The authors are in effect posing the question, if the population of potential programme
participants were to be randomly assigned to strategy and non-strategy groups, would the
two groups differ with respect to pre-intervention competency measures (the six response
variables in Table 8.5), even though assignment to groups was not made until after the
intervention. The inferences in this section of the analysis relate to two separate
populations—a population of cognitive strategy users and a population of non-strategy
users. The inferential process addresses the issue of whether the two samples of
competency scores (cognitive strategy user sample and non-strategy user sample)
represent competency scores from one population of students or alternatively scores from
two separate populations of students, a cognitive strategy user population and a non-
strategy user population.
The null hypotheses tested are of the form, the average competency score of the
population of students who might be exposed to the instructional programme and who are
cognitive strategy users (or would become so at follow up) is equal to the average
competency score of the population of students who might be exposed to the programme
but are non-strategy users (or do not become strategy users at follow up). Put simply this
could be stated as, There are no differences between the pre-intervention competency
scores of cognitive strategy and non-cognitive strategy users.
For the variable Written in Table 8.5 the null hypothesis is H 0 : μ 1 =μ 2 which in words
is, the mean written pre-test score is equal for the population of cognitive strategy and
non-strategy users. The precise nature of the alternative hypothesis is not stated by the
authors. However, by knowing the test statistic value which is shown in Table 8.3 (under
the heading Test) and the reported p-value of 0.0048, it is possible to determine that the
authors were using a non-directional alternative hypothesis and making a two-tailed t-
test. The degrees of freedom, which are a whole number, suggest that an equal variance
estimate of t was used.
In testing the statistical hypothesis of equality of means the authors were comparing,
for example, the average oral latency score of 5.87 for the cognitive strategy group with
the average score of 8.53 for the non-strategy group. The obtained t-statistic of 3.64 for
this comparison was larger than the non-directional, (two-tailed) critical t-value of 3.572
at the 0.001 level. This critical t-value of 3.57 is obtained using the SAS function TINV.
The table of percentage points of the t-distribution shown in Appendix A4 does not have
a value for 38 degrees of freedom.
The appropriate SAS code to evaluate the critical t-value is:
data a;
t=round(TINV(0.9995, 38), .001);
put t=;
run;As the obtained t-value was greater than the critical t-value at the 1 per cent level, then
the authors were able to reject the null hypothesis and conclude that there were some
initial ability differences between groups. They go on to say that the impact of initial
ability differences on the results of the study cannot be discarded.
When reviewing reported results where the independent t-test procedure has been
used, or if considering use of this procedure on your own data, the reader should reflect
on the underlying assumptions on which the independent t-test is based. Taking the
Inferences involving continuous data 297