t-test EDRS Educational Research & Statistics

n Most common and popular statistical test when comparing TWO sample means. n T-tests, though used often with means, can be used on correlation coefficients, proportions, and regression coefficients.

n Strategy of t-test is to compare actual mean difference observed between two groups with difference expected by chance. n Even if the null is true, you should NOT expect two sample means to be identical. n Some difference WILL be present.

Independent Samples t-test n Most common t-test used n Also referred to as unpaired, unmatched, and uncorrelated n 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 n No logical relationship exists between persons in one group and persons in the other group. n All observations---all data are independent of each other.

n Can come about in numerous ways: Ê Persons randomly assigned to one of two groups Ë Persons assigned to a group on the basis of some characteristic--gender; persons who graduate, those who don’t Ì One group of volunteers,other group of nonvolunteers Í 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. ¹ Compare the IQ scores of males versus the IQ scores of females.

Dependent Samples t-test n Also referred to as paired samples, matched-pair samples, or correlated samples. n Used to compare means of two groups when the individual scores in one group are paired with particular scores in the other group.

n Three ways of having correlated samples: Ê Single group of persons measured twice; pre- and post-test scores; persons exposed to exp 1 and then to exp 2 Ë Matching of persons in first and second gps; use IQ or achievement as matching variable Ì Splitting of biological twins into separate groups

Examples Ê Compare the California Achievement Test and ITBS reading scores of the same students Ë Compare the SAT scores of students prior to and after instructional preparation

Reporting t-test results è Type of t-test conducted è t value è degrees of freedom è p value è mean, standard deviation, and n for each group

Reporting t-test Example Students (n = 27) had a mean of (SD = 1.77) on the California Achievement Reading Vocabulary Test and a mean of (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 KM- R 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 (SD = 9.87) and (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.