1. Introduction to the t Test
Chapter 9
Introduction to the t Test

2. t Test for a Single Sample
Compare a sample mean to a population with a known mean but an unknown variance

3. t Test for a Single Sample
Estimating the population variance from the sample scores
Biased estimate of the population variance
Unbiased estimate of the population variance (S2)

4. t Test for a Single Sample
Degrees of freedom
Number of scores that are
“free to vary”
Formula for S2 using degrees of freedom

5. t Test for a Single Sample
The variance of the distribution of means
The standard deviation of the distribution of means

6. t Test for a Single Sample
The t distribution
Varies in shape according to the degrees of freedom

7. t Test for a Single Sample
Cutoff sample score for rejecting the null hypothesis
t table
Sample mean’s score on the comparison distribution
t score

8. t Test for Dependent Means
Unknown population mean and variance
Two scores for each person
Repeated measures design
Same procedure as t test for single sample, except
Use difference scores
Assume that the population mean is 0

9. t Test for Dependent Means
Difference scores
For each person, subtract one score from the other
Carry out hypothesis testing with the difference scores
Population of difference scores with a mean of 0
Population 2 has a mean of 0

10. Assumptions Normal population distribution
t tests are robust to moderate violations of this assumption

11. Effect Size for t Test for Dependent Means
small d = .2
medium d = .5
large d = .8

12. Approximate Power for t Test for Dependent Means (
Approximate Power for t Test for Dependent Means (.05 significance level)

13. Approximate Sample Size Needed for 80% Power (.05 significance level)

14. Controversies and Limitations
Repeated measures designs
Have high power
Standard deviation of difference scores usually low
Weak research design without a control group

15. t Tests in Research Articles
t(24) = 2.80, p < .05