Lecture 8 Emprcal Research Methods I434 Quattatve Data aalss II Relatos Prevous lecture Idea behd hpothess testg Is the dfferece betwee two samples a reflecto of the dfferece of two dfferet populatos or smpl caused b samplg error? Coceptual models wth specfc statstcal tests Dfferet tests depedg o: level, umber of depedet ad depedet varables, betwee or wth subjects set up Statstcal tests SPSS See the recordg of ths lecture I434 Emprcal Research Methods Sprg, Lecture 8 I434 Emprcal Research Methods Sprg, Lecture 8 Toda Learg s of ths lecture Pearso product momet Spearma Correlato Partal Correlato Lear Regresso aalss Multple regresso After toda s lecture ou should be able : to epla the dea behd (partal to lk coceptual models wth regresso model to uderstad output of regresso aalss to perform regresso aalss SPSS I434 Emprcal Research Methods Sprg, Lecture 8 3 I434 Emprcal Research Methods Sprg, Lecture 8 4 Statstcal test ad Scales of measuremet Am Samples Data Level Tests Fd Sgle omal Bomal test, χ goodess-of-ft dfferece sample Ordal Wlcoo sged-raks test Iterval / Rato z-test, Oe-Sample t-test Idepede omal Fsher-Eact test, χ t Ordal Ma-Whte U test Iterval / Rato z-test, two depedet sample t-test, AOVA, MAOVA Depedet omal Mcemar Ordal Sg Test, Wlcoo matched-pars sgedrak test, Fredma Test Iterval / Rato Pared-Sample t-test, repeated measures AOVA, MAOVA Fd omal Cramér s V, ph relato Ordal Kedall, Spearma Iterval / Rato Pearso product momet, regresso aalss I434 Emprcal Research Methods Sprg, Lecture 8 5 Correlato Correlato s the degree of relatoshp betwee two varables. We are terested two propertes of the relatoshp:. Its drecto. Its stregth I434 Emprcal Research Methods Sprg, Lecture 8 6 Postve egatve Zero
Correlato - Drecto Postve : A crease s assocated wth a crease. egatve : a crease s assocated wth a decrease. Scatter dagram stregth of Depedet Varable Zero : a crease or decrease s ether assocated wth a crease or decrease. I434 Emprcal Research Methods Sprg, Lecture 8 7 3 Idepedet Varable I434 Emprcal Research Methods Sprg, Lecture 8 8 Correlato Stregth of The stregth of a ca be see as a epresso of how well data pots ft o a le that represets the relatoshp betwee two varables. Stroger Weaker - + Strog egatve Zero Strog postve Correlato coeffcet s a umerc measure of the stregth ad drecto of a lear relatoshp betwee two varables. I434 Emprcal Research Methods Sprg, Lecture 8 9 I434 Emprcal Research Methods Sprg, Lecture 8 Postve : < r + egatve : - r < Zero : r I434 Emprcal Research Methods Sprg, Lecture 8 Pearso Product-momet coeffcet (r Stadard score, z-score, s the devato of a data pot from the mea stadard devato uts Trasformg data to z- scores makes t possble to compare them, because the are epressed the same ut. ( z z r = s I434 Emprcal Research Methods Sprg, Lecture 8 z =
: Selftest : task 3 score z z 6 7.5 -.38 -.5 4 79..53.7 47.3.7 -.7 7 47.68.87 -.6 9 66.5..6.5 -.7. 4 9. -.75 -.45 5 76.84.64.99 Sum 55 394.7 Mea 9.38 49.6 z = = s SD 8.78 7.85 8 6 9.38 =. 38 8.78 I434 Emprcal Research Methods Sprg, Lecture 8 3 task 3 score selftest ad task 3 score. 75. 5. 5.. 3 umber of completed selftest task 3 scores ( sd Selftest ad task 3 scores... -. -.... -. -. umber of completed selftest ( sd I434 Emprcal Research Methods Sprg, Lecture 8 4 ( z z r = r = - task 3 scores ( sd Selftest ad task 3 scores -... + -. -.... -. + -. - umber of completed selftest ( sd I434 Emprcal Research Methods Sprg, Lecture 8 5 r = ( z z r = = 4.49 =.64 8 : Selftest : task 3 score z z z *z 6 7.5 -.38 -.5.58 4 79..53.7.56 47.3.7 -.7 -. 7 47.68.87 -.6 -.5 9 66.5..6.67.5 -.7. -.43 4 9. -.75 -.45.53 5 76.84.64.99.63 Sum 55 394.7 4.49 Mea 9.38 49.6 SD 8.78 7.85 I434 Emprcal Research Methods Sprg, Lecture 8 6 Correlato coeffcet 3 r =.7 Ths meas that that a a crease the the umber of of self-tests completed s s assocated wth a a crease the the total score for for task 3 r = ( ( z z = Socal Scece r =. -> small effect r =.3 -> medum sze effect r =.5 -> Large effect (Cohe, 99 ( ( ( I434 Emprcal Research Methods Sprg, Lecture 8 7 I434 Emprcal Research Methods Sprg, Lecture 8 8 3
