PSCY 612, SPRING 2008Lecture 8: Psychometrics (cont.)Lecture Date: 3/19/2008Contents1 Preliminary iClicker Questions 22 The Helix Model of Learning 23 Part I: Psychometric Topics (40 minutes; 5 minute break) 23.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3 Latent versus manifest variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3.1 Models Assuming Latent Structures . . . . . . . . . . . . . . . . . . . . . . . 53.4 Unidimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.4.1 The consequences o f non-unidimensionality . . . . . . . . . . . . . . . . . . . 63.4.2 Testing for unidimensionality . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Part II: Advanced Topics (50 minutes; 5 minute break) 84.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.3 Person by item interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.4 Reliability estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.5 Making decisions based upon psychometric results . . . . . . . . . . . . . . . . . . . 114.5.1 What level of reliability do we want/need? . . . . . . . . . . . . . . . . . . . 114.5.2 How do we select items based upon CTT results? . . . . . . . . . . . . . . . 124.5.3 What do we do when items are negatively correlated with the total? . . . . . 125 Part III: Matrix Algebra (cont.; 30 minutes) 125.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125.3 Linear Regression in Scalar Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 135.4 Linear Regression in Matrix Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 1411 Preliminary iClicker Questions•Have you read all t he assigned reading for today (Carmides and Zeller)?•Did you understand the material?•• Did the TA’s provide enough specific examples last lecture?•Did you complete the MRC module?•If you did, how well did you think you performed?•If you did not, what keeps you from completing the module?The lecture today will be divided into three sections as usual, however, I intend to have adeparture from the normal content level. Typically I review the readings in Part I a nd offer moreadvanced level material for Parts II and III. D ue to my travel schedule, your TA’s covered thereadings in the previous lecture and I intend to extend my typical Parts II and III today to span allthree parts. Therefore, today there will be no review of the readings but rather an intensive loo kat the more advance material suitable for a graduate level course.2 The Helix Model of LearningWhen I was in graduate school, my graduate advisor (Lee Sechrest) kept emphasizing that learningrequires hard work. The further you are down the helix of learning, the more work it takes t oachieve mastery. Superficially I understood the concept of the helix but I did not grasp the idea ofthe effort r equired until I realized progress. Lee would often tell me that only through hard workand rep eated exposure would I really learn and that learning never stops. The helix keeps goingup.Let me introduce you to the helix (see Figure 2).The model assumes a hierarchical structure to knowledge. We all can be assigned a level ona helix for each knowledge structure (e.g., a foreign language, mathematics, literature, computerprogramming, and music). The figure to the right loosely represents structural milestones and arenot meant to be definitive but rather illustrative.I bring up the helix model from time to time to reinforce the simple point that learning requireseffort - repeated effort and struggle. My observations during lab, lecture, and through individualmeetings gives me the sense that many of you are putting in the effort to struggle through andmaster this material. I say many but by no means do I mean most. The helix model is merelya heuristic model where you can assess your own effort and advancement. My job is to help youadvance up the helix but we can only achieve success if we both do our parts. I am working hardto improve what I offer you. I suggest you work equally hard to improve what you have to offeryourself.3 Part I: Psychometric Topics (40 minutes; 5 minute break)2Figure 1: The Helix Model of Statistics33.1 Purpose:To discuss topics relevant to Classical Test Theory at an advanced level3.2 Objectives:1. Distinguish between la t ent and manifest variables2. Introduce the concept of unidimensionality3.3 Latent versus manifest variablesThe very nature of CTT mandates that there exists a true score underlying all measurement. Thattrue score may be called many things but psychologists refer to that true score as a latent entity.We already discussed this at length but I want to take a moment to review a …