Melinda K. Higgins, Ph.D. 11 April 2008

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Presentation transcript:

Melinda K. Higgins, Ph.D. 11 April 2008 “Research Design, Sources of Variance & Initial Discussion of Intent to Treat” Melinda K. Higgins, Ph.D. 11 April 2008

Sources of Variance – 1 All data Variations Can of “averages” Residuals Relationships Lack of Fit Pure Error

Collection of Data

Breakdown Sources of Variance (part 1) Actual value P R * Avg response L C Model Prediction F Avg of all data J Y Y = data = avg all data = model prediction J = avg response at factor level C = corrected for mean = Y- R = residual = Y- F = factor = - L = “lack of fit” = J- P = “pure error” = Y-J

Solving Least-Squares Equations (1) n = number of data points (samples = 6) p = number of parameters in model (int and slope = 2) f = number of factor levels (3 “levels” of X)

Solving Least-Squares Equations (2)

Sources of Variance (“SS/df tree”) – 2 SStotal df=n What you usually see as the “SSt” SScorr df=n-1 SSmean df=1 SSresid df=n-p SSfactor/model df=p-1 SSlof df=f-p SSpe df=n-f

Finish SS/df tree for dataset N=6; p=2; f=3 SStotal = Y’Y = 119.00 df = n = 6 SSmean = = 104.17 df = 1 SScorr = C’C = 14.833 df = n-1 = 5 SSfact = F’F = 6.2500 df = p-1 = 1 SSresid = R’R = 8.5833 df = n-p = 4 SSlof = L’L = 0.0833 df = f-p = 1 SSpe = P’P = 8.5000 df = n-f = 3 SStotal=119 df=6 SSmean=104.17 df=1 SScorr=14.833 df=5 SSfact=6.25 df=1 SSresid=8.5833 df=4 SSlof=0.0833 df=1 SSpe=8.5 df=3

SPSS Results – Part 1 (variance components) Variance Components Estimation /Analyze/General Linear Model/Variance Components SSmean SSpe SStotal SScorr But where are SSfact, SSresid, and SSlof?

SPSS Results – Part 2 (Regression) SSfact SSresid SScorr … and SSlof? SSlof = SSresid-SSpe = 8.583-8.5 = 0.08333

VIII. Statistical Resources and Contact Info SON S:\Shared\Statistics_MKHiggins Shared resource for all of SON – faculty and students Will continually update with tip sheets (for SPSS, SAS, and other software), lectures (PPTs and handouts), datasets, other resources and references Statistics At Nursing Website: [moving to main website] S:\Shared\Statistics_MKHiggins\website2\index.htm And Blackboard Site (in development) for “Organization: Statistics at School of Nursing” Contact Dr. Melinda Higgins Melinda.higgins@emory.edu Office: 404-727-5180 / Mobile: 404-434-1785