Two-ctor Mixed Design One Between-Subects ctor nd One Within-Subects ctor /7/ -ctor Mixed Design
Exercise 9. Ech prticipnt in study ttempts to solve ngrms (ttunesd?), which vry in length: 5,, 7, or 8 letters (5 of ech length). Prticipnts re rndomly ssigned to two conditions. In one, they re given the correct nswer fter ech solution ttempt. In the no feedbck condition, the prticipnt is told nothing fter ech solution ttempt. The dependent vrible is the number of ngrms solved. Dt from the study re given here: Length of Angrm eedbck 5 Letters Letters 7 Letters 8 Letters Absent 4 9 4 7 5 7 9 Present 7 8 8 7 7 8 9 9 () Does ngrm length ffect number of solutions? (α.5) (b) Does mount of feedbck ffect number of solutions? (α.5) (c) Does ngrm length nd mount of feedbck interct to ffect number of solutions (α.5). /7/ -ctor Mixed Design
Men umber of Correct Angrms s unction of umber of Letters nd eedbck 5 Correctly solved 5 5 Letters Letters 7 Letters 8 Letters o eedbck. 5. 7.. eedbck 7. 7.7 8. 8.7 Length of Angrm /7/ -ctor Mixed Design
Subect x Tretment Interctions Subect x Tretment Interction t o eedbck S S S Subect x Tretment Interction t eedbck S4 S5 S 4 5 Correct Answers 8 4 Correct Answers 5 5 5 words words 7 words 8 words 5 words words 7 words 8 words /7/ -ctor Mixed Design 4
The Two-ctor Mixed Design: Sources of Vrition Totl Vrition Between Subects Within Subects ctor A Subects within groups ctor B A x B Interction B x Subects Within Groups Length of Angrm eedbck 5 Letters Letters 7 Letters 8 Letters Absent 4 9 4 7 5 7 9 Present 7 8 8 7 7 8 9 9 /7/ -ctor Mixed Design 5
eedbck B B B B 4 ΣA i B B B B 4 Absent A 4 9 4 8 4 7 4 9 49 5 7 9 5 49 8 44 ΣB i 5 78 Present A 7 8 8 7 7 89 4 4 89 7 8 7 5 5 89 4 9 9 79 4 44 ΣB i 5 5 55 5 ΣB 8 77 87 94 ΣX 94 ΣX 454 ( ΣX ) 94 CM.5 4 SStotl ΣX CM 454.5 9.5 TS SSbetween Σ CM b 4 7 7 79.5 8.5 4 4 4 4 4 4 TA 78 i SSA Σ CM.5 79.5 i SS SS SSA 8.5 79.5 9 between Preliminry Clcultions SS T SSB Σ B T SSAB Σ 5.8 SS MSA MSB AB 4 5 ( ( b ) (4 ) 8 b 4 SS B ) () 4 ( )( b ) ()() B Ss w/n groups A A B AB MS within totl between Ss w/n groups within SSA A B MSA MS CM i ( b )( 79.5 SSB totl i 59.5 SS SS 79.5 79.5 9.75 8.85 9.8 9.5 8.5 9 8 5 77 CM SSA SSB SS i between within 5 SSB SSAB 9 59.5.8.7 i 9 4 ) ()() 9.75 87 55.5 59.5 5.5 79.5 59.5 /7/ -ctor Mixed Design
MSA MS A MSB MSAB MS B AB MS 79.5 59.5 B MS SSA A B MS MSA SSB B SSAB AB MSB MSAB SS Preliminry Clcultions 79.5 79.5 9.75 8.85 9.8.8 B SS 8.944 9.8.5 8.944.5 9 4 B B 9.75.7 4.899 9.7.5 Source SS MS Between subects 5 8.5 Type of feedbck 79.5 79.5 8.85 4 9. 9.75 Witihin subects 8 9. umber of words 59.5 9.8 4.9 A x B Interction.8 8.944 9.7 B x.7. Totl 9.5 /7/ -ctor Mixed Design 7
ypothesis Tests Min effect of feedbck : Min effect of number of words : : µ :. µ Reect 8.85 4.99 Reect µ. µ if.5;,4 : µ > 7.7. Reect Reect A x B interction : Reect Reect. if 9.7 µ µ µ : At lest two popultion mens differ. /7/ -ctor Mixed Design 8. if >.49..5;, 4 >.49. : The two vribles do not interct. : The two vribles interct..5;,
Exercise 9. or the ngrm study, exmine the influence of ngrm length within the no-feedbck condition (α.5). Do the sme within the feedbck condition (α.5). Where wrrnted, conduct pirwise comprisons within these simple effects. (α.5) To perform simple min effect nlysis in fctor mixed design, simply perform one-fctor AOVA t ech min effect of interest. If nlyzing the within fctor t levels of the between fctor, use one-fctor, within-subects AOVA follow up with Tukey if wrrnted If nlyzing the between fctor t levels of the within fctor, use one-fctor, between-subects AOVA follow up with Tukey if wrrnted /7/ -ctor Mixed Design 9
