Group B Human

Transcription

1 /9/009 -Tes for wo independen samples aisical Tess A sep-by-sep guide Is here a significan difference beween he abiliies of rained homing pigeons o locae survivors a sea and he abiliies of rained human voluneers? Treamen Time iook for he rainees o locae a survivor a sea (s) Group A Pigeons Group B Human voluneers. ae he null hypohesis (H 0 ). H 0 : µ A µ B There is no significan difference beween he abiliies of rained pigeons and rained human voluneers in locaing survivors a sea.. ae he alernaive hypohesis (H A ). H A : µ A µ B There is a significan difference beween he abiliies of rained pigeons and rained human voluneers in locaing survivors a sea.. ae he level of significance. α Is his a one-ailed or a wo-ailed es? Thisis a wo-ailed es. 5. e-up he able A (pigeons) 6a. Compue for he means of Groups A and B. B (humans) Σ 4 Σ

2 /9/009 6b. Compue for he sandard error of he difference beween means. Σ ( Σ ) 98 + Σ + ( Σ ( 4 ) ( 6 ) ) df 7. eermine he degrees of freedom, df. 8. Use he able for Criical Values of o deermine he ± 9. Formulae he conclusion..0 ince he calculaed value falls wihin he region of accepance, we ACCEPT he H 0. There is no significan difference beween he mean abiliy of rained pigeons and humans in locaing survivors a sea. 6c. Compue for he calculaed. calculaed ( ) ( µ µ ) (7 9) (0) Tes for wo correlaed samples Paricipans hrew dars a a arge. In one condiion, hey used heir preferred hand; in he oher condiion, hey used heir oher hand. Their scores are shown below. Treamen cores obained on a dars game Condiion Preferred hand 7 4 Condiion on-preferred hand Is here a significan increase in he scores when he preferred hand was used?. ae he null hypohesis (H 0 ). H 0 : µ A µ B There is no significan difference beween he mean scores when dars are hrown wih he preferred hand and when dars are hrown wih he non-preferred hand.. ae he alernaive hypohesis (H A ). H A : µ A >µ B There is a significan increase in mean scores when dars are hrown wih he preferred hand raher han when dars are hrown wih he non-preferred hand.. ae he level of significance. α Is his a one-ailed or a wo-ailed es? This is a one-ailed es.

3 /9/ e-up he able A (preferred hand) B (non-preferred hand) 6b. Compue for he sandard error of he mean difference. A B A - B ( A - B ) Σ d ( ) 6c. Compue for he mean difference. Σ 4 5 ( 5 ) Σ d 6a. Compue for he sum of he squares of he difference score, Σd Σ ( Σ ) 79 (5 ) 5 4 6d. Compue for calculaed. calculaed eermine he degrees of freedom, df. df 5 8. Use he able for Criical Values of o deermine he. ±. 9. Formulae he conclusion. ince he calculaed value falls wihin he region of rejecion, we REJECT he H 0 and accep he H A. There is a significan increase in he mean scores of a dar game when he preferred hand is used. 4 ingle Facor Analysis of Variance (AOVA) cieniss suspec ha higher priced cars are assembled wih greaer care han lower-priced cars. A large luxury model, A, a medium-sized sedan B, and a subcompac economy car C were compared for defecs when hey arrived a he dealer's showroom. All cars were manufacured by he same company. The number of defecs for hree of each of he models are shown below. Car Type # of defecs Car A Large Luxury Model 4 Car B Medium-sized sedan 4 4 Car C Economy car 8 6 Tes he hypohesis ha he average number of defecs is he same for he models (a he 0.05 level of significance).

