PSYC 612, SPRING 2010Introduction to MediationLecture Week: 3/2/2010Contents1 Preliminary Questions 12 Part I: Preview of Mediation and Moderation (15 minutes; 2 minute break) 22.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.3 Mediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.4 Moderation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Part II: Demonstrate a Mediational Analysis (40 minutes) 23.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.3 The Data and Mediation Mo del . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.4 Mediation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4.1 The Baron and Kenny method . . . . . . . . . . . . . . . . . . . . . . . . . . 43.4.2 The Sobel Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.5 Mediational Model Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Part II I: Beyond the readings (15 minutes; 2 minute break) 54.1 Purpose: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2 Objectives: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.3 Temporal contiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.4 Standard Errors, Errors of Inference and the Bootstrap . . . . . . . . . . . . . . . . 51 Preliminary Questions• How are the modules going?• Did you read the Iacobucci text?12 Part I: Preview of Mediation and Moderation (15 min-utes; 2 minute break)2.1 Purpose:Provide you with the necessary background information about the topics mediation and moderation2.2 Objectives:1. Introduce mediation2. Introduce moderation and contrast it with mediation2.3 MediationMediation is best explained graphically. I intend to do so on the board so please use the back sideof your paper to draw the figures with me.2.4 ModerationSimilar to mediation, moderation is best explained graphically. I will draw figures that demonstratemoderation.3 Part II: Demonstrate a Mediational Analysis (40 min-utes)3.1 Purpose:Solidify conceptual knowledge with an example3.2 Objectives:1. Describe data and model2. Run mediational analysis3. Discuss results in detail23.3 The Data and Mediation ModelA recent Department of Education report on the “Equity in Athletics” provided us with a conve-nient dataset to demonstrate mediational models. I am only using a small portion of the data forillustrative purposes only. There are probably better datasets than this one but it is current andreasonably interesting so that we can all have some fun. You may find the data on the MRESwebsite; please download it if you care to run the same models I run below.Ns FinAid Recruiting HeadCoaches Revenue ExpensesNsFinAid 0.16Recruiting 0.37 0.61HeadCoaches 0.36 0.72 0.47Revenue 0.55 0.63 0.82 0.59Expenses 0.54 0.66 0.82 0.61 0.98Profit 0.38 0.27 0.51 0.28 0.68 0.55Table 1: Correlation of relevant variablesThe data need litle explanation other than to say that these variables relate to athletic de-partment revenue and expenditures. I am interested in relating student body size (Nstudents) torecruiting expenses and profit. My model would look like the basic mediational model I drew onthe board last week.Figure 1: The mediation model.33.4 Mediation AnalysisThere are many ways to analyze this simple mediational model. Perhaps the easiest is to usethe (now) classic Baron and Kenny method. Other methods exist and most are superior to theirapproach. Instead of dismissing their approach, I think it is always wise to first learn the standardapproach and then learn a contrasting approach so you may appreciate the improvements.3.4.1 The Baron and Kenny methodBaron and Kenny recommended a multi-step procedure via regression equations. These regressionmodels are very simple and can be done by hand if necessary (or even Excel <gasp>). Here goes. . .I will run a total of three models. The first model provides us with an estimate of a.Estimate Std. Error t value Pr(>|t|)(Intercept) 424902.3974 75309.7020 5.64 0.0000Ns 17.9777 4.0398 4.45 0.0000The second model provides us with an estimate of c.Estimate Std. Error t value Pr(>|t|)(Intercept) -1515763.7686 1055060.3974 -1.44 0.1534Ns 254.7679 56.5968 4.50 0.0000The third and final model provides us with estimates of b and c0.Estimate Std. Error t value Pr(>|t|)(Intercept) -4076681.6714 1073907.0492 -3.80 0.0002Ns 146.4152 55.3095 2.65 0.0092Recruiting 6.0271 1.1497 5.24 0.0000We have three models and each of the significance tests passed. Now we must conduct the Sobeltest to assess whether mediation seems reasonable.3.4.2 The Sobel TestDoes the mediation path (ab) exceed zero? In other words, if we multiplied the two paths a andb, would we get a significant indirect path between Number of Students and Profit via RecruitingExpenses? We may assess the signfiicance by using the Sobel test. There are reasons why this testmay not be an excellent arbiter of mediation but for simplicity and thoroughness, we will conductthe Sobel test now and discuss its limitations later.The Sobel test is defined by the equation below.z =a × bqb2s2a+ a2s2b(1)and for our purposes, we can …