Using Statistics To Make Inferences 9
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1 Usg tatstcs To Make Ifereces 9 xtee radomly selected mce of the same age ad stra were radomly assged to oe of four treatmet groups. The varous treatmets were varous dets: Cheeros (0 cal), Cor Flakes (0 cal), Frostyos (30 cal), ad Frosted Flakes (40 cal). The weght ga after week o the det was recorded for each mouse. Is there evdece that the mea weght ga s learly related to cal (calores per ouce) of det? Treatmet Factor A Factor B x y AB Det A Gra B Coatg (cal) Wt ga (g) Cheeros Oats Noe 0 Cheeros Oats Noe 0 Cheeros Oats Noe 0 3 Cheeros Oats Noe 0 Frostyos Oats ugar 30 5 Frostyos Oats ugar 30 5 Frostyos Oats ugar 30 4 Frostyos Oats ugar 30 6 Cor Flakes Cor Noe 0 4 Cor Flakes Cor Noe 0 Cor Flakes Cor Noe 0 3 Cor Flakes Cor Noe 0 3 Frosted Flakes Cor ugar 40 5 Frosted Flakes Cor ugar 40 7 Frosted Flakes Cor ugar 40 6 Frosted Flakes Cor ugar 40 6 = 6, x = 000, y = 64, x = 5000, y = 304, = 880 A smple lear regresso caot provde evdece! = 6, x = 000, y = 64, x = 5000, y = 304, = 880 x y x y x 000 y 48 x y 80 r ce r (0.05) the p<0.05, the correlato s sgfcatly dfferet from zero there would appear to 4 be a relatoshp. MTB > Correlato 'x' 'y'. Correlatos (Pearso) Correlato of x ad y = 0.904, P-Value = MTB > %Ftle 'y' 'x'; Mke Cox 9. Verso
2 UBC> Cofdece For those who are terested Regresso The regresso equato s y = x Predctor Coef tdev T P Costat x = R-q = 8.7% R-q(adj) = 80.4% Aalyss of Varace ource DF M F P Regresso Resdual Error Total Regresso Plot Y = X R-q = 8.7 % y x A we expert grades 0 bottles of we o a scale from 0 to 50. He records the results ext to ther ages We Age core A 5 8 B C 4 4 D 8 5 E 30 7 F 34 7 G H 40 I 4 37 J 44 4 a) calculate the Pearso correlato coeffcet for the age of the we agast the grade gve b) calculate pearma's rak correlato coeffcet for the same data ad commet o the results Mke Cox 9. Verso
3 We Age core 0 A 5 8 Σx 34 B Σx 0678 C 4 4 Σy 45 D 8 5 Σy 6907 E 30 7 Σ 835 F 34 7 G var(x) H 40 var(y) I 4 37 cov(x,y) 73. J 44 4 corr corr 0.76 v 8 α 0.05 r P t t P P t(8,0.05).3 r crt 0.63 (ot essetal) (from tables) Crtcal Values of the Correlato Coeffcet The table cotas the crtcal values of the correlato coeffcet for a two-taled test of sgfcace. P=0. P=0.05 P=0.05 P=0.0 P=0.005 P= Mke Cox 9.3 Verso
4 We Age Rak core Rak d d A B 9 0 C D E F G H I J Total 0 38 r s = r s d Crtcal values of pearma's Rak Correlato Coeffcet Level of sgfcace for two-taled test. P = 0.05 P = Approxmato r s of r, s extremely close. Both show a good postve correlato meag the older the we the better qualty t s accordg to ths partcular expert. Mke Cox 9.4 Verso
5 CORRELATION /VARIABLE=age score /PRINT=TWOTAIL NOIG /MIING=PAIRWIE. Correlatos Correlatos age score age Pearso Correlato.765 ** g. (-taled).00 N 0 0 score Pearso Correlato.765 ** g. (-taled).00 N 0 0 **. Correlato s sgfcat at the 0.0 level (-taled). NONPAR CORR /VARIABLE=age score /PRINT=PEARMAN TWOTAIL NOIG /MIING=PAIRWIE. Noparametrc Correlatos Correlatos age score pearma's rho age Correlato Coeffcet ** g. (-taled)..009 N 0 0 score Correlato Coeffcet.770 **.000 g. (-taled).009. N 0 0 **. Correlato s sgfcat at the 0.0 level (-taled). Mke Cox 9.5 Verso
