variables, we have one
independent variable, two independent groups, and score data.
There are two possibilities (independent groups t-test or
one-way ANOVA). Both are correct and both will lead to the same
decision.
DESCRIPTION: High school
class rankings are compared for those who are engaged in
interscholastic athletics and those who are not.
SELECTION: We are comparing two groups in a differential
research study. The dependent measure is a ranking (ordinal
data), and we want to see if the groups are different on this
ranking. We should compute frequencies or average rankings for
descriptive statistics and a Mann-Whitney U-test for the
inferential statistic.
DESCRIPTION: We are
comparing the rate of salary increase over a two-year period in
two industries (auto manufacturing and computer distribution and
sales). We randomly select 50 people from each of those two
industries. Half of the 50 from each industry is randomly
selected for a two-day workshop on time and priority management.
Then the 100 participants are followed in their career for two
years. The hypothesis is that the workshop will improve the
functioning of participants and will thus contribute to a more
rapid rise in their incomes. Furthermore, it is expected that
this workshop will have a bigger impact on people in a
rapidly-changing field like computers than a more traditional
field like heavy manufacturing.
SELECTION: We have a mixed factorial design, which is
mixed in two ways. One factor is manipulated, and one factor is
nonmanipulated. One factor is a between-subjects factor, and one
factor is a within-subjects factor. The
manipulated/nonmanipulated distinction will not affect the
choice of statistics, but will affect the interpretation. The
within-subjects/between-subjects distinction will affect the
statistical procedure. See Chapter 12 for details about these
issues.
Our dependent measure (rate of salary increase) will produce
score data (a ratio measure). Therefore, we would compute
measures of central tendency (mean, median, and mode) and
variability (variance and standard deviation) as descriptive
statistics. For inferential statistics, we are directed to a
factorial ANOVA, although we are warned that there are many
possible variations on factorial ANOVAs.
This is a complex ANOVA, which was not covered in the text and
cannot be computed using the version of SPSS for Windows that
can be bundled with this text. However, many statistical
analysis packages can handle this complex design. If you had to
compute such a complex ANOVA, you may want to contact your
computer center to learn about the statistical analysis packages
available for your use.
DESCRIPTION: In a cognitive
study, 60 randomly selected college students are tested on a
recognition task. They are all shown 10 objects on a computer
screen that are easy to identify and distinguish. They are then
flashed pictures of those objects or new objects (i.e., not part
of the original set of 10) to either the right visual field or
the left visual field. Their task is to respond as quickly as
possible to indicate whether the picture was new or part of the
original set. The scores for each participant include both an
error score and a reaction time measure. Those scores were
computed separately for each visual field.
SELECTION: We have a single group of participants who are
tested under two conditions (right vs. left visual field
presentation), and we have two dependent variables (error rate
and reaction time), which are computed for each condition. We
are hypothesizing a shorter reaction time, but no difference in
error rate, for pictures that are projected to the left visual
field (processed initially in the right cerebral hemisphere).
Our dependent measures both produce score data. Therefore, we
should compute measures of central tendency (mean, median, and
mode) and variability (variance and standard deviation) as our
descriptive statistics. Since we are using a within-subjects
designs, our two groups (conditions) are correlated. Therefore,
we have two possibilities (correlated t-test or repeated
measures ANOVA). Both are correct, and both will lead to the
same statistical decision.