Pearso Correlato Coceptual model Pearso Correlato - eample Coceptual model Eample Assumptos Iterpretato Atttude towards moble phoe desg Ide score Iteto to select phoe Ratg from to 7 Coceptual model Eample Assumptos Iterpretato I434 Emprcal Research Methods Sprg, Lecture 8 9 I434 Emprcal Research Methods Sprg, Lecture 8 Pearso Correlato - eample Pearso Correlato - assumptos Coceptual model Eample Assumptos Iterpretato Coceptual model Eample Assumptos Iterpretato. Idepedece of observatos. Iterval data 3. Lear relatoshp 4. homoscedastct (the same level of relatoshp throughout the rage of the depedet varable I434 Emprcal Research Methods Sprg, Lecture 8 I434 Emprcal Research Methods Sprg, Lecture 8 Pearso Correlato terpretato s Coceptual model Eample Assumptos Iterpretato Atttude towards phoe lkelhood ratg selectg phoe Correlatos Pearso Correlato Sg. (-taled Pearso Correlato Sg. (-taled Atttude towards **. Correlato s sgfcat at the. level (-taled. lkelhood ratg selectg phoe phoe.4**. 4.4**. 47 Pearso Correlato SPSS Demo Coceptual model Eample Assumptos Iterpretato I434 Emprcal Research Methods Sprg, Lecture 8 3 I434 Emprcal Research Methods Sprg, Lecture 8 4 4
Partal Correlato Coceptual model Coceptual model Eample Assumptos Iterpretato Atttude towards moble phoe desg Socal orm towards moble phoe desg r. z = r rzrz rz rz Iteto to select phoe Partallg out the effect of a thrd varable o the betwee varables I434 Emprcal Research Methods Sprg, Lecture 8 5 Partal Correlato - eample Coceptual model Eample Assumptos Iterpretato Atttude towards phoe Socal orm towards phoe lkelhood ratg selectg phoe Correlatos Pearso Correlato Sg. (-taled lkelhood Atttude Socal orm ratg towards towards selectg phoe phoe phoe.856**.4**.. 4 8.856**.39**.. 8 9.4**.39**.. 9 47 I434 Emprcal Research Methods Sprg, Lecture 8 6 Pearso Correlato Sg. (-taled Pearso Correlato Sg. (-taled **. Correlato s sgfcat at the. level (-taled. Partal Correlato - eample Coceptual model Eample Assumptos Iterpretato Atttude towards moble phoe desg Socal orm towards moble phoe desg? Iteto to select phoe Partal Correlato - assumptos Coceptual model Eample Assumptos Iterpretato. See assumptos Pearso Correlato I434 Emprcal Research Methods Sprg, Lecture 8 7 I434 Emprcal Research Methods Sprg, Lecture 8 8 Partal Correlato terpretato s Partal Correlato SPSS Demo Coceptual model Eample Assumptos Iterpretato Cotrol Varables Socal orm towards phoe Atttude towards phoe lkelhood ratg selectg phoe Correlatos Correlato Sgfcace (-taled df Correlato Sgfcace (-taled df lkelhood Atttude ratg towards selectg phoe phoe..88..55 3.88..55. 3 Coceptual model Eample Assumptos Iterpretato A S I I434 Emprcal Research Methods Sprg, Lecture 8 9 I434 Emprcal Research Methods Sprg, Lecture 8 3 5
Spearma rak for ordal data Usablt ratg, Frequec of use, Rakg of Dfferece Rakg betwee of rakg, d Ver low 5.5 -.5.5 Low.5.5.5 Low 5.5.5 average 8 4 4 hgh 6 5 hgh 3 6 6 hgh 6 8-4 ver hgh 5 8 7 Total.5 6 d 6.5 r = = 8 8 I434 Emprcal Research Methods Sprg, Lecture 8 3 d ( ( =.875 Spearma Correlato Coceptual model Coceptual model Eample Assumptos Iterpretato Beaut of UI Usablt of UI I434 Emprcal Research Methods Sprg, Lecture 8 3 Spearma Correlato - eample Spearma Correlato - assumptos Coceptual model Eample Assumptos Iterpretato beaut of the terface * Usablt of the terface Crosstabulato Cout Usablt