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t-test
EDRS
Educational Research
& Statistics
Most common and popular statistical
test when comparing TWO sample
means.
 T-tests, though used often with
means, can be used on correlation
coefficients, proportions, and
regression coefficients.

Strategy of t-test is to compare
actual mean difference observed
between two groups with difference
expected by chance.
 Even if the null is true, you should
NOT expect two sample means to be
identical.
 Some difference WILL be present.

Independent Samples t-test
Most common t-test used
 Also referred to as unpaired,
unmatched, and uncorrelated
 Used to compare means of two
different groups of scores when NO
score in one group is paired with a
score in the other group.

Independent Samples t-test
No logical relationship exists
between persons in one group and
persons in the other group.
 All observations---all data are
independent of each other.

Can come about in numerous ways:
Persons randomly assigned to one of two
groups
Persons assigned to a group on the basis
of some characteristic--gender; persons
who graduate, those who don’t
One group of volunteers,other group of
nonvolunteers
Two intact gps, assign one randomly to
receive treatment, other is control

Examples
Compare the math scores of
students taught via traditional
instruction versus students taught
via computer-assisted instruction.
Compare the ITBS reading scores of
students with learning disabilities in
listening comprehension versus
students with LD in oral expression
Examples
Compare the NTE scores of
secondary education teachers to the
NTE scores of elementary teachers.
Compare the IQ scores of males
versus the IQ scores of females.
Dependent Samples t-test
Also referred to as paired samples,
matched-pair samples, or correlated
samples.
 Used to compare means of two
groups when the individual scores in
one group are paired with particular
scores in the other group.

Three ways of having correlated samples:
Single group of persons measured twice;
pre- and post-test scores; persons
exposed to exp 1 and then to exp 2
Matching of persons in first and second
gps; use IQ or achievement as matching
variable
Splitting of biological twins into separate
groups

Examples
Compare the California Achievement
Test and ITBS reading scores of the
same students
Compare the SAT scores of students
prior to and after instructional
preparation
Reporting t-test results
 Type of t-test conducted
 t value
 degrees of freedom
 p value
 mean, standard deviation, and n for
each group
Reporting t-test Example
Students (n = 27) had a mean of 35.52
(SD = 1.77) on the California Achievement
Reading Vocabulary Test and a mean of
44.77 (SD = 2.01) on the Iowa Tests of
Basic Skills Reading Vocabulary subtest.
The dependent samples t-test yielded a t
(26) of 8.67 which was statistically
significant at the .05 level.
Another t-test Reporting Example
The remaining correlated samples t-test
comparison between the WIAT and the KMR Math Reasoning subtests approached,
but did not reach a conventional level of
statistical significance, t (60) = 2.74, p < .07.
Students (n = 61) exhibited means of 66.75
(SD = 9.87) and 69.93 (SD = 10.12)
respectively on the WIAT and KM-R Math
Reasoning subtests.
Conclusions reached by a t-test will
ALWAYS be the same as the
conclusion reached by an F test in an
analysis of variance procedure.