Simple Effects ypothesis Tests B t A Source SS MS um. t no feedbck 8. 7.7. Blocks 9.5 9.75 Error.5.8 Totl Effect of : µ : At lest two popultion mens differ. Reect # of if. Reect. words t no feedbck : µ µ µ.5;, 4 > 4.7. B t A Source SS MS um. t feedbck...4 Blocks Error.5.58 Totl Effect of : µ : At lest two popultion mens differ. Reect # of if Do not reect.4 words t feedbck : µ µ µ.5;,. 4 > 4.7. ollow this up with Tukey /7/ -ctor Mixed Design
Tukey s SD post hoc test 8 Men umber of Correct Angrms s unction of umber of Letters: o eedbck Condition 5. 7.. : µ : µ Reect µ µ ypothesis Tests if W >. 85. 4 Criticl difference : MSE w qα;k,í n~ q 4.9. 5; 4, w q 4.9. 5 Letters Letters 7 Letters 8 Letters Preliminry Clcultions á ν ;k,í MSE n~. 8 4.9.. 85 B B B B4 Men. 5. 7.. B..7 * 4. * 7. * B 5.. * 5. * B 7.. * B4. *Reect. In the no feedbck condition, performnce rises progressively s the number of ngrm letters increses. /7/ -ctor Mixed Design
Conclusions We hve used post hoc strtegy to nlyze dt from the ngrm study. Perform the overll AOVA first. If interctions re significnt, nlyze simple min effects with single-fctor AOVAs, from which the tretment MS nd error MS re used. Where wrrnted, conduct Tukey s procedure within simple min effects, using the error MS from the one-fctor AOVA. Which simple min effects do you test? B t levels of A? A t levels of B? Both? This is determined by the reserch problem nd lph. If the post hoc strtegy is to be used on min effects, use Tukey: If the fctor is W-S, use MS B x If the fctor is B-S, use MS /7/ -ctor Mixed Design
Exercise 9. ive hundred introductory psychology students re dministered hypnotic suggestibility test erly in the term. rom this group 8 low suggestibles re rndomly ssigned to three -min induction conditions: trditionl pssive induction, ctive-lert induction, nd unrelted informtion (red the newspper). After the induction, suggestibility ws re-tested. Dt re given t right. The reserchers mke two predictions: () tht, in the ctive lert condition, men scores t prend post-tretment will differ nd (b) tht, post-tretment, the men score of the ctive lert condition will differ from the men score of the trditionl nd control conditions combined. Test ech hypothesis t α.5. Testing Induction Before After Trditionl Active-lert 4 Control /7/ -ctor Mixed Design
Suggestibility score Men Pre- nd Post-Tretment Suggestibility by Induction Pretest Trditionl..7 Active-Alert.7.5 Control.8.8 Test of Contrst Post-Test Contrst AOVA Source SS MS Blocks 7.7 5.5.5 Testing t ctive-lert 5. 5. 4. Error.7 5. Totl.7 L Σ s ψˆ t α, ν.( : µ µ : µ µ Reect t L s ψˆ Reect MSE( t X.5;5 if t <.57or t. ().7 ( ).5. ( ).57 )...... c c ).44. >.57. /7/ -ctor Mixed Design 4
Suggestibility score Men Pre- nd Post-Tretment Suggestibility by Induction Pretest Trditionl..7 Active-Alert.7.5 Control.8.8 Test of Contrst Post-Test Contrst AOVA Source SS MS Induction t fter 9. 4.7 4.5 Error 5.7 5. Totl 4.5 7 L Σ.( µ µ : µ µ µ : µ Reect if t <.or t Reect MSE(.5.984.57 /7/ -ctor Mixed Design 5 s t ψˆ α, ν t L s ψˆ t X.5;5. ().5 ( ( ).... ( ) ) ).7 ( c c ).575.57 >.. ).8.5
Conclusions We hve used n priori strtegy to nlyze dt from the suggestibility study. In mixed design, locte predictions within simple min effects or ech prediction Conduct one-fctor AOVA on the pertinent simple min effect in order to obtin MS error Then perform the priori t-test /7/ -ctor Mixed Design