t -test

tt-test-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.

IndependentIndependent Samples Samples tt-test-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.

IndependentIndependent Samples Samples tt-test-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

ExamplesExamples

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

ExamplesExamples

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.

DependentDependent Samples Samples tt-test-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

ExamplesExamples

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 Reporting tt-test results-test results

Type of t-test conducted t value degrees of freedom p value mean, standard deviation, and n for

each group

Reporting Reporting tt-test Example-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 Another tt-test Reporting Example-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.

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.