4 /9/009. ae he null hypohesis (H 0 ). 4. e-up he able. H 0 : µ A µ B µ C There is no significan difference beween he mean number of defecs of large luxury models, medium-sized sedans, and subcompac economy cars from he same manufacurer.. ae he alernaive hypohesis (H A ). H A : µ A µ B µ C There is a significan difference beween he mean number of defecs of large luxury models, medium-sized sedans, and subcompac economy cars from he same manufacurer.. ae he level of significance. Car Type # of defecs Row Toal (Row Toal) Car A Large Luxury Model Car B Medium-sized sedan Car C Economy car α Consruc he AOVA able: ource of Variaion um of quares egrees of Freedom Mean quare F calculaed F 7. Use he able for Values of he f saisico deermine F ; F BT is V, F WT is V. F 5.4 Beween Treamens BT F BT M BT WihinTreamens WT F WT M WT 8. Formulae he conclusion. BT WT 6. Compue for he values on he AOVA able. Σ( Row Toal) ( ΣRow Toal) 45 (5 ) 4.9 # of replicaes per reamen oal # of samples 9 Σ( Row Toal) 45 Σ( scores ) ( ) 8 # of replicaesperreamen F WT F BT # of reamens # of reamens (# of replicaes ) ( ) 6 BT 4.9 WT 8 MBT 7.45 M MBT 7.45 WT Fcalculaed.48 F F 6 M BT WT WT ince he F > Fcalculaed, i falls wihin he region of accepance, and we ACCEPT he H 0. There is no significan difference among he mean number of facory defecs large luxury models, medium-sized sedans, and subcompac economy cars from he same manufacurer. ource of Variaion um of quares egrees of Freedom Mean quare F calculaed F Beween Treamens Wihin Treamens 8 6 4

5 /9/009 Chi square (χ ) es A recen experimen invesigaed he relaionship beween smoking and urinary inconinence. Treamen Frequency of inconinence Frequency of subjecs wihou inconinence mokers 68 Former smokers 5 on-smokers ae he null hypohesis (H 0 ). H 0 : µ A µ B There is no significan difference beween inconinen and non-inconinen paiens individuals wih regard o heir smoking preferences.. ae he alernaive hypohesis (H A ). H A : µ A µ B There is a significan difference beween inconinen and non-inconinen paiens individuals wih regard o heir smoking preferences.. ae he level of significance. α e-up he coningency able. Observed Frequencies Inconinen o inconinen Toal mokers 68 8 Former smokers 5 74 on-smokers (Row Toal)(Col umn Toal) Expeced frequency Grand Toal Expeced Frequencies Inconinen o inconinen Toal mokers 8()/ (84)/ Former smokers 74()/ (84)/ on-smokers 5()/ (84)/ Compare he observed and expeced frequencies by seing up he chi-square able. χ (O-E) /E Inconinen o inconinen Toal mokers (-96.) /96..9 ( ) / Former smokers (5-9.) /9..5 (-4.7) / on-smokers ( ) / (9-65.5) / χ 6. eermine he degrees of freedom, df. df (# of columns )(# of rows ) ( )( ) 5

6 /9/ Use he able for Criical Values of chi square o deermine he χ. χ 8. Formulae he conclusion ince he calculaed χ value falls wihin he region of rejecion, we REJECT he H 0. There is a significan difference beween inconinen and non-inconinen paiens individuals wih regard o heir smoking preferences. Friedman s es Four expers were asked o evaluae he accepabiliy of brownies made from 0% malunggay-enriched flour, 5% malunggay-enriched flour, and 50% malunggay-enriched flour wih 0 being he highes raing. Original cores Ranked cores Paneliss 0% MEF 5% MEF 50% MEF 0% MEF 5% MEF 50% MEF ae he null hypohesis (H 0 ). The samples come from he same populaion. There is no significan difference beween he accepabiliy of he samples of brownies made from flour wih differen concenraions of malunggay.. ae he alernaive hypohesis (H A ). The samples come from differen populaions. There is a significan difference beween he accepabiliy of he samples of brownies made from flour wih differen concenraions of malunggay.. ae he level of significance. α Compue for Friedman s saisic, calculaed. Original cores Ranked cores Paneliss 0% MEF 5% MEF 50% MEF 0% MEF 5% MEF 50% MEF calculaed calculaed {( ΣR ) + ( ΣR ) + ( ΣR ) +...} A B C ( ΣR + Σ + Σ + A RB RC...) # ofsamplesbeingesed ( ) {( 0.5) + ( 8.5) + ( 5) } 5.5 6

7 /9/ eermine mand n. m # of blocks or paneliss 4 n # of samples being esed 7. Use he able for Criical Values of Friedman s aisics o deermine Formulae he conclusion. ince calculaed falls wihin he region of accepance, we accep H 0. There is no significan difference in he accepabiliy of brownies made from varying concenraions of malunggay-enriched flour.the sample wih he no malunggay was he mos liked while he sample wih he mos amoun of malunggay was he leas liked sample. 7