The study is designed to investigate differences in self-concept in mathematics (MSC)
vs verbal self-concept (VSC) so there are two measures for the same individuals MSC
scores and VSC scores. Beginning in the left column of the decision chart under the
heading design and moving down this column we need to decide whether this is a one-
sample, two-sample or multiple-sample design. In its simplest form, this is a twosample
design, that is two sets of scores, MSC measures and VSC measures, for the same
individuals. We also need to consider under the design heading, the nature of the research
question;
Is the research question concerned with association, prediction or
comparison/ differences between groups (or samples of scores)?This part of the study was concerned with testing whether there were any differences
between MSC and VSC measures within subjects. It is an example of a two-sample
comparison, that is a comparison of two sets of scores for the same individuals. The
response variables are the scale scores for MSC and VSC. Having identified the
appropriate location in the design column ‘2 sample’, we then move along the row until
we intersect an appropriate column describing the type of data distribution for the
response variable, i.e., binomial rank or normal distribution.
In this example the response variables are MSC and VSC scale scores, the authors’
report means and standard deviations for these scores, and, in the absence of any other
information about score distributions, the reader is invited to make the assumption of
continuous response measures which are normally distributed.
The choice of statistical test has now been narrowed down to a statistical procedure
to test for differences with two groups of scores (maths and verbal self-concept). The
only remaining consideration is,
Are the measures (groups of scores) independent or related?Considering all the criteria presented in the decision chart, the final choice of
statistical test is between the independent t-test or the related (paired) t-test. As there are
two sets of measures for the same subjects, this is a within subjects design, and therefore
a related t-test is an appropriate statistical test to see whether there is any difference
between mean MSC and VSC scores. Before using this test a number of other
assumptions specific to the t-test need to be checked (see, Chapter 8). A point which may
cause some confusion is how any gender differences are related to observed within
subject differences in measures of maths and verbal self-concept. The authors simply
completed the within subjects analysis separately for boys and girls.
Skaalvik and Rankin (1994) reported that, ‘Paired t-tests showed that boys in sixth
grade had significantly higher mathematics than verbal self-concept [MSC vs VSC]
(t=3.60, p<0.001). In comparison, girls in the sixth grade had significantly higher verbal
than mathematics self-concept (t=−3.91, p<0.001)’, (p. 424).
Choosing a statistical test 129