of the terface ver low low average ver hgh Total beaut ver ugl of the ugl terface avarage beautful ver beautful 3 Total 3 3 9 Coceptual model Eample Assumptos Iterpretato. Idepedece of observatos. At least ordal level I434 Emprcal Research Methods Sprg, Lecture 8 33 I434 Emprcal Research Methods Sprg, Lecture 8 34 Spearma Correlato terpretato s Coceptual model Eample Assumptos Iterpretato Spearma's rho beaut of the terface Usablt of the terface Correlatos Correlato Coeffcet Sg. (-taled Correlato Coeffcet Sg. (-taled beaut of the Usablt of terface the terface..4..36 9 9.4..36. 9 9 Spearma Correlato SPSS Demo Coceptual model Eample Assumptos Iterpretato I434 Emprcal Research Methods Sprg, Lecture 8 35 I434 Emprcal Research Methods Sprg, Lecture 8 36 6
Wh do we look at regresso models? It helps us to model ad eame the ature of the relato betwee two or more varables. For eample, What s the etwork speed whe or 5 PCs are coected to t? How much of the varato the users Acceptace of Iformato Techolog ca be eplaed b the Usablt of a applcato, the Users trag, ad the level of IT support? What Webct mark for task 3 ca I epect whe I have completed 5 of the ole self-tests? I434 Emprcal Research Methods Sprg, Lecture 8 37 Fttg a straght le to represet the data Depedet, Respose, or or Crtero varable What s the best Le? Idepedet 3 or or predctor varable I434 Emprcal Research Methods Sprg, Lecture 8 38 Least Squares Method Smple Regresso Le Le 4 4 b= Error Le Error Le Error Sum of Squared Errors = ( ˆ = Look for the le wth the smallest SSE Itercept a = a + b Slope I434 Emprcal Research Methods Sprg, Lecture 8 39 I434 Emprcal Research Methods Sprg, Lecture 8 Smple Regresso Smple Regresso Table: Self-tests completed ad overall score task 3 : : task Slope Selftest 3 score 6 7.5. 56. 4 79. 896. 576. b = ( 47.3 946.. 7 47.68 87.36 79. 9 66.5 9.5 84. 8 873. 6 55 394. 7.5 5.. = 4 9. 36. 6. 8 3543 55 5 76.84 9. 65. 55 394.7 873.6 3543. =. 33 I434 Emprcal Research Methods Sprg, Lecture 8 4 Itercept (a I434 Emprcal Research Methods Sprg, Lecture 8 4 The regresso le alwas passes through the pot (, = a + b a = - b 7
Smple Regresso Smple Regresso Table: Self-test completed ad overall score task 3 : Selftest : task 3 score 6 7.5. 56. 4 79. 896. 576. 47.3 946.. 7 47.68 87.36 79. 9 66.5 9.5 84..5 5.. 4 9. 36. 6. 5 76.84 9. 65. 55 394.7 873.6 3543. Itercept a = b 394. 7 55 =. 33 8 8 = 9. 87 task 3 score 75 5 5 selftest ad task 3 score = 9.87 +.3 3 umber of completed selftests I434 Emprcal Research Methods Sprg, Lecture 8 43 I434 Emprcal Research Methods Sprg, Lecture 8 44 Class questo 3 = 8. +.76 Predcted = 8. +.76*umber of of ole self-test completed What s the predcted for task 3 for a studet that completed ole self-tests? Class questo - Aswer 3 = 8. +.76 Predcted = 8. +.76*umber of of ole self-test completed the predcted = 8. +.76* = 35.8 I434 Emprcal Research Methods Sprg, Lecture 8 45 I434 Emprcal Research Methods Sprg, Lecture 8 46 Class questo Class questo - Aswer I geeral, what s the mpact of completg a ole self-test o the predcted of task? 3 = 8. +.76 Predcted = 8. +.76*umber of of ole self-test completed What s the epected total task 3 score for a studet who dd ot complete a self-tests? I434 Emprcal Research Methods Sprg, Lecture 8 47 Completg self-test wll crease the task 3 wth.76 pots 3 = 8. +.76 Predcted = 8. +.76*umber of of ole self-test completed If = tha predcted = a = 8. I434 Emprcal Research Methods Sprg, Lecture 8 48 8
