1. Chapter 11: The t Test for Two Related Samples

2. Related t Formulas

3. Group Assignment of Subjects Matched by IQ ControlReading Program SubjectIQSubjectIQ A120E B105F C110G D95H

4. Before and after treatment differences Person Before Treatment X 1 After Treatment X 2 D A7264-8 B6860-8 C6050-10 D7166-5 E5556+1

5. Formulas for Related Samples t (Where n = number of difference scores)

6. Process of related samples testing µ D = ? D scores Population of difference scores Obtain sample Make inference about µ D

7. Scores on Depression Inventory Before and After Treatment Person Before Treatment X 1 After Treatment X 2 D A7264-8 B6860-8 C6050-10 D7166-5 E5556+1

8. Depression Study Person Before Treatment X 1 After Treatment X 2 DD2D2 A7264-864 B6860-864 C6050-10100 D7166-525 E5556+11 -30254

9. Depression study cont. DD(D - D) 2 -8-6(-2) 2 -8-6(-2) 2 -10-6(-4) 2 -5-6(+1) 2 +1-6(+7) 2

10. Depression Study t computation

11. What is the effect of relaxation training on severity of asthma symptoms: 1.Measure the number of doses of medication needed to counter asthma attacks (over 1 week) Relaxation Training 2.Measure the number of doses of medication needed to counter asthma attacks (over 1 week)

12. Asthma Study 1.H o : µ D = 0(No change in symptoms) H 1 : µ D ≠ 0(There is a change…)  = 0.05 2.t crit (4) = + 2.776 3. 4.Reject H o because t obt of -3.72 < t crit of -2.776 5.Conclusion: Relaxation training significantly reduced the number of asthma attacks, t(5) = -3.72, p < 0.05.

13. Critical regions for asthma study -2.7760+2.776 Reject H o Reject H o

14. Asthma Study Data Table Patient Week Before Training Week After TrainingDD2D2 A94-525 B41-39 C5500 D40-416 E51-416

15. One tailed critical region (df =4) -2.132 Reject H o df = 4

16. Reading Program Data Table Control Reading ProgramDD2D2 Matched pair A615+981 Matched pair B515+10100 Matched pair C1117+636 Matched pair D613+749

17. Treatment 1 vs. 2 Data Table SubjectTreatment 1Treatment 2D A1016+6 B2024+4 C3035+5 D4046+6 E5054+4

18. Assumptions for Related- Samples t test 1.Observations within each treatment must be independent 2.The population distribution of difference scores must be normal 3.Note: #2 is not a concern as long as sample size is 30 or less

20. Before and after data table 1 PersonX 1 (Before)X 2 (After) A15 B1113 C1018 D1112 E1416 F10 G1119

21. Before and After data table 2 Subject Before Treatment After Treatment 11913 23537 32014 43125

22. Reading Program vs. Control Data Table ControlReading Program SubjectIQSubjectIQ A120E B105F C110G D95H