t -test

1. t-test EDRS Educational Research & Statistics

2. 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.

3. 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.

4. 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.

5. 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.

6. 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

7. 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

8. 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.

9. 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.

10. 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

11. 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

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

13. 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.

14. 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 66.75 (SD = 9.87) and 69.93 (SD = 10.12) respectively on the WIAT and KM-R Math Reasoning subtests.

15. 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.