1 / 10

Factorial Design

Factorial Design. One Between-Subject Variable. One Within-Subject Variable. SS Total. SS between subjects. SS within subjects. Treatments by Groups. Groups. Subjects within groups. Treatments. Treatments by Subjects within groups. Differences Between Subjects.

tuvya
Download Presentation

Factorial Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Factorial Design One Between-Subject Variable One Within-Subject Variable SSTotal SSbetween subjects SSwithin subjects Treatments by Groups Groups Subjects within groups Treatments Treatments by Subjects within groups Differences Between Subjects Differences Within Subjects Groups – differences between groups of subjects SS w/in Groups – differences between subjects w/in a group Treatment – differences between subject’s scores across treatments Treat x Groups – interaction between Treatments and Groups Treats x Ss w/in Groups – interaction between Subjects and Treatments hold Groups factor constant

  2. Example Speed (Repeated Measure) Group 1 Group 2 =GT =GM

  3. Calculate MS Divide SS by appropriate df SSbs by #Ss - 1 SSgrp by #Grps - 1 SSss w/in grps by (#Singrp-1) x (# of grps) SSws by #Ss (# Treatments – 1) SStreat by # Treatments - 1 SSTxG by (#grp – 1) (#Treats -1) SSTxS w/in grpsby (#Treats -1) x (n-1) x (# of grps)

  4. Prepare Summary Table 7 What are the appropriate error terms? (the denominators for the Fratios) Interpolation? 8

  5. Repeated Measures Assumptions 1) normality 2) homogeneity of variance 3) compound symmetry - constant variances on diagonal - constant covariances off diagonal A variance / covariance matrix for each group and overall 4) T X Ss interactions are constant across groups - test with Fmax

  6. Example No STRAT Var/Covar Matrix Speed The assumption of compound symmetry is usually replaced by the assumption of sphericity = a constant across all pairs of conditions = .574 = .853

  7. Simple Effects Factorial Design One B-S variable One W-S variable The W-S variable - Separate One-Way ANOVAs (repeated measures) ∙ Error terms pooled = MS T X Ss w/in groups ∙ Or, use the MST X Ss for each separate analysis No STRAT STRAT SSTotal = 67.44 SSTotal = 67.44 SSTotal = 168.04 SSbs = 7.14 SSbs = 5.29 SSTreat = 54.69 SSTreat = 159.19 SSerror = 3.56 SSerror = 5.56

  8. No STRAT STRAT + = 67.44 168.04 235.48 SSTotal SSTotal (overall) + = 12.45 7.19 5.29 SSbs SSbs (overall) + 159.19 = 213.88 SSTreat 54.69 SSTreat + SST X G Why? (overall) = SSerror 5.56 + 3.56 9.12 SST X S w/in group (overall)

  9. Between-Subjects Simple Effects We could do a separate analysis of each level - unnecessary loss of df SSgrp at 5 = = 8.0 SSgrp at 15 = = 4.5 SSgrp at 25 = = 2.0 = SSgrp at 35 = 8.0 MS all 1 df SSerror term = SSw/cells = SSSs w/in grp + SS T X Ss w/in grps Why? MSerror =

More Related