6 3 The research compares the performace of studets studyg Eglsh as a subject ad Iteret HTML ad Javacrpt programmg laguages. Observato suggests that there s correlato betwee the grades obtaed the Eglsh ad the Web Desg courses. The followg totals were obtaed for the varous groups. Result Eglsh (x) Web Desg (y) Σx Σy Σx Σy Σ All Pass Fal Evaluate the correlato betwee the Eglsh ad Web Desg subjects for all studets. Repeat the calculato for oly those who ed. Commet o your results (the scatterplot of the data may be useful). catterplot of Web Desg vs Eglsh Web Desg fal fal fal fal Eglsh Mke Cox 9.6 Verso
7 3 Correlato Betwee Eglsh ad Web Desg ubjects: A Case tudy of tudets at Faculty of Ecoomcs, Ukom Joatha arwoo Result Eglsh (x) Web Desg (y) Σx Σy Σx Σy Σ All Pass Fal Evaluate the correlato betwee Eglsh ad Web Desg subjects for all studets. x y x y 66 x y x y r Repeat the calculato for oly those who ed. x y x y 6 x y x y r Commet o your results (the scatterplot of the data may be useful). The 4 outlers grossly affect the over all correlato. Mke Cox 9.7 Verso
8 MTB > Plot 'Web Desg'*'Eglsh'; UBC> DatLab C; UBC> ymbol. catterplot of Web Desg vs Eglsh (above) MTB > Correlato 'Eglsh' 'Web Desg'; UBC> NoPValues. Correlatos: Eglsh, Web Desg Pearso correlato of Eglsh ad Web Desg = MTB > Ustack ('Eglsh' 'Web Desg'); UBC> ubscrpts C; UBC> After; UBC> VarNames. MTB > Correlato 'Eglsh_' 'Web Desg_'; UBC> NoPValues. Correlatos: Eglsh_, Web Desg_ Pearso correlato of Eglsh_ ad Web Desg_ = The followg data summarses the sales fgures for the te represetatves of a partcular compay. Represetatve umber ales ( 000) Number of vsts Populato (000's) Area (square mles) um um of squares The followg sums of products wll also be useful ales Vsts 76 ales Populato 5680 ales Area Vsts Populato 8450 Vsts Area 9830 Populato Area Varous factors may affect sales, such as umber of potetal clets vsted, the populato ad the area covered the rego assged to the represetatve. Geerate all relevat correlato s to assess whch factors are of prme mportace. Mke Cox 9.8 Verso
9 4 The key totals are ales ( 000) Number of vsts Populato (000's) Area (square mles) um um of squares The correlato s r x ales Vsts 76 ales Populato 5680 ales Area Vsts Populato 8450 Vsts Area 9830 Populato Area x y x x y y Thus for the correlato betwee sales ad vsts we requre r y Note that the dvsors occur varous evaluatos, so that the calculato tme s reduced. Thus for the correlato betwee sales ad populatos we requre r Thus for the correlato betwee populato ad vsts we requre r Ad so o. Usg Mtab the remag correlatos are calculated. Correlatos (Pearso) ales No_vst Pop No_vst Pop Area As oe mght expect, overall the geographc area has a adverse affect, larger populatos result more vsts ad more sales. The am s to have a small area wth a large populato allowg may vsts. Mke Cox 9.9 Verso
10 Crtcal Values of the Correlato Coeffcet The table cotas the crtcal values of the correlato coeffcet for a test of sgfcace. The values may be obtaed from the equato below, wth Oe tal, r P t P t P. P=0.05 P=0.05 P=0.05 P=0.005 P=0.005 P=0.00 Two tal P=0. P=0.05 P=0.05 P=0.0 P=0.005 P= Mke Cox 9.0 Verso
11 Crtcal values of pearma's Rak Correlato Coeffcet The table cotas the crtcal values of the correlato coeffcet for a test of sgfcace. Oe Tal P = 0.05 P = Two Tal P = 0.05 P = Mke Cox 9. Verso
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