Paired t-test: t D I.Introduction To The Repeated Measures Design:What is a repeated measure? II.Finding an Experimental Effect In a Single Group: Before vs. After III.Creating a new distribution t D. IV.Reduces Sampling Error: It’s a more powerful test V.Limited Applicability

Anthony Greene2 Before-After Pre-MeasurePost-Measure Manipulation

Anthony Greene3 It doesn’t have to be “Before-After”

Anthony Greene4 Matched Subject Design For a given study the two groups of subjects could be closely matched 1. Age 2. IQ 3. Blood Pressure 4. Income 5. Education Level

Anthony Greene5 The Basic Idea Standard t-test nx1x1 x2x

Anthony Greene6 The Basic Idea Standard t-test nx1x1 x2x average1317

Anthony Greene7 The Basic Idea Standard t-test Is 13 different than 17? Or different than 0? nx1x1 x2x average1317

Anthony Greene8 The Basic Idea Repeated Measures t-test nx1x1 x2x2 A26 B1317 C2428

Anthony Greene9 The Basic Idea Repeated Measures t-test Create A New Variable, D nx1x1 x2x2 D A264 B13174 C24284

Anthony Greene10 The Basic Idea Repeated Measures t-test Is 4 different than 0? subjectx1x1 x2x2 D A264 B13174 C24284 average4

Anthony Greene11 The Basic Idea The fundamental advantage? The error term in the within subjects design is smaller In the simplified example, the standard error terms would be higher in the two sample version versus the difference test (in this case the s M D is zero) The advantage is that individual differences (2, 13, 24, and 5, 16, 27) are not part of the error in t D

Anthony Greene12 The Basic Idea Are there limitations? The repeated measure design (before – after) must be used cautiously used in many experimental designs 1.Memory Subjects learn 2.Medicine and Clinical Psych Substantial time passes 3.Social Psych Minor deceptions Loss of half the degrees freedom

Anthony Greene13 Distribution of the Paired t-Statistic Suppose x is a variable on each of two populations whose members can be paired. Further suppose that the paired-difference variable D is normally distributed. Then, for paired samples of size n, the variable has the t-distribution with df = n – 1. The normal null hypothesis is that μ D = 0

Anthony Greene14 The paired t-test for two population means (Slide 1 of 3) Step 1The null hypothesis is H 0 :  D = 0; the alternative hypothesis is one of the following: H a :  D  0 H a :  D 0 (Two Tailed)(Left Tailed)(Right Tailed) Step 2Decide on the significance level,  Step 3The critical values are ±t  /2 -t  +t  (Two Tailed)(Left Tailed)(Right Tailed) with df = n - 1.

Anthony Greene15 The paired t-test for two population means (Slide 2 of 3)

Anthony Greene16 The paired t-test for two population means (Slide 3 of 3) Step 4Compute the value of the test statistic Step 5If the value of the test statistic falls in the rejection region, reject H 0, otherwise do not reject H 0.

Anthony Greene17 The number of doses of medication needed for asthma attacks before and after relaxation training.

Anthony Greene18 A Direct Comparison x1x1 x2x2

Anthony Greene19 A Direct Comparison x1x1 x2x2