Chapter 11: The t Test for Two Related Samples

Related t Formulas

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

Before and after treatment differences Person Before Treatment X 1 After Treatment X 2 D A B C D E5556+1

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

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

Scores on Depression Inventory Before and After Treatment Person Before Treatment X 1 After Treatment X 2 D A B C D E5556+1

Depression Study Person Before Treatment X 1 After Treatment X 2 DD2D2 A B C D E

Depression study cont. DD(D - D) (-2) (-2) (-4) (+1) (+7) 2

Depression Study t computation

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)

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

Critical regions for asthma study Reject H o Reject H o

Asthma Study Data Table Patient Week Before Training Week After TrainingDD2D2 A B41-39 C5500 D E51-416

One tailed critical region (df =4) Reject H o df = 4

Reading Program Data Table Control Reading ProgramDD2D2 Matched pair A Matched pair B Matched pair C Matched pair D

Treatment 1 vs. 2 Data Table SubjectTreatment 1Treatment 2D A B C D E5054+4

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

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

Before and After data table 2 Subject Before Treatment After Treatment

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