t = s D Overview of Tests Two-Sample t-test: Independent Samples Independent Samples t-test Difference between Means in a Two-sample Experiment

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1 Overview of Te Two-Sample -Te: Idepede Sample Chaper 4 z-te Oe Sample -Te Relaed Sample -Te Idepede Sample -Te Compare oe ample o a populaio Compare wo ample Differece bewee Mea i a Two-ample Experime Idepede Sample -Te Idepede whe we radomly elec paricipa for ample Aumpio depede variable ha ierval or raio core populaio of raw core form a lea roughly ormal diribuio Homogeeiy of variace variace ( σ ) of each populaio beig repreeed i equal do have o be equal, a log a hey re o radically differe (e.g. more ha wice a much a ) Calculaig for Repeaed Meaure D D Calculaig for Idepede ample Phoo ad Fale Memorie Reearch Queio: Ca old phoo creae or preve fale memorie? (Liday, Hage, Read, Wade, & Garry, 004) 45 udergraduae aked o remember a childhood eve ha, ubekow o hem, had acually occurred. oe group ( 3) give phoograph o help cue heir memory ecod group ( ) o give phoograph Paricipa raed he exe o which heir memory experiece reembled relivig he eve o a cale from o 7 (o a all, 7 a if i were happeig righ ow)

2 Phoo ad Fale Memorie A 6 Sep Program for Hypohei Teig. Sae he reearch queio. Chooe a aiical e 3. Selec alpha which deermie he criical value for he regio of rejecio (e.g.,.05 ) 4. Sae your aiical hypohee (a equaio) Phoo group Corol group Collec daa, ad calculae 6. Ierpre reul i erm of hypohei Repor reul Explai i plai laguage A 6 Sep Program for Hypohei Teig. Sae your reearch queio Ca old phoo ifluece fale memorie core?. Chooe a aiical e comparig mea from wo group paricipa radomly aiged o differe group idepede ample -Te Phoo ad Fale Memorie 3. Selec alpha which deermie he criical value (.05 ) for he regio of rejecio α.05 For he idepede wo-ample -Te df ( ) + ( ) i oher word, df N - i hi cae, df /-.0 (from -Table) Phoo ad Fale Memorie 4. Sae your aiical hypohee (a equaio) H 0 : μ μ H : μ μ Whe H 0 i rue, boh ample repree he ame populaio 5. Collec daa ad calculae e aiic ( ) Phoo 3 Corol x I he differece i mea due o he phoo or imply be due o chace variaio?

3 Properie of he Differece bewee Mea Samplig diribuio of differece bewee mea diribuio of all poible differece bewee wo mea Sadard error of he differece bewee mea adard deviaio of hi amplig diribuio Collec daa ad calculae e aiic ( ) Oe ample -Te Idepede ample -Te μ adard error adard error of he differece Collec daa ad calculae e aiic ( ) Eimaig populaio variace require wo ep:. Compue ed variace (a weighed average) ( ) + ( ( ) + ( ) ). Compue adard error of he differece ( ) + Pooled Variace ( ) + ( ( ) + ( ) ) The average of boh ample variace, oce adjued for heir degree of freedom (df) You have made a miake if ed variace doe o come ou bewee he wo eimae doe o come ou cloer o he eimae from he larger ample Pooled Variace Sadard Error of he Differece x x Phoo Corol ( ) + ( ( ) + ( ) ) (3 )(.48) + ( )(.798) (3 ) + ( ) x x Phoo Corol ( ) + 3 (.47)

4 x x Calculae e aiic ( ) Phoo Corol Phoo ad Fale Memorie Ierpre reul i erm of hypohei.79 >.0; Rejec H 0 Repor reul (43).79, p <.05 Explai i plai laguage The phoo group (M 3., SD.56) produced igificaly higher raig of relivig he fale eve ha he corol group (M.0, SD.34). Whe combied wih oher uggeive echique, old phoo ca coribue o fale memorie. Effec Size Sigifica effec may idicae geuie, bu rivial differece bewee group Effec ize idicae he ize of a differece bewee group he le overlap he larger he differece Effec ize i iflueced by eparaio bewee mea large overlap: mall effec mall overlap: larger effec Effec ize alo iflueced by variaio i each group Ierpreig Cohe d large overlap: mall effec mall overlap: larger effec ame mea differece bu differe effec ize Thee are rough guidelie: Effec Size d Overlap mall. 85% medium.5 67% large.8 53% 4

5 Effec Size: Cohe d Cohe d expree he differece bewee mea i adard deviaio ui mea mea dˆ SD ˆ d for idepede ample: ue weighed average adard deviaio (quare roo of ed variace) Noe: do o calculae effec ize for oigifica reul Effec Size Cohe d alerae equaio ue hi equaio whe calculaig effec ize from PASW oupu dˆ df Noe: do o calculae effec ize for oigifica reul Phoo ad Fale Memorie Ierpreig PASW priou Wha i he effec ize i he fale memorie udy? core Equal variace aumed Equal variace o aumed Idepede Sample Te Levee' Te for Equaliy of Variace -e for Equaliy of Mea 95% Cofidece Ierval of he Differece Mea Sd. Error F Sig. df Sig. (-ailed) Differece Differece Lower Upper dˆ ˆ d df Sig. (-ailed) Repor: (0) -.77, p.07 Noe: whe uig PASW, repor he acual p - value Idepede Sample -Te ad PASW Creae wo variable oe coai level of your idepede variable (here called group ) he ecod coai core of your depede variable (here called core ) Idepede Sample -Te ad PASW Selec from Meu: Aalyze -> Compare Mea -> Idepede Sample T Te Selec your depede variable (e.g., core) a Te Variable ad idepede variable (e.g., group) a Groupig Variable. Selec Defie Group Eer for Group ad for Group Noe: you would eer differe label if you had o amed your group ad Click Coiue; Click OK 5

6 Differece bewee group or from a e value Group Group Muliple Group Kow σ Eimaed σ Idep. Sample Relaed Sample z-e Oe-ample -e Idepede ample -e Relaed ample -e (PASW: paired) People ha ake Lipior have reduced level of choleerol. If reearcher fid a differece bewee group, why do he wo group differ?. radom differece bewee idividual i he group. e.g., more healhy people i oe group. differece bewee level of he idepede variable e.g., Lipior i effecive i reducig choleerol level 6