Chapter 14 Student S T Test for Correlated and Independent Groups

Chapter 14 – Student’s t Test for Correlated and Independent Groups Know and Be Able To Do

1. You should understand that the t test for correlated groups and the t test for single samples are very similar, except that the t test for correlated groups analyzes difference scores rather than raw scores.

2. You should understand that if the independent variable has no effect, μD = 0.

3. You should be able to use the t test for correlated groups to answer the question, “Is it reasonable to assume that the sample mean difference score is a random sample from a population of difference scores where μD = 0 and σD is unknown.

4. You should understand that under most circumstances, the t test for correlated groups is more powerful than the sign test.

5. You should be able to compare the repeated measures and the independent groups designs.

6. You should be able to state H0 and H1 in terms of μ1 and μ2 for the independent groups design.

7. You should be able to define the sampling distribution of the difference between

sample means ( X1- X 2 ) and state its characteristics.

8. You should understand why the z test for independent groups is almost never used.

9. You should understand that the t test for independent groups is derived from the z test for independent groups when σ2 is estimated and substituted into the z equation.

2 10. You should understand the derivation of sW .

11. You should understand why df = N  2 for the independent groups t test.

12. You should be able to use the tobt statistic to analyze data from the independent groups design.

13. You should know and be able to state the assumptions underlying the t test for independent groups.

14. You should know the effect on the t test for independent groups of violations of the assumptions of the test. 15. You should understand that ω2 estimates the size of effect by determining the proportion of variability of the dependent variability that is accounted for by the independent variable.

16. You should be able to compute ω2 for the two group, independent groups design.

17. Using the t equations, you should be able to determine the relationship between power and N, size of real effect, and sample variability.

18. You should be able to compare and discuss the correlated groups and independent groups t tests regarding their relative power.

19. You should understand the difference between the null hypothesis approach and the confidence interval approach in evaluating the effect of the independent variable when using a two group, independent groups design.

20. You should understand how the confidence interval approach allows both assessment of the null hypothesis as well as an estimate of the size of effect.

21. You should be able to determine the 95% and 99% confidence interval for μ1 – μ2 for data from the two group, independent groups design.

22. Having done the analysis in 21 above, you should know how to interpret the result both regarding the size of effect and whether you can reject H0.