Multple Lear Regresso Coceptual model Coceptual model Assumptos Iterpretato selecto Atttude Male Socal orm Geder Female Lkelhood selectg sk Multple Lear Regresso - assumptos Coceptual model Assumptos Iterpretato selecto. Relato betwee depedet varable(s ad depedet varable s lear. Errors are depedet 3. Error s ormal dstrbuted 4. Error s dstrbuted wth costat varace = β + β + β +... + β + e Sum of Squared Errors = ( ˆ = I434 Emprcal Research Methods Sprg, Lecture 8 49 I434 Emprcal Research Methods Sprg, Lecture 8 5 Multple Lear Regresso terpretato s summar Coceptual model Assumptos Iterpretato selecto Summar Adjusted Std. Error of R R Square R Square the Estmate.459 a..95.383 a. Predctors: (Costat, Socal orm towards sk, Atttude towards sk Multple Lear Regresso terpretato s AOVA Coceptual model Assumptos Iterpretato selecto Regresso Resdual Total AOVA b Sum of Squares df Mea Square F Sg. 54.33 7.6 4.9. a.83 6.93 56.86 8 a. Predctors: (Costat, Socal orm towards sk, Atttude towards sk b. Depedet Varable: lkelhood to select sk ( ˆ s = est df where b df = # depedet varables R - betwee predcted ad observed R - Coeffcet of Determato shows the proporto of varato the depedet varable that ca be eplaed b the model Adj. R - Corrected for the umber of Idepedet varables Std Error of the Estmate the accurac of the predcto I434 Emprcal Research Methods Sprg, Lecture 8 5 I434 Emprcal Research Methods Sprg, Lecture 8 5 Multple Lear Regresso terpretato s AOVA Coceptual model Assumptos Iterpretato selecto Regresso Resdual Total AOVA b Sum of Squares df Mea Square F Sg. 54.33 7.6 4.9. a.83 6.93 56.86 8 a. Predctors: (Costat, Socal orm towards sk, Atttude towards sk b. Depedet Varable: lkelhood to select sk Multple Lear Regresso terpretato s Coeffcet Coceptual model Assumptos Iterpretato selecto (Costat Atttude towards sk Socal orm towards sk Ustadardzed Coeffcets a. Depedet Varable: lkelhood to select sk Coeffcets a Stadardzed Coeffcets B Std. Error Beta t Sg. To 7.638..358.34.68.7.3.83.4.5.47.6.353.75 lkelhood. select. sk =.36 +.7Atttude +. 5S + e C Beta stadardsed coeffcets, e.g. sd rse atttude there would be a.4 sd rse sk selecto lkelhood I434 Emprcal Research Methods Sprg, Lecture 8 53 I434 Emprcal Research Methods Sprg, Lecture 8 54 9
Multple Lear Regresso terpretato s Colleeart Coceptual model Assumptos Iterpretato Selecto (Costat Atttude towards sk Socal orm towards sk I434 Emprcal Research Methods Sprg, Lecture 8 55 Usta Coe B.358.68.5 a. Depedet Varable: lkelhood to select sk Colleart Statstcs Sg. Tolerace VIF..4.39 4.89.75.39 4.89 Colleart -Correlato betwee Idepedet varables lmts the sze of R, dffcult to assess predctors, ustable predctor equato (B. o strct rules, but problems whe: Tolerace=/VIF <. Varace Iflato Factor > Multple Lear Regresso Selecto Coceptual model Assumptos Iterpretato selecto Eter force all predctors to the model Stepwse computer selects least umber of predctors to make a effectve model. Cotue to buld model utl ew predctors wll ot make a sgfcat cotrbuto I434 Emprcal Research Methods Sprg, Lecture 8 56 Multple Lear Regresso SPSS Demo Coceptual model Assumptos Iterpretato selecto Atttude Socal orm Geder Male Female Etraverso eurotcsm Lkelhood selectg phoe I434 Emprcal Research Methods Sprg, Lecture 8 57 Summar Correlato coeffcet Epress stregth ad drecto of relato Pearso (terval level Spearma (ordal level Partal Partallg out the effect of a thrd varable o the betwee varables Regresso aalss relato betwee terval level predctor varables ad a terval level depedet varable R Colleart Std Error of the Estmate = β + β + β +... + β + e I434 Emprcal Research Methods Sprg, Lecture 8 58 Ths week practcum et tme o Practcum Judgemet measure Vsual Perceptos Threshold ad just-otceable dfferece Rak order method Pared comparso method I434 Emprcal Research Methods Sprg, Lecture 8 59 I434 Emprcal Research Methods Sprg, Lecture 8
Refereces Cohe, J., (99. A power prmer. Pschologcal bullet, (, 55-59. I434 Emprcal Research Methods Sprg, Lecture 8 6